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DataDemon User Manual

1. Phase Sine 3 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 time sec 2 Connect the Sine wave SFO to Compute Channel gt TimeShift and set the Properties ShiftMode and select ShiftStartTime and set ShiftValue to 2 You will see that the start time on the graph have shifted to the 5th second Projectl x Viewers updated Properties x InputPortsi de Left ChtputPortade Right Execute Time sec Acceptable Data Types Regular Real Multi Channel Signal OuiputDataTspe Regular Real Single Channel Signe E Time Shift Shift tart Time hift alye 2 Sine Shift 5 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 6 time sec If you select SetStartTime and set the StartValue to 1 then the first point of the graph will start at 1 second mark InputPortside Left OnitputPortside Right Execute Time sec AcceptableDiata Types Regular Real Multi Channel Signal CutputDataT ype Regular Real Single Channel Signe Time Shift Set tartTime o tart alue oine Shift 0 1 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 time sec Important Timeshift allows the user to shift the graph along the x axis and the RemoveDC allows the user to shift the graph along the y axis Related Functions Time Shift RemoveDC 3 1 9 Data Merge Connect two one channel signals together to form a one chanel signal Connect two multi channel signals together to form a multi channel signal
2. Press button to transfer the equation in Expression field to Output Channels Here CH10 is added Multi Channel Expression Editor Output Channels Channel Expression 13 IMF_h3 551 4 IMF_h4 51 5 IMF h5 2 lt 1 6 IMF h5 51 7 lMF h7 1 8 IMF h8 1 9 21 S IMF residual 1 2 4 lt 2 4 x2 Square RCADA EEMD 2 1 IMF h1 2 2 IMF h2 23 IMF h3 lt 2 5 IMF h5 12216 IMF_h6 2 7 IMF h7 lt 2 8 IMF h8 2 9 IMF residual cones ane Next the channel 9 of X1 multiplies corresponding time t then add channel 1 of X2 Add channel 9 to Expression field by double clicking X1 9 under X1 then click basic operator in the Toolbox to complete the equation Surely the equation can be directly typed in the Express field X1 9 t X2 1 Expression 1 9 t 42 1 ly To get the absolute value of X1 9 t edit the equation directly to abs X1 9 t X2 1 or highlight X1 9 t part in Expression field then select function abs from the function list and press fn button to complete the equation All internal functions can be added this way Finally click button to transfer the equation to the Output List 13 Channel zl zi abs Expression For the calculation of more than two input signals such as CH1 CH1 CH2 CH2 By Input option can be deployed So the
3. Chirp 1000 STFT 500 400 2 Co eo eo 200 frequency 100 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec 4 fthe properties of TimeCount or FreqCount are changed STFT would re calculate based on the re set numbers of grids Therefore the result resolution and computation time would be affected Now change the TimeCount to 50 it can be seen that the computation runs faster while the result resolution becomes WO Se Tr TOPE EM 2 STFT Fregaxis LinearAxis FregMin 0 Freghlax 500 FregResolutian auto 25 Freqcaunt 25b Timeount 50 Remove True Window Hanning TimeCount Determine the max sample count in time axis of Ehe result frequency Hz Chirp 1000 STFT 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 time sec If the properties of FregMin or FregMax are changed STFT would still calculate in the original frequency range However it will only output the result in the range defined by the properties and would not affect the computation cost Change the FreqMax to 50 the computation time does not decrease Properties El STFT Fregaxis LinearAxis Freqmin 20 FregResalukian auto 2 5 Freqi aunt 255 Timec aunt 50 Removed Tin window Hanning FreqMaxz The maximun Frequency of Ehe short term Fourier transform Chirp 1000 STFT 50 40 frequency Hz Co eo N 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 time sec Related Functions Fou
4. X1 Calumn Veckars True ServerVisible False Dumpaoutkput False AsSource False hal Module As Snurce Specifies True if DaMatlab is to be used as a source Property Name Property Definition Default Value This window is similar to the M file MatlabEditor editor At the right side there is a button to run the DoMatlab Editor which is used to write MATLAB code or None Use to determine whether the data is Column Vectors Column wise when signals are passed True to MATLAB M Use to show and hide MATLAB ServerVisible True Command Window Use to show and hide the information DumpOutput False generated during Matlab processing When DumpOutput is True this roperty is provided to set the Buffer Length d ANA 5000 maximum number of data that can be sent back from Matlab ViewBuffer property is provided to pop up a window to show the Matlab messages generated during the processing When there are multiple input signals this property decides which input signal Heferencelnput is used as reference signal for the default time axis Y DESC of output variable Determine whether DoMatlab should AsSource be changed to a signal source which can be used to generate signal data Matlab Editor is the code editor for DoMatlab The details of basic setting for DoMatlab e g input and output are given below None The 1 input signal Introduction of Matlab Editor Interfaces
5. 3 3 6 Integrate This component performs integration on input signals Introduction Let be an N length signal T 15 5 be the corresponding X axis time axis coordinates the numerical integration using Simple can be denoted as the formula below t d y x dt 235 LM k 0 If Trapezoidal is used the formula is denoted as below 0 fj 1 xdt 2 x t a t Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular and Audio which could be real number or complex number single channel or multi channel Regular The related properties are introduced as in the table below Froperties 5 Integrate Method Trapezoidal StartPosition EndPasikian onset StartPosition Start Position Default value Property Name Property Definition The methods of numerical integration including Simple and Trapezoidal Method Trapezoidal The starting otartPosition The start position in X axis for integration point of the input signal The ending EndPosition The end position in X axis for integration point of the input signal The shift along Y axis after integration LS Example This example shows the integration on a sine wave 1 Click right button in Network Window select Source Sine Wave to create a sine wave change the Properties SignalFreq to 1Hz SampleFreq to 20Hz TimeLength to 1 secon
6. concatenate to one channel Specify Time Column Field Format White spaced Delimiter Mull value Handle Use Mull Value Handle Linear Interp w Time Coordinate Time Unit ero Time Shitt oI Sample Frequency Cy cles day Down sample b Date Axis vss nomm v 92 02 0 File Contents 10 2009 0l z 1l6 009 01 05 17 2009 01 06 16 2009 01 07 116 4009 01 09 16 4009 01 09 16 2009 0l l 15 2009 0l 13 15 Aman nm 12121 A 0 L 100 150 200 time dav Connect GE Source to Compute Filter Trend Estimator Set Trend Estimator Properties Filte Type to HighPass And connect Trend to Viewer Channel Viewer Froperties Module El TrendEstimater FilerTvpe HighPass TrendBasis Period Time Unik Default TrendPeriad default 23 6 GE l saussFilter 0 L 100 150 200 time day Finally replace the time axis with the date information in the file and convert Regular to Indexed signal Using Text Importer again to open CSV file check Data Range Specify Time Column option set Columns 2 to end Now the read in signal is Indexed and time unit is day ai Text Importer Data Range Rows to Columns to end Data direction 1 k Field Format White spaced Delimiter Mull alue Handle Use Mull Value Handle Linear Interp v Time Coordinate Time Unit REN fe Down sample Date Axis poer
7. MultiChannelColumns SingleRow singleColumn ANIARO Row Set which row to extract 0 Column Set which column to extract 0 Example Using Source Advanced Jaehne to create input signal and connect the signal to Compute TFA ShortTerm Fourier Transform All use default settings Connect STFT to Coversion Convert from Spectra and set Rows to 50 in Convert from Spectra properties then display 50 row data using Channel Viewer SIFT FromSpectra 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec In Convert from Spectra properties set ExtractionMode to SingleColumn and set Column to 100 Show the frequency distribution of the 100 column using Channel Viewer SIFI Fromspectra 0 50 100 150 200 250 300 350 400 450 Gs 500 frequency Hz Related Functions STFT Convert from Matrix Chapter 5 Source Signal Flow Object 5 1 Open Data Open a file to be used by DataDemon Properties There are two methods to open a data file The first method is to click on the Kc Import data from file button and select the file you want to load into DataDemon The second method is to right mouse click the Network Workspace and the Network Workspace Menu will pop up From the menu select Source Open Data to select a file to be loaded into DataDemon IPTE Compute k Conversion Open data Source gt a Viewer Custom ave Writer Moise Sine Wave Macros Square Wave Con
8. Sine ToAudia 3 ii m 0 02 0 04 0 06 0 08 0 1 0 12 0 14 0 16 0 18 0 2 0 22 time sec 3 Click on the audio play button on the top right corner of the graph and play the signal A red line will run through the x axis indicating the position of the audio currently being played Sine TaAudio a 0 02 0 04 0 06 0 08 0 1 0 12 0 14 0 16 0 18 0 2 0 22 time Sec 4 You can also use the Zoom X button off the Visualization Window Toolbar to enlarge the area of the Audio signal Sine TnAudin B m 0 05 0 06 0 07 0 08 0 09 0 1 0 11 0 12 time i sec Below are some examples showing how to configure the other options in the Properties Window 1 Create Source Square Wave and connect it to Viewer Channel Viewer Viewer updated 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 2 Change the Channel Viewer s Properties Appearance ViewerHeight to 500 and ViewerWiath to 300 Properties El Appearance BackColor White Viewer Width 500 WiewerHeight 300 ListOrder 0 ViewerHeight Viewer Height Square 0 5 0 5 0 0 2 0 4 0 6 0 8 1 time sec 3 Use the Zoom X Zoom Y or Pan X and Pan Y feature of the Visualization Window Toolbar f you want to maintain the current status you can set the Properties Representation HoldaPlotRange to True Properties LinearAxis Plot Elem Editor PlotEditor VWalueT ype Magnitude Hold Plat Range Tr
9. Square test 0 0 1 0 2 0 3 0 4 0 5 0 6 time sec Now create two Fill NULL Value SFOs to connect from the imported source signal data The first SFO will use the Spline Interpolation fill in method and the second SFO use Monotonic Interpolation fill in method Viewer updated Auta gt B From the results shown in the Viewer there is an obvious difference between the opline Interpolation method thin dark line and the Monotonic Interpolation method thick blue line Square test FillNull 0 035 0 04 0 045 0 05 0 055 0 06 0 065 time sec Related Functions Data Importer Resampling Data Importer 3 1 5 Remove Channel Remove a single channel from a multi channel source Properties This module accepts input of Signal which could be real number or complex number multi channel Regular or Indexed and Audio which could be real number or complex number multi channel Regular Properties El Remove Channel Channel Count qj Remove Channel Channel 1 Select Last Channel False Property Name Property Definition Default Value Channel Count Displays the number of channels NONE Remove Channel select the channel to be removed Channel 1 If Select Last Channel is set as True then the channel to be Select Last Channel False removed will always be the last channel Example Combine a sine wave and a triangle wave and a square wave together connect it to a Remove Channel SFO and to remove the
10. White spaced Delimeter Fixed field ee e Mull Salue Handle Z 11 1E Bite Time Coordinate Time Unit Time Shitt day sample Frequency 1060 cyclesiday Down sample by 1 001 0 935399734 O02 0 255326361 003 0 149701115 004 0 740199369 005 0 506343746 O06 0 837190297 007 0 550990733 009 0 9442 215 009 0 52761984 010 0 9548041243 011 0 196699071 Ole 0 527215996 13 O 362569635 014 0 460716997 Noise 06 00 12 00 18 00 00 00 Date 2 If all rows of the imported data have the same character length you can use customize Fixed field to read in the data Data Range Rows to Columns to Data direction Column basegd d Concatenate ta ane channel Specify Time Column PA Field Format White spaced Q Delimeter ull alue Handle Use Mull Value Handle Linear Interp JY Time Coordi Time Unit sec v Time Shift 0 sel Sample Frequency 1000 cycles fsec Down sampleby 1 Date Axis L tren Ene v 92 92 92 File Contents 001 1234567990 Oe 2345679901 OOS 3456709014 004 4567590123 005 5679901234 d6 6789012z345 The data imported are placed in four channels the first channel contains one character the second channel contains two characters the third channel contains three characters and the fourth channel contains four characters Under Data
11. opline Extrema for Usper Envelope Find Minimum Exlrema Parent Spline Extrema for Lower Envelope Calculate Mean of Uoper and Lower Envelopes Yes Use Residual as Parent Subtract Mean Does Residual Envelope from have more than 2 Parent Data to extrema Produce IMF Candidate Yes subtract it from Does IMF Residual Lifference Candidate meet becomes Residual stopping Criteria No use it as Parent To understand the effects of the above process the following is a brief illustration of the steps taken for an entire sift First the data is inputted into the EMD This is the lod78 dat dataset that is included in the sample data folder of the HHT DPS It contains the differences in the length of day over a period of 9 years Length of Day data The y axis is the difference in microseconds x is the number of days since measurement began 0 5 500 1000 1500 2000 2500 3000 Zoom in of lod78 data Original data is blue the maximum extrema are green and the minimum extrema are red 400 450 500 550 600 650 700 Zoom in of lod78 data Original data is blue the maximum envelope is green the minimum envelope is red and the local mean is purple 20 40 760 730 900 520 240 abu The first IMF found from lod78 It is then subtracted from its originating signal in this case lod78 for others it would be the current residual generating the residual signal 500
12. 100 hea milital E 111 txt chirp1DO0 tfa chirp10000 tfa 1 1 basic vsn demo02 basic vsn 1 demo03 basic vsn demoO4 basic vsn 1 05 mixer vsn 19 demo06 resample vsn demo0 noise vsn demon8 fft vsn s My Recent Documents demon9 fft vsn demo10 fir vsn 1 demo11 fir vsn 1 demo12 fir vsn i amp demo14 Source vsn demo16 MovingAverage vsn 17 Moving amp verage vsn 1 18 DataSelection vsn 1 19 WaveReader vsn 1 20 SacReader vsn le demo21 VWriter vsn la demo22 STFT vsn 1 24 STFT vsn 1 25 STFT vsn i demo26 Colormap vsn gt Hie Spee chirp 0000 tha 111 tfa chip 000 ta My Network Files of type AIL Cancel d Batch Run Project1 LA r Paramater List From Project Project Viewer amp STFT amp 1 TF Viewer Q output Directory Batch Runs 8 111 chirp10000 8 chirp1 O0 Seles After selecting the DataSource signal files the Output Directory need to be specified Click on J to manually locate an Output Directory In this example C was chosen Browse For Folder Ej Sw 02119100 C BJPrinter O Documents and Settings 2 extra E gt Java O Matlab 3i output i Program Files 2 RECYCLER w Make New Fo
13. 500 400 0 08 300 0 06 200 0 04 100 0 02 00 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Y time sec to Change the Time Frequency Viewer s Properties Representation Value Type Phase and the following image will be displayed Pro Pe Thes valueType Phase auto 0 auto 1 auto 0 auto 500 auto 179 99957859913 ValueType The data representation of the result Square EnMorlet IAAT TLL A WIM JETIT i THE 1 111 IM Il 500 mmm 400 frequency Hz c eo 100 0 L z J L J L J L J J L L J L L L L L qe I 0 4 0 5 0 6 0 7 0 8 0 9 time sec Related Functions Channel Viewer User Interface Map to Real 6 5 XY Plot Viewer Display two signal data one corresponding to the x axis and the other corresponding to the y axis Introduction XY Plot Viewer accepts three main signal data 1 Two signal data Channel 1 is drawn on the x axis and Channel 2 is drawn on the y axis and then the two signals are plotted on the graph 2 Multi Channel data with odd Channels are drawn on the x axis and even Channels are drawn on the y axis and then the channels are plotted on the graph 3 A single channel with multiple data real part is drawn on the x axis and the imaginary part is drawn on the y axis and the two values are plotted on the graph Properties This module accepts input o
14. Applications of NASA HHT Module include Earth Science Biomedical Science Civil Engineering Mechanical Engineering Electrical Engineering Finance and others The Hilbert Huang Transform Data Processing System HHT DPS is original a signal processing toolkit It implements the Hilbert Huang Transform HHT a modern method for signal and data analysis It was developed by the National Aeronautics and Space Administration at Goddard Space Flight Center NASA HHT Module Documentation This documentation includes two segments one is the algorithm descriptions of HHT and the other is manipulation The algorithm descriptions of NASA HHT follow HHT DPS documentation HHT DPS documentation draws upon information from the following sources see patents section for additional sources Bendat Julius S Peirsol Allen G Random Data Analysis and Measurement Procedures New York Wiley Interscience 1986 Blank K Hilbert Huang Data Processing System PIP Report June 9 2003 Cohen Leon Time Frequency Analysis New Jersey Prentice Hall PTR 1995 Hahn Stefan L Hilbert Transforms in Signal Processing Norwood Massachusetts Artech House Inc 1996 Huang Norden E et al The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis Proceedings of the Royal Society vol 454 pp 903 995 London 1998 Huang Norden E et al A confidence limit for the empirica
15. coords For signal and spectra it is time Double array ndim max length For spectrum it is frequency Note Char is string Length is the length of byte or number ndim is the array dimension if the input is numeric nch is the number of channels max is the maximum value Xn FREQ is used to store the sampling frequency of input signal that is 1 Xn Freq Xn DESC intervals 1 If the data is related to sampling such as Signal and Spectra the sampling frequency would be stored in Xn FREQ If the data is unrelated to sampling such as opectrum and Numeric number 1 would be stored in Xn FREQ Storage format of output signal variable Variable Y is the output variable of DoMatlab using the storage format defined in Y DESC whose content is the same as that saved in the Xn DESC The default value of Y DESC is identical to the input signal format defined in Properties Referencelnput of DoMatlab The users can also change Y DESC manually DoMatlab determineds the type of output signal based on Y DESC The table below shows the meaning of each field Filed Name Introduction Default vane The name of the input signal B LI d DoMatlab The type of signals Currently available types are Signal Numeric Optional Signa pre opectra channel mu name e g CH1 me None names The starting point of signal starting point of signal It is _ The sampli
16. visine RCADA EEMD 0 0 1 02 01 3 04 5 0 6 07 0 8 time sec On an Intel Dual Core E6300 2 8GHz computer it takes 1 65 seconds to complete the calculation for DataDemon However it takes 376 60 for MATLAB to finish The difference is more than 200 times Refer to demo68 1 in C Program Files DynaDx DataDemon demo HHT The signal is Hello voice wave Selection ToAudia 0 0 1 0 2 0 5 0 4 0 5 time Sec In RCADA EEMD properties set Number of Ensembles to 200 and Noise Level to 0 25 Observe the signal in the 3 channel The result is shown below switch ToAudio 0 2 4 4 c c 0 2 0 5 0 4 0 5 time Sec In RCADA EEMD 2 properties set Number of Ensembles to 1 and Noise Level to 0 1 Observe the signal in the 3 channel The result is shown below Switch ToAudio D 0 1 0 2 0 4 0 5 time sec After playing the sound after EEMD decomposition it shows that the result of the 1 EEMD sounds clearer and the result of the 2 EEMD has noises Helated Functions RCADAInstant frequency RCADA Spectrum References Norden E Huang Zheng Shen Steven R Long Manli C Wu Hsing H Shih Quanan Zheng Nai Chyuan Yen Chi Chao Tung and Henry H Liu The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non Stationary Time Series Analysis Proceedings of the Royal Society Vol 454 No 1971 1998
17. 2 3 1 Signal Flow Object Status Click on a Signal Flow Object to select it When a SFO is selected the SFO box in the Network Window will look like the box is pressed in The Properties Window will display the information of the current selected SFO You can hold down Control on the keyboard and select multiple SFOs to move them around the Network Workspace Network IX ie amp t Project 1 Project Project2 x ViewerZ updated 2 3 2 Connecting Signal Flow Objects With Signal Flow Diagram DataDemon simplifies the tedious process in analyzing signal data All you have to do is to create simple Signal Flow Diagram and connect Signal Flow Objects together The the signal then is analyzed and the result is caculated 1 connect two or more Signal Flow Objects There are two methods to connect SFOs together The first method is to create two SFOs and click on the output of one SFO and drag it to the input of the other SFO The second method is to create a SFO and then right mouse click on it and select a second SFO from the Network Workspace Menu The SFOs will then be automatically connected together Mouse click drag the output port of the Sine SFO to the input port of the Viewer SFO X aes Select the Sine SFO and right mouse click to select EEMD SFO from the menu ImfPhaseDiff MMPF The advantage of the second method is that when you try to creat
18. 3 95 3 38 2 73 2 08 1 62 Data Spectra Yalue Type GainReference Cursor Color Colormap gt P am ae Lr The graph displayed by Spectra X axis displays the time and the y axis displays the frequency Depending on the settings e g Magnitude Phase etc each point on the graph will change its color based on the new calculated values demo25 STFT STFT 1500 ri ww tcm 0 5 1 X 0 900068027210884 Y 752 941176470588 Val 1 74921074438702E 05 The red cross on the graph displays the value of the current point in the lower left corner The point can be changed by moving the mouse over to the chosen spot and left click the mouse to select the desitination The graph on the left of the main graph displays all the values along the vertical red line marked on the main graph On the left graph the y axis is the frequency and the x axis is the index value The graph on the bottom of the main graph displays all the values along the horizontal red line marked on the main graph On the bottom graph the y axis is the index value and the x axis is the time Click on the 4 Marginal Freq Time to switch the left graph and the bottom graph to time frequency analysis 0 204637702309 0 291597575038 0 416771718191 0 439524551414 0 459315403474 0 475097041935 r CAAA A nmm A 388 0 206504315190 0 39318
19. In the discrete case let X t be a N length time series where is time coordinate the autocorrelation formula is N 1 YS N 1 lt r lt N D 0 i e X r is equivalent to mean square value V N X 1 0 Properties This module accepts input of Signal which could be real number single channel Regular and Audio which could be real number single channel Regular The output format is real signal channel Regular signal This module does not have any other properties to be set Example In this example perform auto correlation on a sine wave a white noise and the mixed signal of these two signals 1 In Network Window select Source Sine to create a sine wave and change its Properties DataLength to 2 seconds and keep the frequency to 10 Hz Perform Compute transtorm AutoCorrelation on this signal and then plot the result using Viewer Channel Viewer Project1 x Viewer updated Iv Auto gt m TimeUnit Sec 2 SamplingFreq 1000 Daktalength 2001 SignalFreg Amplitude Arniplitudecrrset Phase TimeLength Time length in unit Sine Corr 2 1 5 1 0 5 0 0 5 1 1 5 2 time sec 2 The figure above shows the auto correlation of the sine wave with different delay i e the in the original formula Perform FFT transform on the output of AutoCorr It is shown that the frequency of the output signal of AutoCorr is 10 This verifies
20. OutputTvype SplitComplex bul Module DutputType The output type of Hilbert Transform Sine Hilbert time sec 4 Repeat step 2 and change the Output Type to InstantFrequency only The output would be the instantaneous frequency at every time point of the input signal InstantFrequency Inst Freq Method Simple Module Hilbert Sine Hilbert 0 4 0 5 0 6 time sec Channel Viewer is not able to plot the diagram in complex plane for analytic function Z t Viewer XYPlot has to be used Use Viewer XYplot to plot the output of Split Complex to obtain the diagram of analytic function Z t in complex plane Changing the ViewerWidth and ViewerHeight to an equal value i e 350 would make the proportion of x axis and y axis to be identical vPlot updated Auto gt E Sine Hilbert 1 Hilbert2 CH2 O 1 1 Hilbert2 CH1 Related Functions XYPIot Hilbert Spectrum Reference http en wikipedia org wiki Hilbert_ transform 3 6 5 AutoCorrelation AutoCorrelation is defined as the convolution of a signal with itself and it can be used for correlation analysis AutoCorrelation analysis can reveal signal periodicity and how fast a signal varies in time Introduction Mathematically the definition of autocorrelation is R lim x x 4 z dt Too 4 where x r is the conjugate of x t T is the signal period and is the time delay
21. Set the Date and Time for the data values 2001 01 01 0 0 0 Related Functions Viewer Fill NULL Value Viewer Fill NULL Value 5 2 Noise Noise is able to create seven different types of Noise signal waves Introduction Following are the descriptions for each noise definition Noise White noise Gaussian Noise opeckle Noise Equation libe 0 E f D fuut E Pink Noise Brownian Noise Blue Noise Fs o lt Fx Of Ex ra zx f Description The noise that has a wide range of frequencies of uniform intensity where E is expected value It has an autocorrelation which can be represented by a delta function over the relevant space dimensions Gaussian noise is noise that has a probability density function abbreviated pdf of the normal distribution also known as Gaussian distribution Speckle type noise its amplitude is either zero or one it is controlled by the probability P Pink noise or 1 f noise is a signal or process with a frequency spectrum such that the power spectral density is proportional to the reciprocal of the frequency Brownian noise is the kind of signal noise produced by Brownian motion hence its alternative name of random walk noise Blue noise s power density increases 3 dB per octave with increasing frequency density proportional to f over a finite Violet noise s power density increases 6 dB
22. wv Cancel 5 Click on to execute a Batch Run and click on to stop a Batch Run 6 Output Directory is where the result of a Batch Run will be saved If the source of the Batch Run is already a saved file then the Output Directory will be automatically named to match the saved source file name e g Source file name is CAProject vsn then the Output Directory will be set as C Project If the source file is newly created and haven t been saved yet then the Output Directory will have to be manually entered in the Output Directory field or click on 2 to designate an output directory from existing folders After a Batch Run has been successfully executed all the Viewers included in the Batch Run will automatically output a graph and if Writer is connected then Writer will output signals into the Output directory Shown below are two examples of the Batch Run process e Example 1 To modify the parameter of a Batch Run After open Crtl O project demo 22 and open the batch run dialog click on m button four times to create four Run profiles Batch Run profiles Currently the new Run profiles are empty 2 Run demo22 STFT fre f ik td JE E Output Directory C Program Files DynaDx DataDemon data Batch Runs EE T 1 Runz Runa Rung Click on Add Parameters to open the Parameter List You can also add parameters through right clicking on the Batch Runs window
23. After pressing CI we can get the updated figure below Sine 0 1 0 2 0 3 0 4 0 5 0 7 0 8 0 9 1 time sec Move the mouse on the HRegion the user can drag the HRegion to other locations in the drawing area Other annotations can be moved in the same way Sine 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 6 0 9 1 time sec Sine 0 0 1 0 2 0 3 0 4 0 5 0 5 0 7 0 6 0 9 1 time sec Helated Functions Channel Viewer Sine 6 2 Box Plot Viewer Professional Only Introduction Based on the median the first quartile and the third quartile of a group of numbers Box Plot Viewer plots boxes The lines connected with these boxes represent the maximum and minimum value so that statistical property of the data is shown Properties This module accepts real number complex number single channel multi channel regular and Indexed signal or audio input and supports multi signal input The user could refer to Channel Viewer for Appearance Fonts Colors Grid and Title parameters Specific parameters for Box Plot Viewer are introduced below Properties BrushColor LightGray Bordercalor BB Black TicksLabel4ngle MaxMarkerstyle Circle MinMarkerstyle Crossi MeanMarkerstyle FilledSquare ModeMarkerstyle Mone Parameters of Box Plot Viewer Property Name Property Definition Edi perty Value BrushColor The brush color inside the Box LightGrey BorderColor The brush color for the border of the Box
24. Example Compare with NASA Hilbert Transform NASA GZC outputs instantaneous frequency or instantaneous amplitude In this example LOD78 is still decomposed and then all IMFs are transformed to frequency or amplitude with time 1 Still use Source Import data from file to read tfa file LOD78 tfa in the installation directory default to be C ProgramFiles DynaDx DataDemon demo HHT Next perform Compute NASA HHT NASA EMD and LOD78 would be decomposed into many IMFs LOD7Z 8 NASA EMLD 0 500 1000 1500 2000 2500 3000 time day 2 After NASA EMD connect the module Compute NASA HHT gt NASA GZC whose property OutputType is default value In the same time connect the module Compute NASA HHT NASA JHIilbertTransform whose property SmootPoint is set 1 to compare results from GZC results LOD7 8S NASA EMD NASA GZLU 0 500 1000 1500 2000 2500 3000 time day LOD 8 NASA EMD NASA Hilbert 0 500 1000 1500 2000 2500 3000 time day 3 From NASA GZC and NASA HilbertTranfom both connect the module Compute Channel Channel Switch The Active Channel of SFOs is 4 CH4 and after Channel Switch connect Viewer Channel Viewer to observe results Result of HilbertTransform is smoother than result of GZC Viewers s00 1000 1500 2000 2500 2000 time day j Related Functions Hilbert Transform RCADA Instant Frequency 3 7 3 4 NASA Hilbert Spectrum NASA Hilbe
25. Huang N E M L Wu S R Long S S Shen W D Qu P Gloersen and K L Fan 2003 A confidence limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis Proc Roy Soc London 459A 2317 2345 ZhaoHua Wu and Norden E Huang 2009 Ensemble Empirical Mode Decomposition A Noise Assisted Data Analysis Method Advances in Adaptive Data Analysis Vol 1 No 1 2009 1 41 http rcada ncu edu tw research1 clip reference htm 3 7 2 IMF Property A signal can be decomposed into several IMFs and a residue after processed by EEMD The functionality of IMF Property is to show characteristics of each IMF and validate the decomposition from EEMD Introduction IMF decomposed by EEMD has one characteristic that the number of extrema and the number of zero crossings either be equal or differ at most by 1 To validate the decomposition result of EEMD we can use this module to show characteristics of each IMF For every IMF this module lists the number of zero crossings and extrema the average frequency of zero crossing the orthogonal relationship between IMFs and the power ratio Properties P TOPE EN propertytirid Ww Gis A scil El IMF Property IMF Property Report for EMD El Module Mame IMF Property InputPortSide Left AcceptableDataTypes Regular Real Single Channel Signal Report Display a report showing IMF properties for all channels Property Name Prope
26. In the Network panel press and hold left mouse button drag the mouse and cover target SFOs then release the mouse to select them Press Ctrl C for coping and Ctrl X for cutting as shown below TF Viewer updated Finally press Ctrl V for pasting selected SFOs in the Network panel Viewer m updated Now let us show how to move SFOs In the Network panel press and hold left mouse button drag the mouse and cover targeted SFOs then release the mouse to select them Hold Ctrl key and click select one SFO via left mouse button hold the left mouse button and make sure that the group of SFOs is selected TF viewer m updated Bo Q In the Network panel move the mouse to the target location then release the left mouse button and Ctrl key TF Viewer m updated Auto Q 1 4 Properties Window The values of the SFO in the Network Workspace can be edited within the Properties Window below the Network Workspace Below is the Properties Window of a Sine wave and the options to change the display of the graph can be edited under Properties Source Properties TimeLlniE TimeLength SamplingFreg DakaLength SignalFreg Amplitude AmplitudeOfFsek Phase TimeStart Time Start Start Eire In the Properties Window click on to expand the information under Module Class refers to the type of source the SFO belongs to Name shows the name of the SFO and can be renamed Outpu
27. In these six points t 0 4s 2 t 0 4055 y f 2 1756 2 5 0575 the maximum is 5 50575 2 1756 3 33015 In these six points the S value is shown as below vy Diff 600 0 38 0 295 0 4 0 405 0 41 0 415 time Sec The Compute Math Diff gives the gradient If the S and J values are both exceed the critical value that is the Bump which is needed to be corrected Properties This module accepts real numbers single channels regular signals and audio inputs the format of the input signal is the plural and single channel spectra data Properties are set up as the below table Property ix Module E Remove Bumps Output Type Signal Jump Threshold 0 59329541 72138154 Jump Threshold Ratio 0 3 Slope Threshold 2593 29541721381338 Slope Threshold Ratio 0 3 Number of iterations 1 StartPosition EndPasition end 0 132 Property Name Property Definition Default Value Signal removing the signal after the Bump or the Output Type Jump Singal Bump the Bump or the Jump signal 9096 of the If the increasing decreasing value exceeds this maximum value Jump Threshold threshold this point is considered as the candidate point of the entire signal Jump Threshold If the maximal increasing decreasing value is Hatio J mii 1 0 3 90 of the If the absolute value of the gradient exceeds this maximum SlopeThreshold threshold this point is considered as the candidate point gradient of the entire
28. M M Malin _ E EN TT zm F3 section window also supports auto hide feature to automatically hide the window when it is not in use Click on the Ell icon in the Network and Properties Window to configure the window to auto hide to the side of the main window area as shown in the image below File Edi view Layout Tools Help a wi Ta SA rd dy Kc a _ Projecti X a T m un lt gt In next section menu bar and other program functionalities will be explained 1 2 Pull down Menu In the top left section of the program there is the menu bar which consists of several pull down menus File Edit View Layout Tools and Help The menu options such as Edit View and Tools are used for editing and configuring Visualization Window and it will be explained in the Visualization Window chapter Only the contents of File Layout and Help will be explained in this chapter Data Demon 1 0 powered by Visual Signal Beta Ele Edit View Layout Tool File allows you to create open and save project files in the DataDemon format VSN Edit view Layouk Tor New Project Ctrl h Open Project Chri 1 Save Project Ctrl 5 Save Project s Ctr 4 Load Macro Save Macro Ctrl M Close Close All Exit Alt F4 When saving a project you can choose whether to save the calculations during this project or not If Yes is clicked al
29. Noise adjust its Properties Noise Type to Gaussian Time Length to 10 seconds connect to Kernel Smooth Density then link to XY Plot Noise KsDensity Gaussian kSDens itf c DJ Et 0 KSDensityx On the other hand directly gragh Noise using the Viewer Histogram Viewer set Properties BinCount of the histogram to 50 Percentage to True then the following histogram is shown in the viewer DIEM 5 Properties Module El Representation Binc aunt 50 Colori 9 Gray Colorz Transparent BrushStyle Horizontal Percentage True TValueTvpe Magnitude DrawLine alse Percentage Switch percentage mode Histogram The basic concept of the two graphs is the same Kernel smooth density uses kernel function to express probability as a continuous density function while the histogram uses the value interval to calculate the probability of occurrences and in this model the area above X axis is 1 for the density function whearas the Y axis of the histogram is directly the occurrences If you adjust the Properties Width of KSDensity a little bigger to 1 2 you can see that the resulting curve is smoother Tvpe Gaussian Mo of Points 100 Width 1 2 4 Kernel Smoothing Density Noise KsDensity Gaussian m ha kSDens ity tii c 0 1 2 3 4 KSDensityx Helated Functions Histogram Noise XY Plot Heference T Hastie R Tibshirani and J Friedman The Elemen
30. O nzN 1 win N 1 0 otherwise Hamming Hamming 2 T n E otherwise 0 53836 0 46164 cos Gauss The properties of Inverse Fourier Transform are given as follows Properties propertyrid Resolution The multification Fackar of time resolution of the inverse Fourier transform The property of Inverse Fourier Transform is Resolution which has identical meaning as that in Fourier Transform The number of signals in Inverse Fourier Transform would be twice as many as the Resolution value Example This example uses Source Module to generate a combined signal of two sine waves 1 In the Network window use Source Sine to create a sine wave In window of Properties change the Name filed to Sine freq 10 The default value of Signal frequency is 10 Hz Change TimeLength field to 0 9 sec FFT example Viewers updated moe gt m Properties TimeUnit 1000 DataLength SignalFreg amplitude Arnplitudeorrset Phase TimeStart TimeLength Time length in unit 2 Create another sine wave and set it Siganl Frequency to 3 TimeLength to 0 9 second Then add Compute Mathematics Mixer modules to combine these two signals and use View Channel Viewer to plot the output FFT example X Viewer3 updated TimeUnit TimeLength SamplingFreg DataLength SignalFreg Arnplitude Arnplitude or rset Phase TimeStart SignalFreg The Fre
31. Properties This module accepts input of Signal which could be real number single channel or multi channel regular and audio Property Name Property Definition Default Value The new position of the signal to be connected The new position is otartPosition relative to the reference signal The default value is the end position of the reference signal Set the reference signal Heferencelnput StartPosition is relative to the reference signal Example The original siganals are Source Noise and Source Sine Wave then Data Merge is applied to produce a longer signal for further calculation The steps are 1 Choose Source Noise in Network panel set TimeLength to 2s and Amplitude to 1 5 Then choose Source Sine Wave set TimeLength to 1 5s and SignalFreq to 100 Both SFOs are connected to Viewer Channel Viewer for display as shown below Properties lx Properties 1 Module Module E Source Noise White TimeUnit sec El Source TimeLength 15 TirmeUnit sec SamplingFreg 1000 TimeLength 2 DataLength 1501 SamplingFreq 1000 SignalFreq 100 DataLength 2001 Amplitude 1 Amplitude 1 5 AmplitudeOffset 0 Amplitudecrrset Time Start Phase 0 Time Stark 0 Mose 0 2 0 4 0 8 1 1 2 1 4 1 6 1 5 2 time Sec Sine 1 0 1 0 2 0 4 0 6 1 1 2 1 4 time Sec 2 Connect both Noise and Sine SFOs to Compute Channel Data Merge set Data Merge parameter Reference nput
32. number of signals with the signal length of n the S has number of signals with the signal length of n The ICA is to find a matrix W that satisfies S WM or M AS WzA4 Where A is lt w ig 44 There are two assumptions in the ICA S is independent signal to each other one S at most has the Gaussian distribution Application Cocktail Part Problem The ICA could be used for decomposing the mixing sound signal assuming the speed of the audio signal is infinite we set number of mics at different positions to receive number of different sound signals The ICA could decompose the mixing signal to the original sound signals If the dm di the ICA could dump noise signals to a redundant signal which improves the contrast of the signals Algorithm description This module calculates W and S by the Fixed Point The description is shown as below The independence of the signal could be described by the Non Gaussian distribution This method is similar with calculating the zero position of the derivative of the Cost Objective Function The W is caculated by the Newton interation method For n 1 Maxlteration df Max fax f dW f W p M AW W H a Computing one column of the W Deflation Method Computing all columns of the W Symmetric Method NOTE the Deflation method could accumulate Round Off errors so the Symmetric method is used more often b The Cost Functio
33. sec Period Trend e lt mcm gt q meee ee i ss Signal after the low pass filter i e the trend passes through and the oscillations are filtered out Moise IGaussFilter 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 time sec 0 9 FFT spectrum after filtering X axis is the period Moise IGaussFilEer FF T 0 5 0 1 0 2 0 3 0 4 0 5 0 7 0 5 0 9 1 time sec It shows that the low periods high frequency oscillation have been filtered out Properties This module accepts input of Signal which could be real number single channel or multi channel regular and Audio Ihe input signal format and the output signal format are identical Properties El TrendEstimater FilEer Tvpe LowPass TrendBasis Period Time Unit Default TrendPeriad default 0 Property Definition Value E LowPass low frequency can pass Filter HighPass high frequency can pass LowPass ByPass frequency between and F can pass Set Period or Frequency as the reference Trend Basis 4 Frequency parameter If Trend Basis set to Period the parameters are as following Property Name Property Definition uid dd Value Trend Pernod If the period is higher than this value then it is considered as trend Corresponding parameters Unit Set the unit for TrendPeriod Default Time Unit The time unit for the input signal Sec If Trend Basis set t
34. 4 The information in step 3 can also be obtained by using the property of DumpOutput in DoMatlab First as shown in the figure below change the content in DoMatlab Editor to X2 DESC and preserve Y X1 to define an output signal DoMatlab Editor DER Help amp Examples Matlab script file DESC Yl X Turn of the editor and change Properties DumpOutput to True After changing the DumpOutput DoMatlabe would save all information shown in the command window DoMatlab MatlabEditor Ui Matlab script filexz DES Calumn Veckars True Server visible True DumpoOurpue BufFerLength 5000 ViewBuFFer ReferenceInput 0 Sine MinInputPorks 1 i ViewBulfer Browse the output buffer DumpOutput records can be seen in Properties iewbuffer Therefore if any errors occur during the DoMatlab operation the error messages generated in Matlab are still available MATLAB Script Output Dump MATLAB Script Output Dump Output Buffer Script Execution On 2009 2H 18B E F 10 23 03 Execution Time 1 234375 sec A2 DESC EMD type Signal channelCount 8 channelNames 9x12 char lengths 1001 Starts 0 intervals 1 0000e 003 Units sec formats Regular coords 141001 double 5 The meaning of properties in Reference Inout is shown below Go back to Network click Sine and change the Properties Time Unit to minute the SamplingFreg to
35. Amplitude 0 1 AmplitudeoFFsek Phase Symmetry 0 5 Time Start 0 Properties Basic Statistics View Statistics Basic Statistics for Square u Unbiased Moment Estimation True Trim Fraction 0 05 Trim at Ceiling False Basic Statistics for Square Basic Statistics for Square Basic Statistics E Channel Surm 1 7 Min 0 1 0 1 Mean 0 0017 Connect Square to Hypothesis Test Set TestType z Test Sigma 0 03 then use View Test Results to observe the testing results The SignificanceLevel calculated from the data is greater than the default value we can not reject the null hypothesis We have to believe the null hypothesis that the instrument is not biased Properties lx El Hypothesis Test View Test Results Hypothesis Tests for Square TestT ype z Test Mean 0 Sigma 0 03 SignificanceLeyvel 0 05 Hypothesis Mull ul Hypothesis Tests for Square General 3 Hypothesis Tests for Square z Test channel CH1 Rejected False aignificanceLevel 0 0733 Cl Low 0 00016 CI High D 00355 If we set the SignifianceLevie to 0 1 in the Hypothesis Test and make the range bigger to reject the null hypothesis then use View Test Results to see the test result The SignificanceLevel calculated from the data is smaller than the default value We can reject the null hypothesis and believe that the instrument has bias and need to be adj
36. Dimensions extraction original matrix Example Use DoMatlab to create a 3 3 random matrix the elements are 0 86 0 63 0 37 0 22 0 66 0 69 0 99 0 56 0 78 Extract a matrix from starting element 0 0 and ROI Dimensions 3 1 the result is 0 7800 0 00 0 00 If the starting element is 2 2 and ROI Dimensions is 3 3 exceeds the dimension of the original matrix the result matrix is 0 7800 O OO oO OO The elements outside the dimension of the original matrix are set to O References Gilbert Strang Linear Algebra and Its Applications 3rd edition 3 9 5 Extract Vector Extract vector from matrix not limit to two dimensions If the extracted vector is larger than the matrix elements are filled with O value Properties This module accepts real number complex number and Numeric data And the output has the same format as the input EERE EERE EERE EE EERE EEE EEE EERE ahhh EEE EERE EEE EEE EERE EEE EERE EERE Column Vector True vector Direction 1 Start Indexes 0 0 Vector Length 1001 Module Property Definition Default Value Name The direction to extract vector from O position If there is a 4 dimension matrix Vector MM 0 row Tu the direction of 2 means to extract vector TN Direction direction along the 3 dimension so called the depth Column If true the output vector is column based True Vector Otherwise the output is row based Start Indexes T
37. Instantaneous Frequency Normalizing Iterations 5 Module The instaneous frequency is nsta ToRegular NHHT EEMD Ch31MF _h3 nstant Frequency 0 15 860 1870 1880 1800 1000 1010 1020 1830 1840 1950 1080 1070 1980 1090 2000 Date Related Function RCADA Instant frequency RCADA Spectrum Hilbert Transform References http rcada ncu edu tw research1 clip reference htm Norden E Huang Zheng Shen Steven R Long Manli C Wu Hsing H Shih Quanan Zheng Nai Chyuan Yen Chi Chao Tung and Henry H Liu The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non Stationary Time Series Analysis Proceedings of the Royal Society Vol 454 No 1971 1998 Huang N E M L Wu S R Long S S Shen W D Qu P Gloersen and K L Fan 2003 A confidence limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis Proc Roy Soc London 459A 2317 2345 3 7 5 RCADA Spectrum RCADA Spectrum is Hilbert Spectrum method provided by RCADA Introduction Please refer to hittp rcada ncu edu iw researchi him or 3 5 4 Hilbert Spectrum section Properties This module accepts input signal of real number single channel or multi channel regular and audio Property Min Freq Freq auto 0 5 Output Freg Divisions 25b Time Divisions 1024 Smoothing True Normalizing Iterations 5 Property Defini
38. Peak Detection module Related instruction Peak Detection 3 8 8 Teager The Teager Energy Operator is a nonlinear differential operator based on the time frequency product It could be used for analyze the modulation of the signal Based on the modulation the instantaneous frequency and amplitude are defined Introduction Based on the AM FM model the signal could be rewrited in the following way x 1 a t cos 1 t atm dm 8 U Q 4 lanki XQ Where is the Carrier frequency is the Information signa 4 0 0 atit J S the maximum frequency offset is the instantaneous amplitude is the initial phase angle Defining the Teager Energy Operator as x r x t Ar An Va Oe _ p where 7 is the period of sampling Based on the linear narrow modulation the upper formula is approximated as below p atr cos 2 t 0 f T 8 a t sin Q 1 i N x t x t Ar Defining yu backward difference And then 0 o sin Q 0 P zGpEHG T U x n 4a t sin VivGO A0 Y QO acos 1 4 V x 1 V x Vp An 4 V Dx 10 la t These are the instantaneous frequency and amplitude Properties This module accepts real numbers single channel signals and multi channel signals The Regular signal or the audio input has the same format o
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40. The properties are DashStyle Solid separated in Texts Width 1 Properties of Ellipses Lines Rects rectangular annotation Propert Default Property Definition Name Value The starting point of figure s coordinates The coordinates otart X 0 Y 0 are set at the bottom left corner for Ellipses and Rects End The ending point of figure s coordinates The coordinates X1 Vat are set at the top right corner for Ellipses and Rects ME Properties of Texts Propert Default Property Definition Name Value Text Content of Texts TEXT Position Coordinate of Texts X 0 Y 0 TextColor Color of Texts Hed Font of Texts include size style font It depends on the Arial Textfont system installation oize 10 Properties of HRegions horizontal area and VRegions vertical area Propert Default SUAE Property Definition Name Value Position The starting coordinate point to plot the figure 0 Position2 The ending coordinate point to plot the figure 1 Pixellndent The width of the blank border 0 Color Color of the starting point Red Color of the ending point The color between Position and Color2 Position2 is the gradient color from Color1 to Color2 based White on the whole figure ratio Properties of HLines horizontal line and VLines vertical line Property Name Property Definition Default Value Position The location coordinate point of the line 0 Pixellndent The width of the blank border 0 Example Add ann
41. X2 5 h amp X2 7 _ 7 X2 8 residual To the right of the Output Channels there are 3 buttons They can be used to move the output channel up and dow or delete output channels Once the output channels are ready press OK or Apply to complete The Output Channels can be displayed via Channel Viewer 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Set output signals to be X and X1 press Appy and view the result with Channel viewer Both signals are the same since X X1 1 Holt hannel Expression Editor Input List E X1 EMD X1 1 dMF_h1 X1 2 h25 X1L 5 X1 4 hd X1 5 h55 C 16 IHE X1 7 IbIE 151181 NGHE h amp 5 X1 9 1 10 AMF residual a C0 2 EMD X2 1 TMF_hi1 X2 2 dMF_h2s 2121 C 204 h43 215 h55 206 h amp 5 X2 7 C 2 8 residuals LLLI Math 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1 time sec Also the Expression can carry out calculation for gt lt Iz etc Create Noise signal and set NoiseType to Brown display the signal using viewer Channel Viewer Nase 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time Sec Connect Noise SFO to Compute Mathematics Math and display the output signal of Math with Channel View
42. added into input signal for ensemble NoiseCancellation Specify if inverse noise was added for True EMD process NoiseType Added noise includes white noise or WhiteNoise _ gaussian noise If True users could set the noise seed True UserDefineSeed False seed is set according to current time cce ie initial value of noise seed re The standard deviation of gaussian noise pot Example This example displays decomposition of LOD78 Length of Day by NASA EMD and decompose signal by the Intermittency Test method of NASA EMD 4 Use Source lmport data from file to read tfa file LOD78 tfa in the installation directory default to be C ProgramFiles DynaDx DataDemon demo HHT Next perform Compute NASA HHT NASA EMD LOD78 would be decomposed into many IMFs LODZ8 NASA EMD 500 1000 1500 2000 2500 2000 time day 5 In NASA EMD the property set Method to Ensemble EEMDNumber to 1000 The result is displayed below Property eift criteria 3 MaxImfCount 10 J 1 1 Er Module E NASA EMD Method Ensemble Prediction Type PatternPrediction ExtremaSift EEMDNwumber 1000 EEMDEpsilon 0 1 UserDefineseed Time Noise Type Y hiteN ois 4 LOD FS MASA EMD 0 0 5 1 1 5 2 2 5 3 Time sec 6 Reopen a new project and Use SourceImport data from file to read tfa file intermit test tfa in the installation directory default
43. day month or year TimeLength Set the value of time selected in TimeUnit Set the Phase in degree When the phase value is non zero the entire waveform Phase appears to be shifted in time by the entered amount symmetry set at 0 5 is equal symmetry where the left of the inflection point takes up oymmetry 0 5 half of the period E g Symmetry 0 2 0 5 means that the left of the inflection point takes up only one fifth of the period TimeStart Set the start time for the data Example Create a Square wave 1 Create Source Square Wave Project x Viewer updated Square 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec In Properties Source SamplingFreq is set to 1000 and SignalFreq is set to 10 2 Set the Properties Source SignalFreq to 5 Amplitude to AmplitudeOffSet to 0 2 Phase to 0 Symmetry to 0 4 TimeStart to 2 5 the graph is shown in the image below Symmetry Symmetry modifications to the wawe shape 2 5 2 6 2 7 Related Functions Viewer 2 8 2 9 Square 3 time sec 3 1 3 2 3 3 3 4 5 5 Triangle Wave Explanation is given for the Source Triangle Wave Introduction A 6xt CLys8 5 f x EFT Sx t Sqr Sqr up 3 1 1 1 Where A amplitude f sampling frequency 5 phase at to offset from X axis the ratio s is shown in the image below Properties Properties TimaLlnit TimeLength
44. graph from the drop down menu to use the Show Value button on the Visualization Window Toolbar When there Show value are multiple inputs knowing which graph UNE E Channel shows what value can be rather difficult So selecting a channel from the drop down menu the user can specify the graph to perform the Show Value button located on the Visualization Window Toolbar 3 Representation Properties Representation TimeLlint LegendPosition Draw Style AAxisTvpe Plot Elem Editor VY WalueType Hold Plot Range arin aM ex Y Min Y Max Show Title Show xAxis Show Axis None Line Linear Axis PlotEditor Magnitude False auto 0 auto 1 autn 1 2 auto 1 2 True True True Multi Channel Display The display method For multi channel Sedi Variable Property Name Property Definition Val aiue Depends on the input TimeUnit Displays the time unit of the data signal data s time unit Select the position None TopLeft BottomLeft TooRight BottomRight and LegendPosition P s 4 None RightOutSide to display the legend on the graph select between Line and Steam to determine DrawStyle Line how the graph is drawn Select the representation of the x axis XAxis Type l LinearAxis choose between Linear Axis and Log Axis Click on the Plot Editor button next to the field to edit how the graph is displayed from the PlotElemEditor line color line thic
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46. just add one into which becomes to read four characters into channel Example If was entered in the Fixed field to read from a row with the numbers 123456789 then 1 is included in the first channel 2345 is included in the second channel 67 is included in the third channel 8 and 9 are disregarded NULL Value Handle option allows user to choose a method to fill in missing values such as NULL or NaN Currently methods are Fixed value Prev value Next value Linear Interp Spline Interp and Monotonic Cube TIPS For more information on filling in missing values please look up on Resample in Chapter 3 1 7 Property Name Property Definition Default Values Select the time unit from psec nsec Time Unit sec minute hour day week month 30days and year 365 adi Time Set the starting time of the data Sample Set the Sample Frequency 1000 pm Set the Down Sample rate With every increment of the value the sample data is reduced to save time during calculation Note The Sampling Frequency value will be automatically Down sample by recalculated depending on the down sample value E g Sampling Frequency 1000 with Down sample 2 will result in creating an imported Source SFO wtih Sampling Frequency 500 Examples 1 Import a Multi Channel Signal Data Load a multi channel signal data file The data is s
47. n the field of Properties AverageLength it can be seen that the default value is 0 1s Similarly it can be seen that the value of AverageCount is 101 which means that every output point of MA is the average of 101 points centering at the corresponding point in the input signal Finally use Viewerto plot the result Project 1 X El Moving Average FilterT ype LowPass Ayveragelength 0 1 Module Mixer MA 1 0 1 rj 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec 3 Following step 2 change AverageLength to 0 2 to perform Moving Average again to generate a new figure named MA2 And use Viewer to plot the result Projecti x Froperties Module Moving Average Filter Type LowPass AverageLength 0 2 AverageLength Average length in time unit Mixer MA 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec 4 Comparing the results obtained in step 1 2 and 3 it can be seen that increasing Average Length can reduce the noise in the input signal significantly However the drawback of this filter is that the sharp edge of the original square wave becomes more and more flat as the Average Length increases 5 Next after changing the FilterType to HighPass perform Moving Average again It can be seen that the result is the input signal subtracted by the output of MA2 Properties Module El Moving Average HighPass Ww AyveragelLength 0 1 FilterType Result park lowpass means t
48. result Viewer updated hello EnMorlet 10000 8000 frequency Hz D O O I o o o 2000 0 0 2 0 4 0 6 0 8 1 12 1 4 time sec 2 After EnMorlet perform Compute TFA Marginal Time whose property of The MarginalMethodg is set as Magnitude In the result the x axis is set as time while the y axis is set as amplitude Properties lx El Marginal MarginalMethod Magnitude Module Module hello EnMorlet Marginal Time 0 06 0 04 0 02 0 0 0 2 0 4 0 6 0 8 1 1 2 1 4 time sec 3 Change MarginalMethod to Complex which means that Marginal Time integrates the time frequency signal directly El Marginal MarginalMethod Complex bal Module MarginalMethod Specifies a complex component to sum hello EnMorlet Marginal Time 0 04 0 0 2 0 4 0 6 0 8 1 1 2 1 4 time sec 4 Next perform Compute TFA Marginal Frequency following EnMorlet In the result the x axis is frequency while the y axis is amplitude Project1 x Viewer updated Auto gt E hello EnMorlet Marginal Frequency 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 frequency Hz Related Functions STFT Morlet Transform Enhanced Morlet Transform 3 6 Transform This module provides common transforms for different signal processing 1 2 Fourier Transform Inverse Fourier Transform Discrete Cosine Transform Inverse Discrete Cosine Transfo
49. sTime Relative Threshhald True Threshhold Ratio 0 4 Use EMD True Target Frequency 40 Default Property Name Property Definition Value Judging whether the peak threshold is the square Fal of the differentiation of the signal 5 Differential Output Type The type of the output could be the Peak vs Time PeakVsTime or the Peak To Peak Interval Whether the relative threshold or the absolute Relative Threshold threshold is used The ratio of the benchmark of the peak and the maximum value 0 0 1 0 Threshold Ratio Threshold value The user difined threshold Whether the EMD is used for filtering the trend Using EMD and the high frequency part of the signal Target Frequency The signal above this target is romoved otandardDeviation Judging wether the IMF is convergent or not Max Sifting The maximum iteration time of the IMF Iterations Example the wave form of the manual signal Generating the wave by the Source Custom Wave with default properties the Expression is sin 2 pi 10 t cos 2 pi 20 t And the figure is shown as below CustomVave 0 1 0 2 0 3 D 4 0 5 0 6 D 7 0 8 0 9 1 time seg And then link the wave to the Peak Detection with default properties The result is viewed by the original Viewer Viewer 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time seg Viewer 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time seg The PeaktoPeaklnterval is shown as bel
50. single channels and multi channels regular signals audio signals the type of the output is real numbers single channels and multi channels regular signals Properties are the same as the properties of the original MSE but an algorithm option is added Detailed introductions are shown as below Property Multi Scale Entropy MinScale 1 Max Scale 20 5cale5tep 1 Match Points 2 Match Tolerance 0 15 E Rolling Multi Scale Entropy Algorithm Auto Overlap 89 WinSize 99 GlobalSTo False Property Name Property Definition Default Value Setting the type of the algorithm Auto Brute Sort and Sliding K D Tree The Brute is the original algorithm of the MSE the Auto is the automatic selection When the width of the watch is larger than 5000 points and the memory is sufficient the Sliding K D Tree is used otherwise the Sort is used Method Auto MinScale Setting the minimum of the computation scale MaxScale Setting the maximum of the computation scale ocaleStep Setting the step of the computation scale MatchPoint oetting the number of the match points MatchTolerance Setting the tolerance of the match Depending on Overlap Setting the number of the overlap points the length of the signal Depending on the length of the signal Setting the size of the watch window The unit is WinSize point Setting whether the STD of the entire signal is computed or not GlobarSTD False Example The measurem
51. such as mat tfa txt csv etc And sound signals can be saved as wav files m Data Viewer Select a SFO Signal Flow Object and click on the Data Viewer button to open up a new window detailing the information of the signal Data Viewer ANM Channel Information Histogram Channel 1 gt From Step 1 500 1 0 99999989 0 99999822 0 99999101 0 99997158 1199995061 4 M Force Update Force Update will force all SFOs to be recalculated again 5 Batch Run Batch Run allows user to configure and run multiple instances of the Signal Flow Diagrams created in the Network Workspace Any property variables of the SFO can be edited in the Batch Run instance to allow greater flexibility and it saves time for not requiring to edit the original Signal Flow Diagrams in the Network Workspace Batch Run allows user to play around with property variables within the Signal Flow Diagrams And changes made to the variables can be tested through multiple Batch Run instance for result comparison 1 3 3 Network Control Area At the bottom of the Network Window is the Network Control Area Network SFO Update progress of a SFO 1 Auto You can check the box Auto to automatically update any SFO you have edited or added This can save you time if the SFO doesn t require much time to update But there will be some SFOs which will require long period of time to compute and it is not effi
52. that the auto correlation of a periodic signal preserves the frequency of the input signal Prajeck1 x Viewers updated v Auto gt m Sine Corr FFT 0 4 0 2 0 2 4 6 8 10 12 14 16 18 frequency 3 Create a White noise and then repeat step 1 The result is shown below Project1 X 3 Noise Corr 2 1 5 1 0 5 0 0 5 1 1 5 2 time sec 4 Use Compute Mathematics Mixer to mix the sine and white noise and then perform the auto correlation operation The result is shown below Mixer Corr 2 1 5 1 0 5 0 0 5 1 1 5 2 time sec Related functions Cross Correlation Source Mixer Reference http en wikipedia org wiki Autocorrelation 3 6 6 CrossCorrelation Cross Correlation performs convolution on two time series for cross correlation analysis In order to reveal the characteristics of an unknown signal the common practice is to perform cross correlation on this unknown signal with a well known signal Introduction Mathematically CrossCorrelation is defined as oo x x y 00 where is the time delay In discrete case let X xy xix xy 4b Y Yy to be a N length and a M length time series respectively the cross correlation with time delay j is given as z l XY R EP i i The length of the result of cross correlations is N M 1 R is asymmetric and its maximum value is subject to the in
53. time sec Related functions Channel Switch Mixer Viewer Source 3 3 4 Math Professional Only Do point to point math calculation for input signal Interface Introduction This module accepts input of Signal which could be real number or complex number single channel or multi channel regular and audio To active the module click the button Im to the right of the field Properties Expressions Then MultiChannel Expression Editor is popped up as shown below Property El Math ReFerenceInput D Noise Expressions 1 Expressions Ei Toolbox rw Ep Rh fe ae 4 IL lt li ee Eee By Channel Channel Expression CH1 X1 1 Input Signal List Output Signal List The pop up window has three panels Input Signal List Toolbox and output Signal List The operation procedure is as following select the signal from the Input Signal List define math equation in the Expression field of Toolbox the calculated result becomes one of the Output Channel in the Output Signal List Below explains each of the functionality Input List Input List displays the signals connect to the input end of the Math SFO By default the input signal is multi channel and each channel is displayed as a tree map shown in the graph The 1 input signal is denoted as X1 in the Expression of Toolbox the 2 signal is denoted as X2 etc The number in the square bracket represents the channel sequence of
54. time sec 3 Zoom Y Firstly click on the 7 Zoom Y button and then click on any part of the graph and drag it along the y axis As you release the mouse button after dragging the highlighted area will be zoomed in and displayed cing VV VEU VV V 1 Sine 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 4 2 Zoom Rect Firstly click on the P Zoom Rect button and then click on any part of the graph and drag a box As you release the mouse button after dragging the selected box area will be zoomed in and displayed This function combines the affect of Zoom X and Zoom Y aine 0 35 0 4 0 45 0 5 0 55 0 6 time sec 5 Pan X Pan Y Pan X and Pan Y buttons allows you to move along the x axis and the y axis of the graph respectively 6 F Show Value Firstly click on the Show Value button and then move the mouse onto any part of the graph There will be a horizontal and a vertical blue line which will intercept a data point on the graph and the value of that point will be displayed at the bottom left corner of DataDemon program Data Demon 1 0 powered by V1sual Signal Beta Ele Edit View Layout Tools a Hmm 9959 Alis Viewer updated Auto Q Q Properties Module Representation Module index 309 x 20 309 y 7 Preference Preference allows you to edit some configuration regarding DataDemon Default Plot Size allows you
55. where c represents the c channel The output signal Z can be used to calculate real signals There are 6 types as shown below c x J y f i0 _ 4 i0 z y J Je Ae Magnitude A Phase 6 Real Part x Imagine Part Gainref is the Gain reference Gain 20xlog 42 Gainref 2 Power Spectrum A Properties This module accepts input of Signal which could be complex number single channel or multi channel Regular or Indexed Audio which could be complex number single channel or multi channel Regular Numeric which could be complex number single channel or multi channel Regular or Indexed and Spectra which could be complex number single channel or multi channel Regular The output format is identical to the input signal except that it is a real number Property is Map Method with a default value of Real Part i e the real part of the input signal mag Part represents the imaginary part Magnitude is the absolute value of the complex signal Phase denotes the phase Gain is used to set Gain Reference for Power Gain calculation and Power Spectrum is the power of Magnitude Properties El Map to Real Map Method RealPart Default Property Name Property Definition dii Value select the signal type which the complex signal should be converted to The method options are Magnitude Phase RealPart ImagPart Gain and Powerspectrum MapMethod RealPart Example T
56. 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 time sec 2 Use Compute TFA Morlet Transform to perform calculation on the input signal and then use TF Viewerto plot the result It can be seen that the higher is the frequency the larger is the frequency spread and therefore the worse is the transformation performance Project X TF Viewer updated Auto i pem Morlet Transform 400 0 1 gt O D 200 0 05 o D 0 0 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 time sec Related Functions Short Term Fourier Transform Enhanced Morlet Transform Viewer References 1 A Wavelet Tour of Signal Processing 2nd Ed 2 Y N Jeng C T Chen and Y C Cheng The Enhanced Morlet Transform via Iterative Filter to Study Turbulent Data Strings The 6th Aslan Computational Fluid Dynamics Conference Taiwan August 2005 3 5 3 Enhanced Morlet Transform Professional Only The drawback of Morlet Transform is energy spread at high frequency due to the decrease in resolution Please refer to Morlet Transform section for more details Enhanced Morlet transform calculates signal with Gaussian function to resolve energy spread issue at high frequency Introduction Before applying wavelet transformation the input signal multiplies with a Gaussian function to remove the small amplitude c
57. 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 3 Set the Properties Source SignalFreg to 3 Amplitude to 2 5 AmplitudeOffSet to 1 5 and TimeStart to 2 the graph is shown in the image below 3 eignalFreq AmplitndeOtiset Phase Tomes tart SignalFreq The frequency of the to be generated signal Sine 4 2 0 2 2 1 2 2 2 3 2 4 2 5 2 6 27 2 8 2 9 time sec Related Functions Viewer Square Triangle Viewer Square Triangle 5 4 Square Wave Explanation is given for the Source Square Wave SFO Introduction AT V E f X t T x 0 Sqr Sqr x0 A V st o0 lt t lt 0 ral f Where A amplitude f sampling frequency 6 phase at to V offset from X axis the ratio s is shown in the image below Properties A mplitudeOffset Phase Symmetry Times tart Symmetry modifications to the wave shape Default Property Name Property Definition Value Set the time in ps ns us ms sec minute Sec TimeLength Set the value of time selected in TimeUnit 1 Set the number of Sampling frequency the SamplingFreq 1000 amount of data values be sampled Set the length of the data SamplingFre DataLength MEL Sam ee reme TimeUnit 1 Set the maximum displacement of a periodic PTS Wave 10 AmplitudeOffSet Set the amplitude offset Set the time in ps ns US mS sec minute TimeUnit 1 hour
58. 1000 1500 2000 2500 3000 2 5 TS 0 5 500 1000 1500 2000 2500 3000 This residual is then put through the sifting process The EMD continues generating signals until the residual signal contains less than two extrema The process is then finished Intermittency Intermittency is a method of removing certain frequencies from an IMF This is done during the sifting process directly after an IMF is found but before it has been subtracted from the residual According to the EMD Flow Chart this would occur between the steps titled Does IMF candidate meet stopping criteria and Yes subtract it from Residual Difference becomes residual The algorithm for intermittency is as follows From the IMF distances between zero crossings are calculated If the distance is greater than the user defined threshold value the signal between the two zero crossings are zeroed out If not that section of the signal is retained The distances between zero crossings the value for which threshold is compared against in intermittency Intermittency is useful for collecting oscillations of similar scales to reside in one IMF which will avoid mode mixing from an IMF The threshold is measured in the integer value of number of points It is not affected by the time offset or timescale of the signal Example of an IMF before and after an intermittency threshold of 20 is used The blue dashed line is the IMF prior to intermittency The red
59. 54 IMF residual 0 0196 0 0106 0 0209 0 068 0 098 0 116 0 416 0 54 1 The diagonal of the matrix is self correlation so the value is 1 For the other elements the maximum value is between IMF h7 and IMF h8 It means that there exists strong correlation between them Most correlation absolute values among elements are less then 0 1 it means that there is no correlation between them Related Functions Covariance Matrix Orthogonality Matrix Merge To Multi Channel Channel Viewer RCADA EMD Reference Cohen J Cohen P West S G amp Aiken L S 2003 Applied multiple regression correlation analysis for the behavioral sciences 8rd ed Hillsdale Nu Lawrence Erloaum Associmtes 3 4 4 Equiphase Statistics For a fixed period length M Equiphase Statistics calculates the statistics of the same phase under this period such as month average week average etc Introduction Let 150 1A v1 be a series the length is N The period of Equiphase Statistics is set to M M N Then this series can be divided into K Ceiling N M small series Ceiling x means to map the number to the smallest integer not less than x Let small series be reprensented by where k is the small series number j is the element in the series then C 1 n y E 0 lt lt 1 0OxkxK 1 As shown below sec N Equiphase Statistics picks elements with the same phame in each asa group to calculate i
60. ARR 71 CHAPTER 3 COMPUTE SIGNAL FLOW OBJECT EE EE Kr En ede ts EENEN RAEE 75 3 1 PE E E E A AT IN rae ee ie EE E e 76 TINIE SE CEM 77 T E MT 81 84 NN Y 88 Sls EE 93 STE REPE EN 109i 97 NEC NEN LS c Cmm 100 Nm MED cic E 105 XP NEED UP Ro c 109 3 1 10 li i Viso AEG PT 113 9 2 p 117 SN SER LUCR DID Tm 118 Ole ANDI QUEE MERERETUR 126 22s MOVINGAVERAGE FITER Ret bx Rudd e edm bens tud Eds 130 3 2 4 ITERATIVE GAUSSIAN FILTER PROFESSIONAL enhn 136 3 2 5 TREND ESTIMATOR PROFESSIONAL ONEY iunt0393023295miReeP UsM PATE aD DEN 142 147 wad vmm 150 3 3 A E I 153 el BREMON D EEEE ETAT EEEE EE EA A AE EEE A EEA 154 oS EE T a T E A EA EEEE E A E 158 E EA POE E E s 165 acd AATE PROTE ONGI F anaa E E A E ETA O EEE ENET EAR 169 oo D E E E A AE E E R 180 om c E EE ce ees TA EEEE EEA nee pg eas AEE EA 184 DD e a 189 3 4 STATISTICS TROFE SIONAL NEY J riporre aE E ert 210 S MEE 9 PA ET EE ATN 211 D COVARIANCE MATRIK PEDRO EM UE 220
61. AboveBelow set threshold to determine whether the information is RunThreshold greater than or less than the threshold If it is Auto Auto the input data is same as the average oet the criterion to reject the null hypothesis the proportion under normal distribution The most oignificanceLevel commonly used values are 0 1 0 05 or 0 01 The 0 05 smaller the significance level the harder it is to reject the null hypothesis Test methods Null two tail RightTail right end where the average input data must be greater than Hypothesis the sample mean LeftTail left tail where the Null average input data must be less than the sample mean Examples These examples will explain the use of various testing methods Example 1 Suppose a weighing instrument with no load the average weight is 0 0 and the standard deviation is 0 03 Before each experiment we will use no load to do the correction Lets repeat reading for 1001 times and use the information gathered to examine if the instrument has bias First we set the null hypothesis to no error in weighing for the instrument and then we use Z test to test First use Source Square to generate a group of weighing data Amplitude is set to 0 1 then connect Compute Statistics Basic Statistic Under Basic Statistics press View Statistics observe the Mean Properties El Source TimeUnik Sec TimeLength 1 SamplingFreg 1000 DataLength 1001 SignalFreg 10
62. After Viewer s processing result in the following charts How fast do the ants gather Numbers of Ants Linear Regr of Numbers of ants Number of ants 0 2 6 8 10 Time sec It is important to know that when it is time series view the result by Channel Viewer rather than XY Plot The relationship between two groups of data The corresponding format is XY Connect the first group of data and the second of data with this device in order Connect LeastSquareFit s result and data X and data Y to Merge to Multi Channel Connect XY Plot to view the result This process is shown as following flow chart When connect to the ToMulti the order must be Linear Regress X Y or X Y Linear Regress The result can be shown correctly only under this circumstance XY Plot can edit this process and the Hooke s law s chart as the illustration Hooke s law 6 8 Spring length cm e oO c 1 1 2 14 1 6 1 8 2 Force 9 These are two fundamental ways to use this device Linear regression make the decision that use TimesSeries or XY based on the numbers of input If there is only one input Linear regression will regress every time of channel and value of this input and then output the x of x at b In case of two inputs the first one is X and the second one is Y After using the XY s way to regress the outputs of regression formula are x and y If there are multiple channels
63. E Ta 6499959 H Down sample by 1 Count 650000 Range 1805 6 sec 0 1605 6 Date Axis Use Date Axis Start Date Time 200101001 2 4 fos fos selected Channels 1 MLII W 2 Wv5 Import Cancel E WFDB Importer and SAC Importer are relatively similar They both have Signal Information Data Range and Data Axis The only difference is that WFDB has an additional option of the Selected Channels 5 1 3 Text Importer Opening csv and txt file types will open up a Text Importer The Text Importer is more complicated than the other two importers Data Range Rows 1 ES to end aml 1 to ena Data direction Column based Concatenate ta one channel 29 Specify Time Column Field Format Hull value Handle M Use Null alue Handle Linear Interp Time Coordinate Time Lint sec Time Shift 0 sec sample Frequency 1000 Ey clez zec Down sample by 1 Date Axis Enable Start Date Time 200101 1011 od Jos od File Contents QOL L 6369702e 16 O 0627905195 OOS 0 125333234 004 0 197381315 005 0 249699997 006 0 309016994 Un 00S 0 425779292 009 0 491753674 010 0 595926795 011 0 597795252 Ole 015 O 664547106 014 0 728968627 The fields in Data Range are explained in the table below Property Name Property Definition Default Value Rows Enter
64. FE DaMatlab Editor gt Matlab script file Y Al DoMatlabe Editor Appearance is shown as above and the functionalities of buttons are introduced below 1 Button represents opening M file 2 lH Save the content in DoMatlab Editor in a M file 3 lt Turn off the editor 4 Clear contents in Script area 9 l Is the button to run the script In addition there are two tabs in DoMatlab Editor Script and Help amp Example Script is the workspace for users to write MATLAB codes The default instruction is Y X1 The Help amp Example page detailes the input and output format in DoMatlab and provides simple examples DoMatlab Editor Ed 18 1 Input signals are stored in xl DATA etc as 5 vectors of cells Each cell represents a channel For 5 example to access channel 2 in input 1 type Xl DATA Pup For a Spectra type signal each cell contains a zD matrix The variable format of input signals DoMatlab allows multiple input sources which are defined as X1 X2 Xn following their input order When a new signal adds to the input DoMatlab would add 5 variables which are X Xn Xn DATA Xn DESC Xn Freq DoMatlab only allows one output signal which is defined as variable Y The meanings of variables mentioned above are explained below X I
65. Filter Type Attenuation Property Definition Value LowPass low frequency can pass Filter Type HighPass high frequency can pass LowPass ByPass frequency between F can pass The parameter for the Gaussian curve in the Attenuation MEE filtering The high frequency value of the filter The low frequency value of the filter Example UL eini Create a input data in the form of 9 then use Iterative Gauss Filter to filter out the component Create a Sine Wave set TimeLength to 10 seconds and the frequency to 3Hz And create a Custom Wave with setting the expression value to be exp t 3 2 and set TimeLength to 10s Then mix these two signals together and display it using Channel Viewer 20 0 1 2 3 4 5 B 7 8 time sec Try to use FFT to observe its characteristics Connect Mixer SFO to terative Gaussian Filter set Filter Type to highPass set FH to 0 5 and set FL to 0 1 Since the Sine wave is at 3Hz it will pass through the filter with FH is below 3Hz 4 Properties hh Properties xj Connect the filtering result to Channel Viewer The result is close to the original signal except the end part Adjusting the parameters of the filter can improve the filtering result Viewer Sine CH1 time i sec Thin Black curve the original Sine Wave thick red curve the signal after filtering Change Iterative Gaussian Fil
66. Filter is defined as M 1 1 kizicT y median x i M 1 Centered on the data take points on both sides to construct a set of array Then find the median in the array to replace the i data In the case when the number of data is insufficient e g M NorN i repeat the edge data to fill the whole array M is supposed to be an odd number In the case of even number it would be made to be odd by adding 1 automatically Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The formats of input signal and output signal are identical xj E Median Filter FilterOrder 101 Module Median Filter Property Name Property Definition n did Value The data length of the median filter i e M is supposed to be an odd number In the case of FilterOrder even number it would be changed to an odd number by adding 1 automatically Example The example shows the procedure of using a median filter to process a signal of a square wave plus speckle noise 1 Right click in the Network Window select Source Noise to generate a noise signal Set the Properties Noise Type as Speckle Probability as 0 25 n addition select Source Square Wave to generate a square wave Use Compute Mathematics Mixer to mix these t
67. Mame chirp1000 GutputPortside Right Real Single Channel Wi DutputDataType Data Type 2 From Chirp10000 SFO select Conversion Convert To Audio directly In Properties it can be seen that the Sample rate 44100Hz and Bits Per Sample 16bps These two properties can be changed in the drop down menu Properties Convert To Audio Sample Rate 44100 Hz Bits Per Sample 16 bps Bits Per Sample Set Ehe number of bits per sample The original data is not altered Then check Module in Properties and it shows that the OutputType has been changed to Audio O Module Marne ToAudio InputPortSide Left OukputFPortSide Right n 4AcceptableDataTy Real Multi Channel Signal of Rank 1 Regular Data OuEputDabaTvpe I OutputDatalT ype OuEpuE Data Type 3 Connect Viewer Channel Viewer to ToAudio the tool at the top right of the Viewer could be used to play this audio signal Viewer Updated Auto gt chirp 1000 ToAudia 0 0 005 0 04 0 045 0 02 0 025 0 03 0 035 0 04 0 045 time r ser 1 Related Functions Channel viewer Wave Writer References Microsoft Wave Format http ccrma stantord edu CCRMA Courses 422 projects WaveFormat 4 3 Convert to Regular This component changes the time axis setting of a signal from Indexed to Regular Introduction When reading text files such as txt and csv etc with mport data from file if a row o
68. Norden E Huang et al 1998 and NASA HHT DPS named it as Degree of stationary Introduction For a time frequency distribution H a t Define the marginal frequency as n o 7 t dt T Then Degree of Stationary is computed as follows H o t 1 n s dt Degree of statistic stationary is described as follows 0 1 DSS w At fu BD Ts n Properties This module accepts input of Spectra which could be real number single channel Regular The output format is real single channel and Regular signal TimeAverage is the time span to average 9 TimeAverage over of the spectra data The unit of the time span is samples Example In this example LOD78 is decomposed and then all IMFs are transformed into spectra by NASA Hilbert Spectrum Lastly use NASA DS to observe variation of frequencies 1 Still use Source Import data from file to read tfa file LOD78 tfa in the installation directory default to be C ProgramFiles DynaDx DataDemon demo HHT Next perform Compute NASA HHT NASA EMD LOD78 would be decomposed into many IMFs 2 Then use Compute gt NASA HHT NASA Hilbert Spectrum to connect NASA EMD and furthermore time frequency result is displayed in the TFA Viewer L OD S NASAEMNLD NASA Hibert spectrum 100 LA ec Oo ce el Frequency cycles day Ln ce 0 5 1 1 5 2 4 5 Time das Lastly connect Compute NASA HHT NASA Degre
69. Note the changing of StartPosition and EndPosition would affect the output signal length Properties StartPasition EndPositian Const Module StartPosition Start Position Sine_Int 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Projectl Int Channel Information Histogram Channel 1 Sampling Frequencs 20 Data Count Time Length 0 7000000000000000 Unit Sec E Data Channel Channel Count 1 Channel Channel 1 Min 0 206620200774254 Max 0 109067374959497 Mean 0 020818324012057 S ID Deviation 0 1157560457024725 Related Functions Diff Source Channel Viewer 3 3 7 DoMatlab DoMatlab could be used to input the outcome signal data from DataDemon to Matlab engine and run Matlab codes The Matlab calculation results also could be sent back to DATADEMON Properties and Instruction DoMatlab can accept all output format available in DATADEMON When this component DATADEMON is connected to DoMatlab the code would run the Matlab Command window automatically Basic MATLAB functionalities such as Workspace browser Path browser are provided in Command window Users may reference to MATLAB introduction files for usage instructions MATLAB Command Window E B x File Edit View Window Help Fle Using Toolbox Path Cache Type help toolbox path cache for more info To get started type one of these helpwin helpdesk or demo For product informat
70. OutputFileMame OutputFileName The output Filename Enter the file name as sine and save the file to the location C directory oince Properties Writer WriteNow is set as False the file has not be saved yet Now change the WriteNow option to True and the file will be saved in C directory Select OutputFileName Save in Ge Dell91 00 C 4 BJPrinter L5 Documents and Settings My Recent extra Documents lava Matlab output Program Files 9RECYCLER 9Ssleep_housekeeper System Volume Information temp tmp LO WINDOWS 3 Yanhui File name sine Save as type files WriteNow True N 1 i Pe JutputFileN ame C sine tfa IH dm ri WiiteN ow Write file now If it is true it would also write file when updating Related Functions Csv Writer TFA Writer Wave Writer Cancel 7 5 Wave Writer Export a signal or an audio into a wave file format Properties This module accepts input of Audio which could be real number single channel or multi channel Regular The default output for WriteNow is set as False so the wav file will not be exported to a file Only when this property is set as True then the file will be exported to a target location default location Pro 5 Module E Writer WribeMouw False v OutputFileName C Documents and Settings user m RrEa csv P
71. Please refer to Hilbert Transform For input signal we can calculate its Hilbert Transform as following 0 X Hix v t P V ar TT gd no where 2 is called Hilbert pair of The above equation is equavilent to the 1 taofi convolution between devide i e And P V is Cauchy Principle Value z t x t iy 1 9 a t O r tan 1X x t dO 1 _ MN m Define as the instaneous angle speed and is the instaneous frequency So after Hilbert transform we can obtain 204 99 a t W t To plot the time frequency graph varies based on time WIT When the time is the height along Y axis can be obtained from frequency 217 f la t When the time is the amplitude along Z axis can be obtained from Once the calculation is done for all data points the time frequency graph completes This is Hilbert Transform Since the graph obtained from discrete data points Gaussian function can be applied to smooth the curve If all of the multi channel signal are applied with Hilbert transform the original signal can be represented as following mostly apply to the results of EMD calculation 2 x Af gt qae The rest of the operations are the same as the one for single channel signal Properties This module accepts input signal of real number single channel or multi channel regular and audio T
72. Properties Phase 180 degree unit is in Degree Finally merge three signals into a Multi channel signal using Conversion Merge to Multi channel n this case three sine waves are generated 10Hz 5Hz and 10Hz with phase shift of 180 degree Using Viewer Channel Viewer the signals can be displayed Black curve is Sine blue curve is Sine2 and red curve is Sines E The property of Sine2 is shown here Properties El Source TimeUnit TimeLength SamplingFreq DatalLength SignalFreg Amplitude AmplitudecOfFset Phase SignalFreq The Frequency of the to be generated signal The property of Sine3 is shown here Properties Source TimeLlIniE TimeLength SamplingFreg DataLength SignalFreq Amplitude AmplitudeOfFset Phase Phase The phase in degree Sine TaMulti 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 lime Sec Connect ToMulti SFO to Compute Statistics Covariance Matrix and click Properties View Matrix to show the result in the pop up window The matrix element is self covariance value which is 0 5 12 are covariance between Sine and Sine2 Since the value is very small it means there is no correlation between these two signals C C are also very small It means that there is no correlation between oine2 and Sine3 Signals Sine and Since3 mirror along X axis and the covariance is about 0 5 it shows that two signals are negative correlated El Covarianc
73. The time setting such as Sample Frequency and Time Shift of the 2 input signal is set to those in the 1 input channel The principle of copying time axis setting is that the time points of missing data is filled with O and time points of exceeding the time reference is discarded In order to avoid the operation confusion it is recommended to use two signals that have the same number of channels and the same time axis P TOPE guts EN Referencelnput 1 ToMulti Module Merge To Complex Property Name Property Definition Default value Reference signal Use the real or imaginary The 1 set Heferencelnput part as the reference for time axis and number of input of channels signals Example This example demonstrates two operation modes First merge two single channel real signals to form a single channel complex signal and show how to plot it in a complex plane Second use Merge to Complex to combine two signals which have the same sampling frequency but different time length to form a complex multi channel signal Single channel signal 1 Use Source Sine Wave to generate two sine signals Click the Sine2 icon and then change its Properties Phase to 90 to make it a cosine signal Next use Conversion Merge to Complex to merge these two signals into a complex signal To omplex vYPlot updated Auto n The output signal format of ToComplex IS available In Properties Module OutputDat
74. This module accepts input of Signal which could be real number single channel Regular and Audio which could be real number single channel Regular The output format is complex and signal channel spectra data Properties FreqAxis Line arAxis FreqMin 0 Freghax auto 0 FregResalutian auto D Freglount 25b Timec aunt 2048 RemoveDt True Window Hanning Property Name Property Definition Default Value frequency axis could be LinearAxis Linear measurement LogAxis FregAxis MEM LinearAxis logarithmic measurement LogAxis are mostly used in audio analysis FregMin the frequency boundary for 10 0 5 Sample FreqMax frequency plotting Frequency To define the range of the window function m ES It would affect the size of the window Fre jd Y 4 function The smaller this value the smaller 4 y the window function FreqCount The number of discrete lattice in frequency 256 Use to choose whether remove the DC or HemoveDC rue not before STFT To select different window function in STFT Window For the definitions of window functions Gaussian please reference to Fourier Transform Example In the example below use a Chirp signal as input and then use DataDemon to perform time frequency analysis It can be seen that a frequency which varies linearly with time 1 Press the 2 in the Network tools or use Source Import data from file to read a signal file chirp1000 tfa in the
75. Time Unit picosecond E sample Frequency 1000 cycles p Down sample by 5 Date Axis Enable Start Date Time 2001 M0101 0 4 oz os Time CH 1 2006 06 20 3l ll l56z5000 152 523796080E 65 2009 08 20 31 11 15629000 3 91605427E 3 02 12 1B 31 12 2009 09 20 2000 00 20 2000 00 20 2000 00 20 2000 00 20 2000 00 20 2008 00 20 2000 00 20 2000 00 20 2000 00 20 2008 00 20 18 91 14 15633000 15637000 15641000 15645000 15649000 15653000 15657000 15661000 156 5000 15669000 15675000 641 175E 3 2 64790920E 3 l 1153 8855E 3 Z81 56348551E 65 932 6796e2556E 6 l1 3531Z751E 3 1 856851533E 3 3 01 0lzz5E 3 254 5378154JdE 6 l 7585433zE 3 2 d51243798E 3 5 rpmm 1 ate 1B 31 11 1B 31 15 18 41 16 Note It is not advised to have decimal numbers within the time of the data E g 2005 3 18 15 05 35 01242 1 If you wish to import a data with date and time and it is not in the csv format then you will have to configure the Data Axis and Time Coordinate options In this example Time Coordinate is set as day and Sample Frequency is set as 1000 Data Axis is Enabled and the date and time is set as 2003 03 12 4 hour 6 minute 50 seconds Data Range 1 to lend 1 to Data direction Column based Concatenate to one channel E nm specify Time Column Field Format
76. VIBWEr AINE Aen mm ea UON After mixing MIXET 2 MA mu 2 0 0 4 0 2 0 3 0 4 0 5 0 8 0 7 0 8 0 9 1 time i set After Mixer a Container is added by Container Add Then the compiler area of Project1 Container is added automatically in the Network Panel On the left side of the main window you can find the plot area of the newly added Project1 Container In Container you need to select Container Dataln in the context menu and send input data to Container After Dataln you connect Compute Filter FIR Filter and Compute TFA Enhenced Morlet At the end Container DataOut is connected and computation results are sent to Container s ouput entry a 55 Dataln p E LIIl l l If there are many modules connecting to a Container the user need to set the origin of data by the parameter named InputFrom in the Dataln In this simple example Input is just Mixer DakalIn InputFrom D Mixer Module InputFram Select From inputs contecked to the container in the parent project In addition the user can add Transform Fourier Transform after FIR and show the data by Viewer Channel Viewer DataIn ip 1 Gee EE The result of FFT is default 1 0 5 0 0 10 20 30 40 50 BD 70 80 an 100 frequency Hz The Viewer of this graph is drawn in the Container Return to the original Project results are obtained by connecting the Container to the TF
77. Viewer the X values are based on the Sample Frequency of 1000Hz So every data value is read at 0 001 increments Index X Value CHI CH3 CH4 0 0 1 23 45b 7990 1 0 001 2 34 567 0901 2 0 002 3 45 ove 9012 5 1 5 Import Matlab file format MATLAB MAT Importer will import mat file format MATLAB which is created in binary format HATLAB MAT Importer sample Frequency amp start Time Sample Freq oyelesisec Time Unit Date Axis D Bis A V2 72 9 elect Variable eme x j lixi DOUBLE v The configuration for the MATLAB MAT Importer is exactly the same as the Text Importer 5 1 6 Import wav or mp3 file format If the file imported is wav or mp3 these two types of sound format will directly create a Source SFO onto the Network Workspace and will not open any file importers Project x Viewerz updated Windows XP 20000 20000 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 time sec Property Name Property Definition Default Value Data Range Contains the options to set the range for the data Enter the range of rows to be read 1 to End Enter the range of columns to be read 110 nue Determine the way to read the data au Data Direction Column based row based or column based Concatenate to Determine if the data is to be displayed in Unchecked one channel channel or multiple channels uncheck Determine if the time information already exist in the signal data Che
78. also be mixed However for all data groups which are higher than three the weights are all set as GainN Therefore it is not encouraged to use one Mixer to mix more than 3 groups of data It is recommended to use multi layer Mixer to achieve mixture of more than 3 groups of data The figure below shows an example using this method to mix multiple signals Viewer3 updated Auto gt Related Functions Channel switch Multiplier Sine Square 3 3 3 Multiplier This component multiplies multiple input signals Introduction Mathematically assume N groups of signal sources X t where time axis t and sampling frequency of every signal are not necessarily to be identical The mixed signal Z t is Z t X t XO X t In this module because the time axis of input signals are supposed to be different the minimum sampling frequency freq in all input signals is extracted first and then all other signals are re sampled by freq After the time axis of all input signals are unified the signals are multiplied at every time points Properties This module accepts input of Signal which could be real number or complex number single channel Regular and Audio which could be real number or complex number single channel Regular Multiple signal input is also allowed This module does not require default values It can perform multiplication on signals which have different length and sampling freque
79. and Remove Channel is completely the opposite Channel Switch preserves a single selected channel from a multi channel signal data and Remove Channel removes the single selected channel from a multi channel signal data Related Functions Merge to Multi Channel Channel Switch 3 1 6 ReplaceValue Replace a particular value in the signal data Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular Properties Module El ReplaceValue ReplaceFrom ReplaceTo 0 ReplaceFrom The value to be replaced Property Name Property Definition SED n diis Value ReplaceFrom Set the value to be replaced ReplaceTo Replace the set value with this new value Example Change the maximum value of the square wave to another number 1 Create a Source Square Wave and connect it to a Viewer Channel Viewer Viewer updated v Auto Q Q o o Co o A 0 5 0 6 0 7 0 8 0 9 time sec 2 Now connect the Sine SFO to Compute Channel ReplaceValue and set the ReplaceValue SFO s Properties ReplaceValue HeplaceFrom to 1 5 Now all the values of the square wave which was originally 1 will become 1 5 Viewer updated Auto Q Q Module El Replace alue ReplaceFrom 1 ReplaceTo Replac
80. and TimeStart to 0 3 the graph is shown in the image below Properties E Source TimeLlniE TimeLength SamplingFreq DataLength SignalFreq Amplitude AmplitudeofFset Phase Symmetry TimeStart Amplitude nfiset The amplitude offset Triangle 0 8 time sec Related Functions Square Wave Sine Wave Viewer 5 6 Custom Wave The users can input equations to create signals via this module Properties samplmeFreq 1000 DataLength 1001 Times tart 0 sin 2 p1 10 1 Expression Using the expression to generate the signal jmd Property Definition Mn TimeUnit The unit of time second minute hour day month year second TimeLength length of time 1 SamplingFreq The frequency of sampling 1000 tar or cee emcees TimeStart The start point in time 0 Expression oet the equations to calculate the signal where expression can use sin cos tan exp and asin etc math functions which are the same as functions in the fn menu of Math module Please also refer to math functions for C3 language Please note the expression of power is written as pow a b Example Build a quasi steady signal in which the time is direct ratio with the frequency Under the menu of Source Custom Wave the user set the TimeLength to be 2 The setting of the Expression is as below xj E Module E Source TimeUnit sec TimeLength 2 samplingFreq 1000 DataLength 2001 Times
81. determination Recently he developed a new method the Hilbert Spectrum Analysis specifically to process non stationary and nonlinear time series He developed the Empirical Mode Decomposition method that is the basis for the Hilbert Huang Data Transform Dr Norden Huang is a member of the National Academy of Engineering Kizhner 2004 Instantaneous frequency Frequency is often defined as the reciprocal of the time length of an event such as the period Instantaneous frequency is the ability to calculate the frequency based on instantaneous rate of change of the phase function For a simple oscillation the instantaneous frequency is identical to the traditional frequency defined as the reciprocal of the period The instantaneous frequency provides sharper more local results for describing nonstationary and nonlinear processes Intermittency A natural phenomenon in turbulence when certain scale of motion will occur sporadically Here we use it to designate the method of removing a sporadic signal from a given IMF Intrinsic Mode Function Any function that satisfies the following conditions that the number of extrema differ from the number of zero crossings by no more than one and that the mean of the envelopes defined by the maxima and minima is zero IMFs are generated using the Empirical Mode Decomposition process and are useful for obtaining the instantaneous frequency via the Hilbert Transform Linear The conditions
82. file into information that can be read and processed by DataDemon um Text Importer Data Range Rows 1 Ea to end Columns Eal to End Data direction Column bazed Iv Concatenate to one channel Specify Time Column Field Format White spaced Q Delimeter Fixed field Mull Value Handle Use Mull salue Handle Linear Interp 1 Time Coordinate Time Unit Im Time Shift sec Sample Frequency 1000 Cy cles sec Down sample by 1 E Date Axis Enable File contents If the imported file is not supported by DataDemon a warning message will pop up image below asking the user whether to read the file as plain text or use Text Importer to import the file The user will be required to configure the Text Importer on how a text file is to be read e g how to set the time frequency and data range Onestion File extension pdt is nat supported of Text Importer Description MATLAB file format SAC Seismic Analysis Code is used for Seismology DataDemon file format Comma separated values Wave file format Mpeg1 audio layer3 file format signal file format used biomedicine Pleas refer to www physionet org for more information 2 k save Data to File Au Export data to Excel These two operations can also be found under Writer Signal Flow Object SFO The result obtained from a SFO can be exported and saved into various file formats
83. from the mouse menu shown in the image below KJBatch Run demo22 STFT 5 lt gt we Output Directory C Program Files DynaDx DataDemon data Batch Runs Emil Runz Runa Rung Add Batch Run x x Remove Batch Run w Armes After clicking on Add Parameters from the mouse menu the Parameter List will appear from the left of the Batch Run window as shown in the image below 3 Batch Run demo22 STFT ELSE iA A GEX Output Directory C Program Files DynaDx DataDemon data Paramater List From Project demo22 STFT Batch Runs amp Chirp 1000 9 amp STFT Run2 Viewer2 Runs amp _ FFT Hund s Viewer3 amp TFViewer Suppose that you want to change the FreqCount value of STFT First locate the variable FreqCount under Short Term Fourier Log STFT by clicking on to expand the list Check the box corresponding to FreqCount and highlight is then click on gt or to insert the variable to one or more Run profiles Batch Run demo22 STFT DPA 8 QQ S Output Directory C Program FilesvDynaDxNDataDemondata P aramater List From demo22 STFT Batch Runs 1 e 00 Runt Runz Freg amp xis Linear amp xis Run3 FreaMin 0 Rund FreqMax auto 500 FreqgResolution auto 25 FreqCount 256 RemoveDC l
84. functions For information on the Fourier transform please refer to http en wikipedia org wiki Fourier transform Generalized zero crossing method of calculating local frequency values using the distances between zero crossings and extrema Gibbs phenomenon Often seen in results after a Fourier transform is applied there is a series of oscillations that permeate data in areas of discontinuities As the Hilbert transform is implemented through two Fourier transform proposed by Gabor Gibbs phenomenon will also show up whenever the end of the data when spliced showed a jump Hilbert David Renowned mathematician for who first observed the functions later named Hilbert transform by Hardy For more information refer to http en wikipedia org wiki Hilbert Hilbert Transform Used to derive the analytical signal from data This information can be used to calculate the instantaneous frequency Hilbert Huang Transform A system for obtaining the instantaneous frequency of a signal It involves applying the Empirical Mode Decomposition algorithm to the data to derive the Intrinsic Mode Functions which the Hilbert Transform is then applied to calculate the instantaneous frequency Huang Norden E Norden E Huang is a senior fellow at NASA Goddard Space Flight Center He holds a doctoral degree in Fluid Mechanics and Mathematics from the Johns Hopkins University Dr Norden Huang has worked on nonlinear random ocean waves spectrum
85. generated by x A sin at 0 Where A amplitude angular frequency 5 phase at to offset from X axis and sampling frequency is defined as f I Properties Properties El Source TimeUnit TimeLength SamplingFreg DataLength SignalFreq Amplitude Armplitudecrrset Phase Tire Start Property Name Property Definition Set the time in ps ns us ms sec minute TimeUnit hour day month or year TimeLength oet the value of time selected in TimeUnit Set the number of Sampling frequency the SamplingFre pne amount of data values to be sampled Set the length of the data SamplingFreq x DataLength 9 TimeUnit 1 Set the maximum displacement of a periodic Amplitude v AmplitudeOffSet Set the amplitude offset TimeStart Set the start time for the data Set the Phase degree When the phase is Phase non zero the entire waveform appears to be shifted in time with specified value Example Create a Sine wave 1 Create Source Sine Wave Project X Viewer updated 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec In Properties Source SamplingFreq is set to 1000 and SignalFreq is set to 10 2 If you set the Properties Source Phase 90 then the Sine Wave will become a Cosine Wave Properties El Source TimeUnit TimeLength SamplingFreq DabaLength SignalFreq Amplitude AmplituideofFset TimeStart Phase The phase in degree Sine 0 0
86. in one input the TimeSeries can draw the regression line and original data according to what the previous paragraph depicts But when use XY to regress two first channels of the two inputs will regress each other The output channel s order is x1 y1 x2 y2 etc If we want to draw all of the X Y data and their regression line the chart can show in correct order only if the input order of XY Plot channel should be x1 y1 x2 y2 In order to get the parameter of this regression line navigate to the View Regression Parameters in Properties and it will pop on the window below General Linear Regression parameters for X Force and Y Spring Length Linear Regression parameters Intercept StdDev of Errors iCH1 Then users can look up the linear parameters As shown in the figure Slope is the a in linear formula The Intercept is b Error StdDev is the mean absolute difference of every data and regression which can be used to the reliability of the regression line Properties This module accepts real number single or multiple channel regular signal and audio signal as input Property Name Property Definition Default Value The relationship between a group of automatic selection data and time unable to change TimeSeries XY The relationship between two groups automatic selection of data unable to change Related Functions XYPlot 3 5 TFA Time Frequency Analysis This module
87. in the drop down menu there are also Fixed decimal display and the Scientific decimal display The second option is to configure how many decimal places that will be displayed and the default is 3 decimal places Click on the E Refresh button when either of the options has been changed and the calculations will be updated with the new display settings Basic 5tatistics for Noise Basic Statistics GeometicMean 0 617 HannoncMean TrunmedMean Median Sta Dies Variance Vanatonloef Property Name Property Definition General Statistics generated by the program Scientific notation e g 1 234E 001 Fixed Fixed point notation Displaying numbers behind the decimal point Below are the Signal Flow Objects which contain Report Window Reporter Component Option DoMatlab Correlation Matrix Covariance Matrix Orthogonality Matrix Quartiles and Quantiles Batch Run IMF Property 1 5 Visualization Window b Data Demon 1 0 powered by Visual Signal Beta Noise Corr 1 0 8 0 6 0 4 0 2 0 0 2 0 4 0 6 0 8 Viewer6 updated time sec sine aX 1 Appearance BackColor White ViewerWidth 700 ViewerHeight default 180 ListOrder 0 E Channel 0 5 time sec Module El Representation Sine Corr ViewerWidth v 3 Viewer Width lt A When Viewer SFO is created a graph corresponding to the SFO source will be shown on the Visualization Window The g
88. mean frequency of BP OUS to that of LBFV over each cycle CH13 The ratio of mean frequency of BP RatiocycleR to that of RBFV over each cycle If input BFV2 exists The ratio of instantaneous CH14 ampRBP amplitude over each cycle to STD of the corresponding IMF of BP The ratio of X instantaneous CH15 ampLBFV amplitude over each cycle to STD of the corresponding IMF of LBFV The ratio of instantaneous CH16 amplitude over each cycle to STD of p the corresponding IMF for RBFV If input BFV2 exists CH17 ini T The initial time of identified cycle CH18 end T The end time of identified cycle CH19 IS To test whether this cycle is under normal or arrhythmia epoch CH20 Ratio of number of bad points huge ralo Bac BP frequency jump to cycle length for BP Ratio of number of bad points huge CH21 ratio Bad points LBFV frequency jump to cycle length for LBFV Ratio of number of bad points huge CH22 ratio Bad points RBFV frequency jump to cycle length for RBFV If input BFV2 exists The ratio of number of points with CH23 phase difference between BP and jeu ee ISI LBFV gt 0 8pi or 0 8pi to cycle length The ratio of number of points with CH24 ratio BP RBFV phase difference between BP and RBFV gt 0 8pi or lt 0 8pi to cycle length If input BFV2 exists Row 5 the number of cycles Row 6 column ID of phase shift for BP LBFV Row 7 column ID of phase shift for BP RBFV If
89. method test3 NaN FillNull 2 0 2 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec 3 Select Linear Intero method instead and the way the values are filled in will be considerably different FillMethod LinearInterpolation ka Module kr FillMethod The Filling null value method test3 NaN FillNull 2 0 2 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec 4 n the Data Importer there is also an option to fill in the missing value but this feature is different from the Fill NULL Value SFO Data Range Rows 1 H to ena E Couma 1 to ena Data direction Column based Concatenate to one channel Specify Time Column 1 4 Field Format White spaced Delimeter C Fixed field eee 70 ona Handle v Use Null Value Handle MonctonicCube Dee T MS Prev value sec ime Next Value Sample F seth ie le by ample Frequency 1000 Spline interp own sample by 1 Date Axis Monotoniccube E Enable Start Date Time 2001 21 01 Y fos fos fos 0 127840489 0 111903615 0 607851202 gt nan nan 0 150341712 0 455931637 0 842262235 0 830413999 nan 0 311482553 nan 0 122181234 014 0 000388949644 Import a data which has missing values and intentionally unchecked the box of Use NULL Value Handle in Data Importer The imported value and graph is shown in the image below Projecti viewer Updated
90. of the SFO Empty status means that the SFO is newly created and haven t been updated yet There is no line shown below the name of the SFO in an empty status Updated status means that the SFO have been updated and the status is displayed by a dark blue line below the name of the SFO Outdated status means that the SFO have previously been updated but now it is outdated and is in need of an update The outdated status is displayed by a light blue line below the name of the SFO Network p 9 Bab Projecti Project2 EEMD 10 00 12 01 50 v Auto gt 2 2 3 Input and Output SFO Types There are three types of input and output SFO They are the input only SFOs output only SFOs and the SFOs which contains both input and output 1 2 Output only SFO This type of SFO consists of output port only SFOs such as Source and Viewer Annotation are all output only SFOs 7 Input only SFO This type of SFO consists of input ports only SFOs such as Viewer and Writer are all input only SFOs Input and Output SFO This type of SFO consists of both input and output ports It is able to accept data through its input port and process it and send it out through its output port SFOs such as Conversion have both input and output ports 2 3 The Usage of Signal Flow Objects Controlling Signal Flow Objects how to select configure and connect Signal Flow Objects in the Network Window
91. one of the signal waves to display 1 Create a Source Sine Wave and a Source Triangle Wave and connect the two SFOs into a Conversion Merge to Multi Channel to create a multi channel signal data Project x Viewer updated Properties E Source TimeLlnik TimeLength SamplingFreq DataLength SignalFreq Amplitude amp mplituideOfFset Phase TimeStEart SignalFreq The Frequency of Ehe Eo be generated signal Viewer WU m fo a ta TEN s 2o s Change the SamplingFreq of both Sine and Triangle SFO to 1000 SignalFreq to 6 and 15 respectivley 2 Output ToMulti SFO to a Channel Viewer SFO In the Channel Switch SFO you can change the Properties Active Channel to Channel 1 or Channel 2 to read either the Sine wave signal or the Triangle wave signal 0 1 Projectl Properties El Channel Switch Channel Count Active Channel Select Last Channel Module Active Channel Select the active channel 0 2 0 3 0 4 Properties Channel Switch Channel Gaunt Active Channel Select Last Channel f Module Active Channel Select Ehe active channel Channel 1 0 5 time sec 2 Channel 2 False 0 6 0 7 0 8 0 9 Channel 2 B 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Related Functions Merge to Multi channel Viewer Source 3 1 2 Data Selection select a time frame from a source data to be analyzed Properties This modul
92. per octave with increasing frequency Violet Noise F x i siose C density proportional f over a finite frequency range Properties Properties TimeLength SamplingFreg DataLength Amplitude AmplituideOfFset Time Stare Property Name Property Definition Set the time in ps ns us ms sec TimeUnit minute hour day month or year Set the value of time selected in TimeLength oet the number of Sampling frequency SamplingFreq the amount of data values to be sampled Set the length of the data SamplingFreq DataLength 9 x TimeUnit 1 Amplitude AmplitudeOffSet Set the amplitude offset TimeStart Set the start time for the data There are two more variable options In Gaussian Noise and Speckle Noise Default Value Sigma Gaussian the sigma value for Gaussian Noise Set the probability of occurrence for Probability Speckle aes 0 005 Speckle Noise Example Property Name Property Definition Analysing noise waves 1 Create seven different types of noise through Source Noise and connect each source SFO to a Viewer Channel Project x white 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec Gaussian 4 2 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec opeckle 1 0 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec pink 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec b
93. position Column wise is False n x m complex double array the columns represent different frequency the rows represent different time and every element represents the time and frequency of the corresponding position Where mis the length in the discrete time space n is the length in the discrete frequency space Note that the spectra data only support single channel Column wise is True m x n double array or complex double array Column wise is False n x m double array or complex Numerics double array Where mis the number of rows and n is the number of columns Both are for original input data The definition of structure fields in Xn DESC are shown below Field Name Definition Name of the input signal Char 1 length Signal Numeric Spectra Type type j 2 Char 1 length of signal The number of input signal channel count Integer channel Char arra channel names of channel e g CH1 y nch max length lengths Data length of a channel i ndim 1 The time starting point of signal Double array starts Itis meaningless for Numeric ndim 1 The signal sampling period Itis Double array intervals meaningless for Numeric ndim 1 BEEN be unit of time or frequency The signal time axis format formats Currently Regular and Indexed are available Char array ndim max length X coordinates of input signal
94. same data is analyzed by the FastSTFT and the STFT Based on the 2 8GHz Intel E6300 Dual Core computer the computation times are 0 35 second and 21 84 second Setting the Frequency Resolution to 250 the computation time of the FastSTFT is 0 3593 second the computation time of the standard STFT is 64 2343 second Helated Functions Short term Fourier Transform Enhanced Morlet Transform Heference A Wavelet Tour of Signal Processing 2nd Ed 3 8 2 Remove Bump Due to the measuring hardware such as calibarion and baseline deivation the collected signals could have discontinuities as Bumps or Jumps shown below Selection 475e toy 4 2Bek 7 4 24e 07 56 56 5 57 57 5 time day This module removes these Bumps and then smoothly reconstructs the signal Selection Remove Bump azr8ser q 277e 07 56 56 5 57 57 5 58 58 5 59 time i dayi Introduction This module decides whether Bumps or Jumps happen by the intersection of two conditions If there are a series of values that exceed the critical value and increase decrease continuously and progressively If the gradient of the data point exceeds the critical gradient Jeri Here we show the difference of the J and the S There is a Bump in the signal at the time of 0 4 second Zooming in this zone we can find that they are five discrete points 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 0 385 0 39 0 295 0 4 0 405 0 411 0 415 0 42 time sec
95. sampling on the signals Ar Ar The re sampling methods are the same as the ones in the Resample component with 7 methods Users can also set sampling period manually However some constraints may apply For consistency of input and output signals the sampling period must be less than or equal to 1 5 times of Att The computation logics of re sampling are briefly introduced as follows If co 1 7 gt 15x Min At the following methods are used to calculate the ili 0 I filling data between x and x Fix Use fixed value as filling value Prev Use value of the preceding point as filling value Next Use value of the subsequent point as filling value Linear Interpolation Use the preceding and subsequent points to perform inear Interpolation opline Interpolation Use Spline to fill values Monotonic Cubic Spline This is a 3 degree interpolation with damping It has better performance than Spline in the case of processing signal with large slope like square wave because it can avoid large vibration No Fill No additional value is added NaN If 175 0900 L5x Min At the value which is corresponding to the input signal of x would be output directly to the corresponding position X in the output j4l signal RemoveFillGap RemoveGap discards the time axis T of the input signal uses the starting time to re calculate the time axis T of the mi t and the minimum samplin
96. sec Time sec 4 0 30 60 90 120 Ado degree 2 2 X B 0 30 60 90 120 Time sec The above figure is an illustration of the MMPF procedure Continuous BP and BFV signals panels in the 1st row of a healthy subject collected under baseline supine conditions are used for this example The dominant oscillations of BP and BPV due to physiologic breathing can be extracted by the EMD algorithm panels in the 2nd row These two oscillatory modes can then be compared with each other as shown in the 3rd row panel Note that the oscillatory component of the BFV blue curve consistently leads that of the BP red curve This phase relationship is an important marker of healthy autoregulation The instantaneous phases of these two oscillations can be calculated by the Hilbert transform and their difference is shown in the bottom panel As apparent in this 2 minutes period the phase shift between these two oscillations varies around an average value of 67 degrees indicated by a dark green dashed line Note that the example shown here reveals a relatively slow respiratory period cycle length 7 sec Typical subjects have a faster breathing rate however similar BFV BP phase shift behavior is observed In contrast pathologic impairments of dynamic cerebral autoregulation can significantly reduce this phase shift Therefore the phase shift index may serve as a sensitive biomarker of autoregulation Obtaining a reliable index of dynamic
97. see if the variance for customer waiting time will be smaller with 1 processing window The null hypothesis is that the variance for customer waiting time will not decrease when the number of processing window decreases We will perform Var Test First use Source Noise to generate customer waiting time data for 101 customers Set SamplingFreq to 100 Amplitude to 4 5 AmplitudeOffset to 10 Then connect to Compute Statistics Basic Statistic Under BasicStatistics press View Statistics to check Variance Properties x Module El Noise White El Source TimeUnit Sec TimeLength 1 SamplingFreg 100 DatalLength 101 amplitude 4 5 AmplitudeofFsek 10 TimeStart 0 Basic Statistics for Noise SEE General Basic Statistics Channel Mean ienmeatricMean Harmonichlean Trimmedtean Median Std Dey Variance Connect Noise to Hypothesis Test set TestType var Test Variance 10 Because the variance for samples are smaller than default set Hypothsis LeftTail the use View Test Results to check results The SignificanceLevel calculated from the samples is smaller than the default value The null hypothesis is rejected we can say that the variance for customer wait time is smaller under single processing window Lee eee ee ee eee ee Properties El Hypothesis Test View Test Results Hypothesis Tests for Noise TestType var Test Variance 10 Si
98. series Max The biggest number in the series Mean Calculate average Geometric Mean Calculate geometric mean Harmonic Mean Calculate harmonic mean Trimmed Mean First quartile Median Third quartile Quartile otdDev Variance VarianceCoef Skewness Kurtosis oemivariance SemiStdDev The mean without the 1 and last numbers 1 quartile of the series The median of the series The third quartile of the series Quartile of the series Calculate the standard deviation of the series Calculate the variance of the series Coefficient of variation The skewness of the series The kurtosis of the series semivariance of the series Semi Standard deviation of the series oome options have parameters that need to be set The parameters for Quantile please refer to the documentation for Quartiles and Quantiles For the definition of other statistics please refer to the documention for Basic Statistics Examples Use a set of Brownian Noise as input signal calculate rolling statistics Right click in the Network panel to add Source Noise adjust Properties Noise Type to Brown then use Viewer Channel Viewer to graph results Properties MoiseTwvpe El Source TimeLlniE TimeLength time SEC And connect Compute Statistics Rolling Statistics to the right of Noise The Default statistics is Mean window default width is 2 Graph results with Channel Viewer El Rolling Statistic
99. sine wave 1 Create Source Sine Wave Square Wave and Triangle Wave to connect them all to a Conversion Merge to Multi Channel to make the three waves into a Multi channel signal data Set the SamplingFreq as 1000 and set the Sine SFO s SignalFreq as 5 Square SFO s SignalFreq as 8 and Triangle SFO s SignalFreq as 15 to observe the different waves on the graph Praject1 x Viewer updated Auto gt TimeUnit TimeLength SamplingFreg DatalLength SignalFreg Amplitude amplitudecfFsat SignalFreq The Frequency of the to be generated signal Sine ToMulti time sec 2 Connect Merge to Multi Channel SFO to Compute Channel RemoveChannel and select Properties Remove Channel as Channel 1 sine wave Viewer Updated Properties Remove Channel Channel Count 3 Remove Channel Channel 1 Select Last Channel False Sine ToMulti CH1 Removed 0 3 0 4 A 0 0 1 Y 3 Now set the Properties Select Last Channel as True and you ll see that Hemove Channel will automatically change to Channel 3 and the triangle wave signal Channel 3 will be removed 0 9 time sec Properties Module El Remove Channel Channel Count 3 Remove Channel Channel 3 Select Last Channel True Select Last Channel Automatically selects the last channel if true Sine ToMulti CH3 Removed 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Important Channel Switch
100. tart 0 sin 200 pow 1 2 Expression Using the expression to generate the signal Viewing the function with Viewer as below Custamwvave time Then the user can validate that the frequency has direct ratio with time using the short term Fourier transform The setting and the frequency time figure is shown as below CustomWave STFT 140 120 100 m T 80 Du D 60 40 20 time sec 1 3 20 t The user can also build a wave of tan e TimeUnit sec TimeLength 1 SamplingFreq 1000 DataLength 1001 TimeStart 0 Expression atan exp 3 20 t CustamwWave 1 5 0 0 0 1 0 2 0 3 0 4 0 5 0 6 oF n a 0 9 1 time sec Related Functions Channel Viewer ShortTerm Fourier Transformation Math References http msdn microsoft com en us library system math_methods aspx 5 7 Advanced 5 7 1 Impulse Professional Only The user can build a pulse signal with the Impulse module Introduction liz Mo lusu Given t as the time a series with N elements is A perfect pulse signal X can be presented as u 0 X t 2 A u t T Vg u t 0 0 where T is the starting time of the pulse A is the amplitude Mo is the offset of the amplitude In this module the user can implement three kinds of pulse signals including Gaussian Square and Decay signals TYPE DEFINETION INTRODUCTION This signal presents the Normal Distribution in tim
101. the sample is smaller than the default value so we reject the null hypothesis and we can say that the test score for the class is affected by the teacher absence Froperties x El Hypothesis Test View Test Results Hypothesis Tests for Noise TestType t_Test Mean 55 SigniFicanceLevel 0 05 Hypothesis Mull Hypothesis Tests for Noise 5 General 3 13 Hypothesis Tests for Noise t Test Rejected True aignificanceLevel 0 02868 CI Low 442 CI High 54 4 If we change the SignificanceLevle in Hypothesis Test to 0 01 to make the range of rejection of the null hypothesis smaller then use View Test Results to check results The SignificanceLevel calculated from the sample is greater than the default value we can not reject the null hypothesis So we have to accept the null hypothesis and believe that the test score was not affected by teach absence Properties lx El Hypothesis Test view Test Results Hypothesis Tests for Noise TestType t_Test Mean 55 SigniFicanceLevel 0 01 Hypothesis Mull Hypothesis Tests for Noise 5 General 3 ty Hypothesis Tests for Noise t Test Channel CH1 Rejected False Significancelevel 0 0288 Lowy 47 5 CI High 56 1 Example 3 For example a bank has 5 windows for processing The variance for customer waiting time variance is 10 minutes Now we change to only have one window for processing We will examine 101 clients to
102. the SFO is the output port In this example it will transfer the data generated by the EEMD out to its output port All SFO s output port can be connected to one or more SFOs The position of both Input port and Output port can be changed within the Properties Module of a SFO In the example below nputPortSide Input is changed to and now the blue triangle is moved to the top Properties Module Name EEMD Input Port Side Top v Output Port Side Right lt Input Port Side 3 Name The name EEMD is created by default when you select EEMD from the Network Workspace Menu Edit the Properties Name to change the Name field Module Name EEMDTest Input Port Side Top Output Port Side Right lt Name 2 2 2 Status Update and Control There is a small square box located in front of the name of the Signal Flow Object This box indicates if the SFO is currently active or not If the SFO is active it should be displaying an orange colored box Active means that the SFO is currently calculated and it is connected to the network When the orange box is clicked it becomes a transparent box indicating that the SFO is currently inactive Inactive means that the SFO is not calculated and it is disconnected from the network An inactive SFO will not output data into any connecting SFOs Network The Update Status has three status and they are visible by looking below the
103. the intervals in both axis as 1 The unit of x and y axis Y DESC units sec Hz Set the unit of x axis as second Set the unit of y axis as Hz The discrete type of x and Y DESC formats Regular Regular Set the discrete type in both axises as equidistant y axis Regular Note in this table the relationship between x y axis and the row column in the array is based the assumption that Column wise is set as True The property of Y_DESC coords only needs to be set when the time axis format is Indexed and it is not required in this example Run DoMatlab after closing DoMatlab Editor Go back to Network window and click DoMatlab to see the Properties OutputDataType The output signal format is Real Single Channel Spectra of Hank 2 Regular Regular Data and it could be connected to Viewer Time Frequency Viewer to plot the time frequency diagram RRRRHAHRRARRAHARERRHRERERERRRRREE TF Viewer Auto Matlab2 InputPortSide Left OutputPortSide Right 4cceptableDataTypes Real Multi Channel Signal of Rank any Regular Data z OuUtputDataT ype ia OutputDatal ype Data Type PEAKS Ol aea frequency t Hz F J mm 10 B 5 10 15 20 25 30 35 an 45 time sec Related Functions Viewer Differentiate Integrate Source 3 4 Statistics Professional Only This group of modules provides statistical cal
104. the range of rows to be read 1 to End Columns Enter the range of columns to be read 1 to End mM Determine the way to read the data Data Direction Column based either row based or column based Determine if the data is to be displayed Concatenate to in one channel or multiple channels Unchecked one channel uncheck Determines if the time information already exist the signal data Check to Specify Ti select the column representing the time dac RES i P ng Unchecked Column information NOTE After checking the the data will be displayed in the Index format In Field Format there three options to select White Spaced Delimiter and Fixed Field User can select the White Spaced option to separate each data by the white spaced character most txt files go by this method User can select the Delimiter option and choose from the drop down menu to separate each data either by character or the TAB character User can select the Fixed Field option to customize how the data is to be read The character allows one character to be read from each row to form a channel character allows two characters to be read from each row to form a channel and character allows three characters to be read from each row to form a channel To read more than three characters into a channel
105. the same algorithm as the MATLAB code published at RCADA however it provides more parameters such as boundary condition and random number generator The result obtained from the module is the same as the one from RCADA MATLAB code And the module runs at least 200 times faster than RCADA MATLAB code Introduction Please refer to http rcada ncu edu tw research1 htm for details Properties This module accepts input signal of real number single channel Regular and Audio The properties are introduced below E EEMD Method Number of Ensembles Noise Level 0 1 El EEMD Stop Criteria Max Sifting Iterations 10 Module Property Default Property Definition Name pony Value Set the boundary condition Clamped Spline Nature Cubic oplineType NotAKnot pne yp opline or Not A Knot Detailed in the table below The realization number of adding noise for EEMD The resulting IMF of EEMD is the average of corresponding IMF Number of X from all realizations For example if Ensumble number is 20 Ensembles 20 there are 20 runs of EMD for the original signal with added noise The final IMF is the average of these 20 groups of IMFs Th li f noi he signal It is th Noise eus e amplitude of noise adding i1 e signa 8 0 1 percentage of the standard deviation of the original signal Max Sifti M The maximum number of sifting procedure 10 Iterations Number of The max number of IMF channel 1 IMFs Modif M Set the endpoint
106. the signal to double the signal length k of Fourier Transform for better spectrum resolution In the Window properties there are 6 common window functions which can be used to smooth the discrete signal and therefore remedy the numerical error caused by boundary effects Property Name Property Definition Default Value To remove the shift along the y axis makin RemoveDC 9 7 True the signal average to be zero To set the lower frequency boundary of the Fourier Transform ofthe Max Fourier Transform which varies based on the input signal To adjust the Fourier Transform resolution The approach is to multiply the input data point with the Resolution for increasing the Resolution transform resolution then use Cherp Z Transform to obtain high resolution Fourier Transform Use window function to reduce the leakage effect on the Transform The window Window functions include 6 types Barlett Blackman Flat Top Hanning Hamming and Gauss whose definitions are given below Window Function Window Function Definition and Diagram Barlett Barlett Em N 1 2 otherwise Blackman Blackman x 07 4 cos 2 N 0 otherwise FlatTop FlatTop Iu 1 1 93 cos 207 1 29 cos 0 388 cos SU 0 032 cos RE N 1 N 1 N 1 N 1 O lt n lt N 1 0 otherwise Window Definition and Diagram Function Hanning Hanning 2 10 5 0 5 cos
107. to change the graph dimension in the Visualization Window Output Directory sets the Writer SFO s default output location when saving a file Graphic Export Format allows you to set the types of image file format that will be saved during a Batch Run Pre Collapsed Property allows the category name entered to be compacted showing a next to the category name in the Properties Window as shown in the image below ub Preference Default Plat Size with Height 180 Output Output Directory for Writer C Program Files iDynaD Data Demon Graph Export Format during batch runi Pre Collapsed Property Categories ENTER to separate start up Options d Start Matlab Engine at Start up if installed Help Langauge must restart English E Representation Module There are two configuration listed under Start Up Options The first option is the Start Matlab Engine at Start Up and the second option is the Help Language which will support a range of language NOTE Currently only English is supported 2 Image Toolbar There is a hidden tool bar on the top left corner of every graph Move your mouse cursor to the top left corner of a graph and the hidden image toolbar will be displayed The image toolbar is used to synchronize different graphics together so that they can be zoomed or moved with the same increment The other feature is to move the graph up or down providing there is more than one graph Jus
108. total length average The unit is time Automatically adjust To show the number of signals js AverageCount based on corresponding to AverageLength AverageLength Example In this example a square wave frequency 2Hz amplitude 1 duration 2s is mixed with a White Noise amplitude 0 5 duration 2s and then processed by the Moving Average Filter Different AverageLengths are set to observe corresponding effects 1 Right click and select Source Square Wave to create a square wave Change its Properties TimeLength to 2 and SignalFreq to 2 Right click again and select Source Noise White Noise to generate White Noise Change both White Noise and TimeLength to 2 and Amplitude to 0 5 Finally right click and use Compute Mathematics Mixer to mix these two signals and use Viewer to plot the result Properties E Source 4 TimeLlniE EHE TimeLength 2 SamplingFreq 1000 DataLength 2001 SignalFreq Amplitude 1 b Amplitude 0 Phase 0 3 SignalFreq The Frequency of the to be generated signal Properties El Noise 4 MoiseTvpe White E Source TimeLlniE Sec TimeLength 2 SamplingFreq 1000 DataLength 2001 E Amplitude 0 5 Arniplitudecrrset 0 T Amplitude The amplitude Projecti Viewer updated Auto gt m 0 8 1 1 2 1 4 1 6 1 8 2 time sec 2 To conduct Moving Average on the input signal right click on Mixer and select Computer Filter Moving Average
109. via Generalized Zero Crossing method Introduction Please see 3 7 5 3 NASA GZC Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The output format is real number and signal channel spectra data RECEN lus number of discrete lattice in requency axis The number of discrete lattice in time axis 1024 Example In this example LOD78 is decomposed and then all IMFs are transformed into spectra by NASA GZC Spectrum 1 use Source Import data from file to read tfa file LOD78 tfa in the installation directory default to be C ProgramFiles DynaDx DataDemon demo HHT Next perform Compute NASA HHT NASA EMD LOD78 would be decomposed into many IMFs LOD7Z S NASA EMLD 0 500 1000 1500 2000 2500 3000 time day 2 Then use Compute NASA HHT NASA GZCSpectrum to connect NASA EMD and furthermore time frequency result is displayed in the TFA Viewer LOD S NASAEND NASA GZCSpectrum D 1 0 08 0 06 0 04 Frequency cycles day 0 02 0 500 1000 1500 2000 2500 S000 Time day Related Functions Hilbert Spectrum RCADA Spectrum 3 7 3 6 NASA Degree of Stationary This module quantifies variety of each frequency form spectrogram The algorithm of this module is implemented according to definition of Degree of Statistic Stationary
110. white nose and a sine wave Both signals have the default values in Properties Use the Compute Transfrom Fourier Transform to process each signal and then use Compute Conversion Merge to Multi channel to merge both signals to form a signal with two channels ToMulti updated Ie Auto B p 2 Use Split Complex to process this complex signal and use Viewer Channel Viewer to show the result Change Properties Channel Multi Channel Display Viewer to List Viewer updated I Auto gt Properties Multi Channel Display List Show value Channel Channel 1 Module El Representation TimeLlint Multi Channel Display The display method For multi channel ToMulti SplitComplex 0 50 100 150 200 250 300 350 400 450 500 frequency Hz 3 Finally use the Data Viewer to observe the output format of Split Complex In the table the odd channel is the real part of the signal while the even channel is the imaginary part Viewer updated Project Split Complex Channel Information Histagram Channel 1 Data Count 501 Time Lengi 500 Unit Hz E Data Channel Channel Cc 4 0 021409504959 0 032731395015 6 3191237633771 0 0002013445692 Channel U 0z38241056738 0 027208941725 z 505475852547 000415242895 Min 2481955703752 0 4 711847158453 Max 0 027441338737 0 027471215768 6 186092549850 0 000657001786 0 035091467925
111. 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec Helated Functions Channel Viewer Time Frequency Viewer Short Term Fourier Transform 0 001 0 0008 0 0006 0 0004 0 0002 5 7 2 Jaehne Professional Only Build Jaehne signal Introductions 110 l l Given t as the time a series with N elements is The Jaehne signal is 0 511 i X t A xsin where is the amplitude and s is the offset of the amplitude Properties Properties Module Source TimeUnik SEC TimeLenath 1 SamplingFreq 1000 DataLength 1001 Amplitude 1 AmplitudeOfFset 0 Time Stare Property Name Property Definition ideni Value The unit of time ps ns us ms sec minute hour day TimeUnit Sec month year TimeLength The length of time 1 SamplingFreq The frequency of sampling i e data points in unit time 1000 DataLength total length of the pala i e the ae of sampling 1001 points It equals SamplingFrequency TimeLength 1 Amplitude The amplitude of the signal 1 AmplitudeOffSet The offset of the amplitude 0 TimeStart The starting time of the signal 0 Example Build the Jaehne signal and do a time frequency analysis of the signal Build the signal with Source Advanced Jaehne and viewing its results with Viewer Channel Viewer Jaehne 0 1 0 4 0 9 0 4 0 5 0 7 0 9 0 9 time Sec Connect the Jaehne to Comp
112. 0 SamplingPeriad 0 001 TimeLlniE SEC StartFreq 0 EndFreq 500 FregUnit Hz Pr r Property Definition Default Value Name Column Time series of input signal is the column of the True Major matrix Output signal format TimeDomainSignal DataT ype yP FreqDomainSignal TimeFrequencySpectra TimeDomainSignal If DataType is TimeDomainSignal more properties can be set Property Name Property Definition Default Value otartDateTime Start time of output signal 0001 1 1 12 00 00pm SamplingPeriod Sample Period of output signal 0 001 TimeUnit Time unit of output signal Sec If DataType is FreqDomainSignal more properties can be set Property Name Property Definition Default Value otartFreq Start frequency of output signal 0 EndFreq End frequency of output signal 500 FreqUnit Frequency unit of output signal Hz If DataType is TimeFreqSpectra more properties can be set Property Name Property Definition Default Value otartDateTime Start time of time axis in output signal 0001 1 1 12 00 00pm SamplingPeriod Sample period of time axis in output signal 0 001 TimeUnit Time unit of time axis in output signal Sec StartFreq Start frequency of frequency axis in output 0 EndFreq End frequency of frequency axis in output 900 FreqUnit Frequency unit of frequency axis in ouput Hz Example Using Source Noise and Sine Wave creates two signals connect them to Compute TFA ShortTerm Fourier Transform separately the
113. 0 0 100 200 200 400 500 BD Bt ant 1000 Frequency Hz Related Functions Notch Filter 3 2 7 Notch Filter Notch Filter is band reject filter used to remove a specific frequency Introduction Notch Filter is used to remove a specific frequency For example the frequency we want to remove is 60 Hz The frequency response function is shown as follows Impulse NotchFilter F F T 0 002 0 001 0 50 100 150 200 250 300 350 400 450 500 Frequency Hz Properties This module accepts all kinds of inputs of signal such as real number single channel multi channel regular signal or audio signal The formats of input signal and output signal are identical The definition of property is shown as follows Property 1 x Module El Notch Filter CenterFrequency 60 DecibelPoint 3 Bandwidth 0 01 Property Name Property Definition Default Value The center frequency which is supposed to be CenterFrequenc 4 y removed DecibelPoint will get Specify the range of frequencies which is BandWidth specified at a level of DecibelPoint The unit is pi radians per sample Example 1 Build an Impulse source Impulse Shape is set as Square and Singlelmpulse is set as True Then connect Compute Transform Fourier Transform Lastly the distribution of frequency is shown by Channel Viewer Property Impulse ImpulsesShape Square Start T Width 0 SingleImpulse True Positivelmpulse True
114. 0 007092078750 1 191177670701 0 000948307293 Mean Related Functions Noise Sine Merge to Multi Channel FFT 4 8 Convert to Indexed When processing the data time or date intervals usually are fixed regular However there are exceptions that the time interval of the result is not equal Indexed Convert To Indexed can convert a regular data into a new Indexed data based on the uneven time interval of an Indexed signal Properties This module accepts two input signals one Regular signal of Real number Complex number single channel or multi channel Regular and another Indexed signal of Regular number Complex number single channel or multi channel Indexed The output is an Indexed signal of Real Complex single channel or multi channel data Example Download GE General Electrical Co stock open price between 2009 01 02 and 2009 12 09 from Yahoo Finance Yahoo Finance Link and save the data as a CSV file Since market closes on Saturday Sunday and Holidays we skip to read in the date information for now Using Text Importer to open the file uncheck Data Range Specify Time Column option set Columns 2 to end uncheck Date Axis Auto option set Time Coordinate Time Unit to day and set Sampling Frequency to 1 So the data read in as Regular and time unit is day Then connect to Viewer Channel Viewer for data display HE Text Importer Data Range Rows to Columns to Data direction Column based
115. 0 0234 0 0413 IMF_h3 0 0295 0 331 1 0 204 0 0144 0 0149 IMF_h4 0 133 0 0957 0 204 1 0 0405 0 0618 IMF h5 0 0305 0 0234 0 0144 0 0408 1 0 029 IMF residual 0 00669 0 0413 0 0149 0 0618 0 029 1 Percentage Power Power 30 IMF hi 0 000267 IMF_h2 0 000875 IMF_h3 0 0122 IMF_h4 0 358 99 6 There two options a refresh button at the top of the Reporter Window The first option is the way for displaying the decimal numbers The default is General decimal display In the drop down menu there are also options of Fixed decimal display and the Scientific decimal display The second option is to set how many decimal places to be displayed and the default is 3 Click on the T Refresh button when either of the options has been modified and the calculations results in the table are updated with the new settings In this example it shows that the residual is the original Exp function while Sine function is IMF5 The other IMFs are signals generated in the EEMD decompostition However due to their very low Power they do not cause difficulties for evaluation Related Functions EEMD Channel Viewer 3 7 3 NASA HHT DPS Professional Only NASA HHT Module based on NASA HHT DPS is integrated and developed by DynaDx Corporation Typical uses for the NASA HHT Module include Time frequency Analysis Non stationary data analysis Noise filtering Feature Extraction ahd many more
116. 00 100 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Move the mouse cursor to the top left corner of the top graph first graph and the Group tick box will appear Check the Group tick box leave the number as 1 and then select Sync X 1 j5mc Q X Ov Oxy Noise 4 B D 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Now repeat the same steps done to the top graph and apply it to the bottom graph second graph Move the mouse cursor to the top left corner of the bottom graph and the Group tick box will appear Check the Group tick box leave the number as 1 and then select Sync X ELM 1 syn 9X OY OX Noise Morlet 400 300 frequency Hz 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec To demonstrate the usefulness of synchronization select 4 Zoom X from the Visualization Window Toolbar and drag the mouse from 0 4 sec to 0 7 sec on the x axis You will see that both graphs will be zoomed into the 0 4 sec to 0 7 sec area Noise Morlet frequency Hz Using Pan X on one of the graph will move both graphs along the x axis The above example uses Sync X so toolbar features involving x axis can alter the graphs But if you wish to move in the y axis direction or move in the x axis and y axis direction then you can select Sync Y or Sync XY instead Shown in the image below is an example of 45 Zoom Y Nnise Maorlet frequency Hz 1 6 Preference Preference sets the def
117. 000317043980 0 000325772996 0000327095739 0 000308503316 0 000336313927 0 000 89504 0 000387040916 0 000373964303 0 000377107382 0 000375314990 gt From 43003 MAG 0 001982103298 0001999351640 0 002006053071 0002000135112 0 002034724548 0 002037959525 0 002012566524 0001569200156 0001973199842 0 001946277701 0 001904672280 0 001852431538 0 001797490891 0 001781810851 0001750282193 0 001678445234 0 001604659948 0001525657712 0001496625761 0001391019195 0001367502532 0 001 332042122 0 001271 324270 Sup PHASE 8 466443051927 i N 500 9 458505460563 8 916093448039 9 279018965491 8 6413388047159 B 598585640255 8 313479414871 7 767314296441 8 501705477808 9 053419777725 9 564165276772 9 769616514672 9 493555355656 1041470762458 10 67311711715 10 60815528079 11 17428755860 11 76166984771 11 66982839149 12 98510670853 14 03287333427 16 15535065865 15 87056880026 16 44559050532 17 12047712700 Channel Information Histogram Channel 1 Ej Data Channel E Channel Value Type Channel 1 Magnitede T 9 00 3 2 Filter This module provides several regular filters which are used to remove some components from input signal based on different signal characteristics 1 FIR Filter Fundamental Finite Impulse Response Filter 2 MedianFilter
118. 008 8 60 71 There are several functions associated with MMPF module 1 MMPF It s different from the method above lt Estimates mean phase differences over each cycle for BP and BFV 2 MMPF Imf Used to extract IMFs from MMPF output MMPF PhaseDiff Used to extract phase differences from MMPF output 4 ImfPhaseDiff A method to compute phase differences on two single channel IMF signals 5 MMPF Auto Macro A user defined macro 6 MMPF Expert Macro A user defined macro 7 Transfer Function Analysis The method was introduced for the analysis of continuous recordings of BP BFV and is widely used 8 TFAPhaseDiff Used to extract phase differences from TFA output 3 11 1 MMPF The algorithm contains 2 steps 1st use RCADA EEMD to calculate IMFs from BP and BFV singals 2nd calculate mean phase differences over each cycle for BP and BFV Properties This module accepts input signal of real number single channel Regular and Audio The proprertise are introduced below Parameters Number of Ensembles Noise Level UserDefineSeed Seed Minimum Frequency Maximum Frequency Auto Output 100 0 2 True 0 4 True ALL 111 Property Definition Default Value UserDefineSeed BP Selected Mode BFV 1 Selected Mode BFV 2 Selected Mode Minimum Frequency Number of Ensembles The number of ensembles The amplitude level of the normally distri
119. 1 3 MMPFPhaseDiff MMPFPhaseDiff is used to extract phase differences from MMPF output Properties This module accepts input signal of real number multiple channel Regular The properties are introduced below 4 MMPF PhaseDiff PhaseDiff Group BP BFV1 Property Name Property Definition Default Value PhaseDiff Group Select a phase shift group BP BFV1 or Example Noise Level 0 2 UserDefineSeed True Seed 1 Minimum Frequency 0 02 Maximum Frequency 0 4 Auto True Output ALL ae 4 MMPF PhaseDiff PhaseDiff Group BP BFV1 You can refer to demo96 in C Program Files DynaDx DataDemon demo MMPF The data used in this example is also in this folder BP 01 TRIAL LICENSE 0 50 100 150 200 250 300 Time sec BF 01 0 50 100 150 200 250 300 Time sec The extracted BP_BFV1 phase difference is as the following BP_BFV1 PhaseDiff TR LICENSE 20 40 60 90 100 120 140 Time sec Related Functions RCADA EEMD Hilbert Transform 3 11 4 ImfPhaseDiff ImfPhaseDiff is used to compute phase difference between two single channel IMF signals Properties This module has no property Example You can refer to demo97 in C Program Files DynaDx DataDemon demo MMPF The data used in this example is also in this folder BP 01 TRIAL LICENSE 0 50 100 150 200 250 300 Time sec BF_01 PETRA TRI 0 50 100 150 200 250 300 Time sec The selec
120. 2 624 6 7 ERROR BAR VIEWER PROFESSIONAL ONLY eese e e esee essen 629 CHAPTER 7 PER Me ay ODI CT seseriai bpene 632 7 1 WRITE DATAS BXPORT 633 ied 622m 111 P E es 637 had icr wi iyi J 640 7 4 VU T 643 7 5 646 CHAPTER 8 MACRO AND CONTAINER SIGNAL FLOW OBJECTS ccseeeeeeeeeee e eee hn 648 8 1 MACRO PROFESSIONAL ONEY Piedad eS d Ka EC UEM 649 8 2 CONTAINER PROFESSIONAL ONLY 654 Chapter 1 User Interface 1 1 Introduction This chapter introduces the layout and user interface of DataDemon version 1 4 0 The user interface Ul of DataDemon is simple and easy to use and it utilizes many customizable characteristics to suit your personal preferences The following image shows the UI of the DataDemon after the program is executed 9 Data Demon 1 0 powered by Yisual Signal Beta File Edit View Layout Tools Help Pull Down Menu ave Projecti ET S re Visualization Window Network Window EnMorlet updated Properties 4x Properties Window The UI User Interface is divided into three major sections network w
121. 2 1 4 1 6 1 8 2 time sec eo Besides the low pass filter above the high pass filter is shown below Math 0 5 0 10 20 30 40 50 60 70 frequency Hz BandPass The BandPass filter is shown below Math 0 5 0 0 10 20 30 40 50 60 70 frequency Hz BandStop The BandStop filter is shown below Math 0 5 0 0 10 20 30 40 50 60 70 frequency Hz Bypass All frequency components can pass through the filter Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The main property of FIR Filter is FilterType which has 5 options LowPass HighPass BandPass BandStop and ByPass LowPass is used to remove frequency components which are higher than F1 while HighPass is used to remove components which are lower than frequency F1 BandPass is used to retain components which are between frequency F1 and F2 while BandStop is used to remove them ByPass allows all components to pass through i e the output signal is the input signal Definition of properties and default values are shown below El FIR BandPass 10 F1 10 MormalizedF 1 MormalizedF 1 F2 50 FilkerOrder 101 MormalizedFz 0 E Module FilerOrder 101 Module FilterType FilterT ype FIR Type The result of Bypass will be the same as the input FIR Type The result of Bypass will be the same as the input
122. 2 5 793 95 5 794 54 5 TUS 75 5 time sec And then linking the singal to the RR interval to process the signal and setting the Type to be the TwoElectrode Projecti x Module El RR interval Type TwoElectrode v Unit milli olt ain 700 DCyvalue 0 100 R R interval 200 400 600 800 1000 1200 1400 1600 1800 time sec Because the first 3000 points of the data are used for reference the start time of the RR interval is at the 9 1 second 7 time sec 100 R R interval Fi amp 10 12 14 18 18 20 time sec The ECG signal is collected from a subject lying on a bed It is the voltage between two electrodes and the unit is Volt liedown sec 5 100 140 200 250 200 350 400 time sec liedown sec 8 9 10 11 time sec Module Delta oltage Unit olt ain 00 DC value And then linking the signal to the RR interval to process the data and setting the type to be the DeltaVoltage the result is shown as below liedown_sec R interval 50 100 150 200 250 300 350 400 time sec 1 This module is very sensitive to the properties of the input signal If the input signal is not the standard ECG signal the module presents a warning and may not be able to finish the computation The user could make the RR interval process for the nonstandard ECG signal by the
123. 200 400 BOL SN 1000 1200 time day Computing the two stocks with the foundation by the PCA and stretching the report the user could find that there are some eigenvalues tending to 0 which shows that there are GE and INTEL components in the foundation al Eeport for FCA Property Eeport for PCA Property Report for Eigenvalues column column Eigenvectors column row 0 438 row L 8B52 rows 0 256 column 0 419 0 448 0 79 Computing GE YAHOO with the foundation by the and stretching the report the user could find that there is no eigenvalue tending to 0 which shows that there is no YAHOO component in the foundation for PCA Property Report for ToMnlti2 PCA Property Report for ToMult2 Eigenvalues calummn1 Ealumnz columns Eigenvectors column column row 0 364 0 207 row 0 725 0 549 rows 0 585 0 91 columns 0 908 0 416 0 0499 References 1 Independent Component Analysis ATutorial Introduction Ch10 James V Stone A Bradford Book 2 Independent Component Analysis Aapo Hyv rinen Juha Karhunen Erkki Oja A Wiley Interscience Publication 3 8 11 ICA Introduction The ICA is the abbreviation of the Independent Component Analysis Description The ICA decomposes a group of mixing signals M MixingSignal to a group of statistic independent signals S Source Signal Assuming that the M has
124. 300 and the TimeStart to 0 5 El Source min Y TimeLength 3 3333333333333335 SamplingFreg 300 DataLength 1001 SignalFreg 5 Amplitude 1 Amplitude Offset Phase TimeStart 0 5 v TimeUnit Time length in unit Then re open the DoMatlab Editor and type in Y DESC After closing the editor use the ViewBuffer to see the messages output from Matlab HE DoMatlab Editor ecrpt Help amp Exemples Matlab script file Y DESC It can be seen that some contents of Y DESC have been set following the RHeferencinput although no output signal i e variable Y has been set in Matlab Editor As shown below Y DESC starts Y DESC intervals Y DESC units Y DESC coords are all identical to those in Referencelnput Sine MATLAB Script Output Dump Output Buffer Script Execution Cn 2008109229 FF 06 06 31 Execution Time 1 0625 sec DESC name DoMatlab type Signal channelltames CHI starts 0 5000 intervals 0 0033 vts in formats Regular coords 1x1001 double Note that the operation of Referencelnput in DoMatlab is a little different from that in other module components such as Merge to Multi Channel Merge to Complex and Math In DoMatlab Referencelnput is used as time axis coordinate for default output signals while other components would directly replace the time axis coordinates of all input signals with the ones set by Referencelnput Use DoMatlab to c
125. 3842195 0 418055873476 0 440549033414 0 4600109571242 0 470290574570 r 389 0 3208525564970 0 39450019953384 0 419371330655 0 441594115404 0 4600919381930 0 470595930027 ee 390 0 370520297677 0 390445757207 D 4207084221 37 44255926 7827 0 401745925032 0 477012215506 r CAA CCBA A 391 0 3725473 0 2961 190 D 42205694 0 44 27430 456258 7A 0 4 781402 ri r4 The image above shows the information of the Spectra the information is stored in the maxtrix format The default display is Magnitude the time and frequency values of the table that are represented in the same way as the graph In the Properties Window on the right bottom corner you can edit how the histogram is to be displayed e g Colormap Type ColorMap Min Colormap Max etc Y Min 0 Y Max 25 Time Unit SBC Data Spectra Value Twpe Magnitude Gamnkeference 1 Cursor Color Red Colormap Jet Colornap Min auto 0 Colonnap Max auto 0 98170954235222 Value Min 0 Value Max 381 70854235222 TH 251251658852 4286 Value std Dev 20237557415129245 Value Mean le du t m I 4 Numeric Numeric data type does not output a graph disaply e g Basic Statistics Quantiles and Quartiles Orthogonality Matrix etc This data type will only be displayed in the table format Below is an example of a Ba
126. 6 0 7 0 8 time sec O O h O Co O pP Related Functions Noise Square Mixer Moving Average Filter Reference http en wikipedia org wiki Median filter 3 2 3 Moving Average Filter By calculating the average of signals in the range of filtering average length Moving Average Filter decreases the noise in discrete time signals and increase the recognizability of peak The advantages of moving average filter are simple theory and fast calculation However compared with other types of filters it has a low filtering ability to separate one band of frequencies from another In spectrum analysis its performance is poor Introduction Let X x x _ be an N length input signal Y y y vy_ be the output If the average length of the signal is M elements for every signal in X the output is amp Yi 2 J The formula above means the convolution of the input signal and a square filter which has area of 1 and length M in time axis Notice that this filter is similar to the Rolling Statistics on the average calculation The difference is how to handle with the edge On the edge in the case when average length M is less than M this filter still calculates average using M Therefore the output data length is identical to the input data length On the other hand the Rolling Statistics only calculates average in the range of given data and therefore the length of output dat
127. 68124553 425779292 4851753674 535826795 587785252 Oooooocoooco OoocooooooQo When opening a SAC file the SAC Importer will pop up When opening a HEA file the WFDB Importer will pop up and when opening any other type of files such as csv and txt the Text Importer will pop up 5 1 1 SAC Importer SAC file type is used for seismology and opening a sac file will open up a SAC Importer SAC Signal Information Name t 7 Channel Count sample Freg 125 cycles Magnitude Unit NENNEN SEC m Down sample by 1 Count 8001 Range 64 008 sec 0 64 006 Use Date Anis Start Date Time 2001011 024 fos p SAC Signal Information displays the Name Channel Count and Sample Freq of the loaded file User can configure the Magnitude Unit Time Unit and the Data Hange of the signal data Data Range allows the user to select a signal range by entering the desired value in the From field start position and To field end position User can also select the unit for Down sample if the user wishes to down sample the data The user can check Data Axis to add a date and a time to the time information 5 1 2 WaveForm Database Importer HEA file type is MIT WFDB format It is used for physiological signals Opening a HEA file opens up a WFDB Importer WEDE Signal Information Mame Channel Count sample Freg owe lesser Magnitude Unit B Time Unit Data Range From fo
128. 7 Writer Signal Flow Object 7 1 Write Data amp Export to Excel The Write Data and Export to Excel functions allows you to export or save DataDemon information into numerous types of file formats Properties Write Data can save data to six different file types MATLAB MAT Files mat TFA Files tfa Text Files txt CSV Files csv Wave Files wav Binary Files vsb ext Files 7 txt Binary Files vsb MATLAB MAT Files mat TFA Files tfa CSV Files csv Audio Files wav mps aac acs mp4 m4a wma Export to Excel will export the data into Excel The first column will be the X Values and from the second columns onwards represents the number of channels Each row in the file contains the data values of the signal Both Write Data and Export to Excel can save the information created by all Signal Flow Objects except Viewer SFOs and Annotation SFOs Example In the following examples demonstrations are given on how to save a real signal spectrum signal spectra signal and numeric signal to a file 1 Real Signal Histogram updated Autoa Q Q Click on the Sine Wave SFO on the Network Workspace and then click on the Save Data to File button the Netowork Window Toolbar to save the information After clicking on the Save Data to File button a Save As window will appear allowing the user to save different types of file formats aama O Gh HTI Oo T 9 B
129. 8 1 time sec 7 Configuring the YValueType option of the Channel Viewer on a spectrum data such as magnitude phase etc Continuing from the above example connect the Square Wave SFO to Compute Transform Fourier Transform FFT and then connect it to a Channel Viewer Square FFT 0 5 0 tilt ft fT LLL 0 50 100 150 200 250 300 350 400 450 500 frequency Hz In the graph the x axis is the frequency and the y axis YValueType is set as Magnitude Now change YValue Type to Phase the y axis represents the frequency of each phase Properties Axis Type Flot Elem Editor TValueTvpe Hold Plot Range arin aM ax Yin YYalueType Linear Axis PlotEditor Phase False auto 0 auto 500 auto 2715 356044974339 The data representation of the result Square FFT 0 50 100 150 250 300 350 400 450 500 frequency Hz When YValueType is changed to Gain an additional option GainReference will appear Gain is defined as unit is dB log is the base of 10 is the GainRef Magnitude and the denominator is GainReference Properties YValueTvpe 3ainReFerence Hold Plat Range arin aM ax Y Min YYalueType The data representation of the result Gain 10 False auto 0 auto 500 auto 381 42472531972 auto 15 1310133740238 Square FFT 300 0 50 100 150 200 250 300 350 400 450 500 frequency Hz Related Functions TF Viewer User Interfac
130. 9 0 000978 3 5E 05 1 09E 05 5 02 08 1 57E 08 3 88E 06 4 38E D7 2 94 07 0 00035 3 5E 05 7 94 05 5 24 06 4 83E D7 2E 07 1 59E 06 1 35E 07 3 18 07 6 94 05 1 09 05 5 24 06 6 57E 06 1 06E 07 2 6 08 5 41 07 1 76E 08 3 46E 08 9 74E 08 5 02E 08 4 83E 07 1 06E 07 8 54E 08 3 34E 08 2 22E 07 4 15 09 1 5E 08 5 1 3bE 08 1 57E 08 2E 07 2 6E 08 3 34E 08 1 36E 08 1 15E 07 3 83E 07 1 72bE D7 2 13 05 3 88E 06 1 59E 06 5 41E D7 2 22 07 1 15E D7 3 32bE D6 Covariance is a measure of how much two series change together If it s positive the change is in the same direction If its negative the change is in the opposite direction The elements along the diagonal line of the matrix are covariances between channels Related Functions Correlation Matrix Orthogonality Matrix Merge To Multi Channel RCADA EMD Reference N G van Kampen Stochastic processes in physics and chemistry New York North Holland 1981 3 4 3 Correlation Matrix Correlation Coefficient is normalized covariance If there are multiple series the correlation coefficient matrix consists of the pair wise correlation coefficient Introduction Katty zna i fyo Viss 2 Let Or Attys J0s FI set YN be two series the definition of Correlation Coefficient is N gt i 0 Pry NO O 2 1 _ Qu where x are
131. A Viewer Container 100 30 60 frequency Hz 20 0 2 0 4 0 6 0 8 1 time sec Container and Macro are almost the same in concept so two points need to be clarified unlike the Macro Container can not exist alone It just can be saved with the Project which it belongs to In Container the Macro can be read and operated the same way as in Project Related Functions Macro
132. A decomposes the mixing signals to un correlated signals the ICA decomposes the mixing signals to independent signals The definition of the un correlated is looser than the definition of the independent E xv Meanwhile the definition of the un correlated is where is the expected value The definition of the independent is pixv piv E geix ge v E e x E et v Properties This module accepts real numbers single channels multi channels regular signals and audio signals Property lx Module El PCA Parameters Method Eig Small Eigenvalue Threshold 1E 08 El PCA Property Report Property Report Default Property Name Property Definition Value Setting the method of the PCA Eig the eigenvalue PCA method method SVD Singular Valued Decomposition Eig small Eigenvalue Setting the threshold below that the eigenvalue is 1E Threshold regarded as a redundant signal ui Number of Output U Setting the number of output components hw Outputing the eigenvalue and the eigenvector as a User H t Spor report defined Example Openting the example demo 82 C Program Files DynaDx DataDemon demo Enhanced demo 82 PCA vsn the user could find three stocks GE INTEL YAHOO Mixing the GE and INTEL by the Mixer with a scale to form a foundation the result is shown as below Mixer
133. As the Fast MSE the Rolling MSE provides three algorithms Brute the original algorithm time comsumption in one dimension is 2 2 zd y oort as the B but with less scale coefficients and SlidingKD tree 3 9047 but with more memory Introduction At first extracting a section of the original data and making the MSE computation t 0 window length 0 2 Moise 0 0 1 02 02 Da 03 08 07 08 09 1 time sec And then translating the watch window towards the right making the MSE computation t 20 04 the overlap is 160 points Noise 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time ser Translating the watch window again and making the MSE computation Moise 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec Until the watch window sweeps over the entire signal 0 3 0 4 0 5 0 6 D T 0 8 0 9 0 0 1 0 2 time serg Assembling the results of all of the watch windows to be a 3D figure the figure is shown as below Selection Fast MSE Entropy Selection Fast MSE Selection Fast MSE Entropy t 0 8 Selection Fast MSE Entropy scale Arranging the results in proper time order and drawing a 3D figure as below Noise Rolling MSE scale 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec The algorithm requires the length of the window to be longer than 25 points and higher than 3 times of the max scale Properties This module accepts real numbers
134. Black D f th he titl FickstabelAngle egree of the angle to arrange the title text below 0 the Box MaxMarkerStyle The symbol for the maximum value of the series Circle MinMarkerStyle The symbol for the minimum value of the series Cross1 MeanMarkerStyle The symbol for the average value of the series FilledSquare Example Create a Brownian Noise and a CustomWave signals are plotted by Channel Viewer then box figures of these two signals are drawn via Box Plot Viewer Generate a noise signal by Source Noise and adjuste the property of the noise to Brown via Properties NoiseType And create a CustomWave using Source Custom Wave and set the equation sin 2 pi 10 t t 2 in Properties Expression Then these two signals are connected to Channel Viewer Viewer 0 0 1 0 2 0 3 0 4 0 5 0 0 1 time i Connect both signals to Viewer Box Plot Viewer the box view is shown below Box Plot 4 Hoise CH1 CustomWavwe CH1 Related functions TF Viewer interface Map to Real 6 3 Channel Viewer The purpose of the Channel Viewer is to convert signal data to graphical display onto the Visualization Window The graph will plot each signal data along the x axis time Properties This module accepts input of Signal which can be real number or complex number single channel or multi channel Regular or Indexed Audio which can be real number or complex number single channel or multi ch
135. Compute TFA Short Term Fourier Transform to open another Viewer T ime Frequency Viewer as shown in the image below Network x TF Viewer updated v Auto QQ SSS SSSR ESSERE EERE SS chirp 1000 0 1 2 0 8 time sec chirp1000 STFT 500 0 004 400 d 0 003 ze 300 m 0 002 200 100 0 001 time sec After the Signal Flow Diagram has been created click on Wy Batch Run button to start editing the Batch Run Network TF Viewer updated Auto Q Q Add parameter once the Batch Run window is open click on P to add parameters Batch Run Project 3 O output Directory Batch Runs Check the box next to DataSource chirp1000 in the Parameter List If there are multiple signal files then you will need to expand DataSource and edit the files you want Next click on Fs to select multiple data files Batch Run Project1 E Batch Runs amp 7 TF Viewer Choose 111 tfa chirp1000 tfa and chirp10000 tfa three files which are located in C Program Files DynaDx DataDemon data to be used for this Batch Run Now three new Runs will appear on the right hand side s ection of Batch Runs lf more files are to be added then click on 5 and repeat the steps batch runs from data files Look in O data gt m 100 atr 100 dat
136. DITION NUMBER cccseeeeee III ee esee 464 9410 EXTERNAL PROFESSIONAL ONLY ENE 467 3 10 1 Iz auc NALDO e 467 3 10 2 ls duc mU ER II ido M 471 S HL NMMPPOMULTIMODALE PRESSURE FILOW ani e breiten 474 3 11 1 477 3 11 2 mM 482 3 11 3 DINIPE us EDIT 484 3 11 4 486 3 11 5 MPT AUTO NAC c 488 3 11 6 IMI FT PE REMA RO TEE 490 CHAPTER 4 FORMAT CONVERSION SIGNAL FLOW OBJECT 492 4 1 IG OC A LIN ETE 493 4 2 CONVERT TO AUDIO AAEE 499 4 3 CONVERT r cs AE ee 504 4 4 a E IEEE ET AE ane EE 513 4 5 MERCO TOC OMETE EEEE E ree 517 4 6 MERGE TO MULTECHANNED mm 524 4 7 OAT EEE EAE 530 4 8 533 4 9 CONVERT TO MATRIX PROFESSIONAL ONLY 537 4 10 CONVERT FROM MATRIX PROFESSIONAL ONLY 0ceccccceesseeteceeesuceeeeceessceeneseeeenes 539 4 11 WONY ERT PROM SPEC LR 542 CHAPTER 5 SOURCE SIGNAL FLOW OBJECT EENES 544 5 1 OEE 545 zelek SAGEM OR ER 546 51 2 WAVEFORM DATABASE IMPORTER octo
137. DataDemon User Manual DataDemon User Manual Version 1 4 0 CHAPTER 1 LISER INTERFACE a ect ace anc a wee Dar Robe EUER ean dan baer ues SR DUR 5 1 1 PRODU O ance sce oe ee 6 1 2 ON TE 9 1 3 ORE WINDOW RUNS 11 NETWORK WORKSPACE AREA TETERA EEE ENFERMO RUP BP PEE the 12 1 3 2 JINBEOWORE WINDOW TOOLBAR 13 1 9 NETWORK CONTROL trer ar ENTERO ET AE EEA DANA AUD DEMEURE 16 im MED dE di qc cr 17 los BATCH RUN PROFESSIONAL ONLY J 27 1 346 TOGGLE SEILCHON MODE 58 9 5 92054990 39 1 4 PROPER IES WINDOW 42 1 5 VISUALIZATION WINDOW EEE ERER E ARETES RAM 48 1 6 PRETEEN L roa e Er EE E ETE EE EE E conics EE 58 CHAPTER 2 NETWORK WINDOW METER Cr 61 2 1 ICH INEO OBJEC PE 62 Zo GNA PLOW OBIEOT TYPES 63 2 2 COMPONENTS SIGNAL FLOW OBJECT RE 64 Zook Drar COUP AN NA en 65 2 2 2 STATUS UPDATE ANID CONTR OD nite TARE EEE ETS 66 222 2 INPUT SFO TYPES 68 2 9 THE USACE OF SIGNAL FLOW OBJECTS Ce Eos Ta aT RAES TERENE PEEL RE DUI Ata PME UIS 69 do SONL FROWN OBIECT STATUS 70 2 3 2 CONNECTING SIGNAL FLOW OBJECTS exi CERE E E R4 RII P
138. Directory Set the output D ancaditestibin encoding Output Encoding utf o Graph Output graph format Graph Export Format during batch run png Reporter Default number of decimal places 3 Set the number of wi digits after decimal point to display Chapter 2 Network Window This chapter explains different types of Signal Flow Objects and how to use them 2 1 Signal Flow Object Right mouse click on the Network Workspace of the Network Window will open up the menu Network Workspace Menu for the Signal Flow Objects Signal Flow Objects are categoried into five types Compute Conversion Source Viewer and Writer Within Compute there are more sub categories such as Channel Filter HHT Mathematics TFA and Transform All the SFO types will be explained in this chapter ork fl x E za 2 Ld Compute Conversion Viewer Writer Macros 2 1 1 Signal Flow Object Types pa Compute Compute is represented as a pink colored SFO It provides different type of signal calculation to the source data SFO With Compute type SFOs the original Source type SFO does not need to be edited and lots of manipulation can be done directly to a single Source SFO Compute type SFOs can be created to apply special calculations to the data of the Source SFOs without altering the original source data Conversion Conversion is represented as a light brown colored
139. E RASC Amm RAEI Tir d NY sine HATT E fie tH T Text Files txt Dal ated ial ELITTEITTETETTTELTTELEEEITTTETTTEEETTTTTTTTTTTTTTTETTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTETETTTETTTTTTTETT If the information was to be saved as the mat file format then inside the file will be two variables from this example it will be Sine x and Sine y Sine x will store the time and Sine y will store the data values The data will be represented in column format For each additional channel a new column will represent the data value for the new channel If you click on the Export to Excel button Excel will automatically open with all the data transferred to the Excel table X Value column stores the time information of the signal and CH 1 column stores the data values So if there is more than one channel e g CH2 CH3 etc then each channel will be listed in their own column X Value 1 8 16 0 001 0 062791 0 002 0 125333 0 003 0 187381 0 004 0 24869 0 005 0 309017 0 006 0 368125 0 007 0 425779 2 Spectrum Signal Export to Excel and Write Data to File on a spectrum signal will result in an output which looks something like this X Value CH 1 Real CH 1 Imag 2 815E 17 0 6 319E 07 0 0002013 2 606E 06 0 0004152 6 186E 06 0 000657 1 191 05 0 0009488 2 084E 05 0 0013279 3 515 05 0 0018665 5 999E 05 0 0027303 C5 X Value column s
140. ERES T 3 Create a new project to test out the macro saved previously Create a Source Square Wave and right click on the Square Wave SFO to open up the Network Workspace Menu and select Macros testMacro to load the testMacro file You can also click on the File option on the main menu and select Load Macro and choose the macro file to load NOTE Project files can be loaded as a macros and vice versa macros can be loaded as projects Compute Conversion Source Viewer gt M Module Gp Data Demon 1 0 powered by isual Signal Beta File Edit View Layout Tools Help 3 7 25 P 8 s _ Project Square 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 time sec Square FFT Viewer3 updated Auto Q Q Properties o 50 100 150 200 250 300 350 400 frequency Hz Square IHaar 0 1 0 2 0 3 0 4 0 6 0 7 0 8 0 5 time sec s Try to save all macros under the Macro folder directory of DataDemon So when you try to access the macros from the Network Workspace Menu it will appear in the menu selection under Macros When loading a macro into a project sometimes you will still be required to manually link the source Signal Flow Objects to the rest of the loaded SFOs NOTE The use of macros is to save the steps in setting up the rest of the Signal Flow Diagram and it is mainly the Source SFOs which are constantly bei
141. ERT HUANG TRANSFORM 344 Ook RORDA EE MD E S E AEE EEEE EE 347 orden METO EE EEE UM 353 ser PTA SARDE e E ET E A T E A 356 3 4 4 RCADA INSTANT FREQUENCY 395 Beles CAD SPECTBUNL Ss spes er RENE 397 3 8 ENHANCED PROFESSIONAL ONLY 2309090 928202029208 80 030A dS 399 3 8 1 FAST SHORT TERM FOURIER TRANSFORM csssssseseee esee sees 401 422 BUN ETE 409 Sooo FAT DICENIDASS IMAT Ue von M 415 3 8 4 FAST ITERATIVE GAUSSIAN FILTER A D pROERISI P EOD PC 418 E ur va ne ores eg ee 420 CON 422 429 Sm m 434 O 437 3 8 10 E 444 3 8 11 P 448 3 9 MATRIX PROTE 453 Sk 453 9 52 UOMAUBDOINUERSE 457 2 5 250g 5 0 458 S74 EXTRACT REGION OP INTERESD NIA EROR 459 m E dac ici dcos gases 461 nr MED Ce LUE cie 463 3 9 7 RECIPROCAL MATRIX CON
142. Fast Iterative Gaussian FilterType LowPass A tbenuatian 0 01 FH 10 FL 2e Module Property aue Default P Def Name roperty Definition Usine The type of the Iterative Gaussian Filter LowPass extracting the low frequency part of the signal Filter Type LowPass HighPass extracting the high frequency part of the signal ByPass reserving all frequency parts of the signal Attenuation The property of the Gaussian curve of the filter FH Filtering higher values of the signal than the FH FL Filtering lower values of the singal than the FL Example Based on the computer with the CPU 2 8GHz intel E6300 3 25GRAM points by computing time figure for computing signals with Brown noises of different lengths by the standard fast version Iterative Gaussian Filter is shown as below Iterative Gauss po tepnsauszcH1 wmm Fast Iter auss C Hz 1 05 2 e 5 3e 05 4 05 5e 05 05 7 05 5e 05 Be 05 1 06 M pte More important the standard Iterative Gaussian Filter can just process 2 million point data with the 3 25G memory the fast version can process 160 million point data Helated instructions Trend Estimater Iterative Gaussian Filter Heferences Yih Nen Jeng Diffusive and Fast Filter Using Iterative Gaussian Smoothing Department of Aeronautics and Astronautics National Cheng Kung University YIH Nen Jeng P G Huang You Chi Che
143. Flow Diagrams in Network Workspace Area And signals can be easily visualized through the Signal Flow Diagrams between Signal Flow Objects SFOs Network Compute Conversion Source viewer nd Network Network Workspace Menu Workspace Area Macros Container Delete Shown in the above image is the Network Workspace Menu that will appear once the right mouse is clicked within the Network Workspace In the Network Workspace Menu contains five categories Compute Conversion Source Viewer and Writer which can be used to display the building blocks of the Signal Flow Diagrams created in the Network Workspace The way to add and edit the five categories will be explained in Chapter 2 and details of the computational aspect of the signal processing and methods will be explained in chapter 3 and 4 In the Network Workspace Area you can easily create edit process and view signal results through a few simple mouse clicks 1 3 2 Netowork Window Toolbar Netowork Window Toolbar has four basic buttons to import and export data 4 Open data from file k Save data to file c Data Viewer this function will be explained in detail in Chapter 1 3 4 and zu Export data to Excel 1 AE Open data from file This function allows DataDemon to import files from formats such as mat sac hea txt csv etc When importing text based files a Text Importer image below will appear Configure the settings to translate the text
144. Fourier Transform then use Channel Viewer to view the result It is the same as the original signal FFT example pa Mixer FFT IFFT 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 time sec Related Functions Short Term Fourier Transform Reference http en wikipedia org wiki Fourier transform 3 6 2 Discrete Cosine Transform and Inverse Cosine Transform Discrete Cosine Transform DCT converts signals to a series of cosine which is similar to the real part in the FFT After the transformation signal energy mostly concentrates in low frequency area This method is applicable in audio and image compression numeric solution of partial differential equation and other fields Introduction There are approximately 8 types of common DCT This module uses the 2 type Let X x x x _ be a N length time series the DCT is defined as below C fork 0 N 1 Y gt X n 0 PNE C i eS TU Qn Da k 2N where C is the DCT coefficient of DCT The inverse DCT is defined as below C for k 0 1 9 2 1 7 M ec YT ER N m 2N l C gt 0 N Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The output formats are real number signal channel Regular signal The properties and settings of the DCT are introd
145. Freg Unit Default TrendFrequency default 0 00 742942050520059 Property 2 Default P Def Mane roperty Definition Value It is the same as the Iterative GaussianFilter LowPass extracting the low frequency part of the signal Filter Type LowPass HighPass extracting the high frequency part of the signal ByPass reserving all frequency parts of the signal Setting the properties based on the Period or the Trend Basis Frequency Frequency If the Trend Basis is set to the Period its properties are defined as below Property ese Default Def Name Property Definition Value Trend If the period exceeds the Trend Period it is deemed as a Period trend signal Corresponding to the Iterative Gaussian Filter FL 2 TrendPeriod FH 4 TrendPeriod Time Unit Setting the unit of the TrendPeriod Default Default Time Unit The default time unit of the input signal Sec lf the Trend Basis is set to the Frequency its properties are defined as below Property m Default P Def roperty Definition valde If the frequency exceeds the Trend Frequency it is deemed as a trend signal Corresponding to the Iterative Trend Gaussian Filter Frequency FL 22 TrendFrequency FH 4 TrendFrequency Frequency Unit Setting the unit of the TrendFrequency Default Default The default f it of the input signal H Frequency Unit e default frequency unit of the input signa Z Example Ple
146. In EEMD Sifting process is used to extract IMF from signals The procedure is as follows 1 a signal x t identify all the local extrema then connect all the local maxima by a cubic spline to obtain the upper envelope 2 Repeat the procedure in step 1 for the local minima to produce the lower envelope 3 Calculate the mean of the upper and lower envelope to obtain a mean curve which is designated as m t 4 Subtract the original signal with the m t and let the result to be A t i e h t x t m t The Sifting process stated above is defined as a process to obtain h t using the m t to subtract the mean obtained from upper and lower envelope With the Sifting procedure EEMD processing method is given as follows After being processed by sifting several times the mean of upper and lower envelope of an original signal should gradually move close to and overlap with the x axis The first IMF will be obtained when the upper and lower envelop is symmetric by the x axis The first IMF is designated as IMF1 Subsequently subtract the IMF1 from the original signal to obtain the First Residue designated as rf Repeat the same procedure for the r1 to obtain IMF2 Then subtract r1 from IMF2 to get the second Residue r2 Conduct the same procedure repeatedly the original signal can be decomposed of several IMF and a final Residue There are two types of Sift Iteration and Stoppage Criterion for EEMD 1 Cauchy type of co
147. In this example use this module to calculate instantaneous frequency form the EMD result of LOD78 Length of Day With time axis frequency variation of each IMF could be observed 1 Use Source Import data from file to read tfa file LOD78 tfa in the installation directory default to be C ProgramFiles DynaDx DataDemon demo HHT Next perform Compute NASA HHT NASA EMD LOD78 would be decomposed into many IMFs LOD7 8 NASA EMLD 500 1000 1500 2000 2500 2000 time day 2 After NASA EMD connect the module Compute NASA HHT NASA Hilbert Transform whose property SmoothPoint is default value L OD s NASA EMD NASA Hilbert 0 500 1000 1500 2000 2500 2000 time day When SmoothPoint is changed to 12 the instantaneous frequency would change smoothly with time Property lx Module 1 NASA Hilbert SmaokhPoinE 1z L OD s NASA EMD NASA Hilbert 0 1 0 05 500 1000 1500 2000 2500 2000 time day Related Functions Hilbert Transform RCADA Instant Frequency 3 7 3 3 NASA GZC This module whose full name is NASA Generalized Zero Crossing is an alternative module for calculating instantaneous frequency and instantaneous amplitude Introduction Generalized Zero Crossing is the most direct method for calculating local frequency that is closely related to the original definition of frequency This method only works with IMF type signals By using the physical prope
148. K Goldberger AL Hausdorff JM Multiscale entropy analysis of human gait dynaiics Physica A 2003 330 53 60 Costa M Goldberger A L Peng C K Multiscale entropy analysis of biological signals Phys Rev E 2005 71 021906 3 HHT Hilbert Huang Transform Hilbert Huang Transform HHT is an empirical signal processing method which can be used to reveal true physical meanings for non stationary and non linear signals Most traditional data processing methods are based on linear and stationary assumptions Only in recent years have new mathematical methods been developed to process either the non stationary data or the nonlinear data However in a lot of systems in the real world the data are most likely to be both nonlinear and non stationary Analyzing the data from such a system is a daunting problem To resolve such a problem Dr Norden Huang at NASA has developed a new mathematic method Hilbert Huang Transform HHT The HHT method consists of two parts empirical mode decomposition EMD and Hilbert spectrum By combining EMD and Hilbert Spectrum in the component of or Hilbert Transform in the component of Compute Transform this method is viable for nonlinear and non stationary data analysis especially for time frequency energy representations In most researches HHT can provide more information about the relationship of time frequency and energy And in most cases HHT can reveal true ph
149. LineColor LineWidkh SmoothMethod Histogram CH1 Noise 4 Select the Properties Representation Active Channel to Channel 2 from the drop down menu Now the graph will plot the signal data for Channel 2 Properties El Representation Active Channel Channel 2 Bintount 2b Colori 9 Gray Colorz Transparent BrushStyle Horizontal Percentage False Active Channel Active channel Histogram CH2 CustomvVave Times 5 Change the Properties Representation BrushStyle to Vertical and the colors on the rectangular bars will now be shaded from top to bottom instead of the default left to right Related Functions Box Plot Viewer User Interface Merge to Multi Channel and Source 6 7 Error Bar Viewer Professional Only Error Bar Viewer is used to draw error lines Introduction Usually in the experiment and the measured data will have errors If you want to show the error in chart to illustrate the reliability or accuracy of the data points you can use Error Bar Viewer Error Bar Viewer can plot the typical style as following Chart with Error bar by Visual Signal 5 1 49 48 47 46 45 44 43 4 2 04 07 04 14 04 21 04 28 Date Example This module requires data upper error bound and lower error bound time series must exist sequentially in the same input If the three time series are not in the same input you can use the module Merge to Multichannel to merge the time series into the s
150. Module E Source TimellniE TimeLength 1 SamplingFreg 1000 DataLength 1001 Amplitude 1 Arniplitudecrrset 0 Time Start T Impulse FF T 0 002 0 001 0 0 50 100 150 200 250 200 250 400 450 500 Frequency Hz 2 Connect Impulse Source with Compute Filter CombFilter Connect Notch with Compute Transform Fourier Transform The result is shown by Channel Viewer It is can be seen that 60 Hz is removed Impulse NotchFilter FF T 0 002 0 001 0 50 100 150 200 250 300 350 400 450 500 Frequency Hz 3 Change Notch Filter s DecibelPoint into 10 and BandWidth into 0 001 The removed frequency and range become sharper Irnpulse NotchF rter F F T 0 002 0 001 100 150 200 250 200 350 400 450 500 Frequency Hz eL C er Related Functions Comb Filter 3 3 Mathematics his group of modules processes signals or relationship between signals mathematically whose components are listed below 1 2 Hemove DC To remove the direct current component of signal Mixer To add or subtract several signals using identical time scale Multiplier To multiply several signals using identical time scale Math To input mathematical formula for signal calculation Diff To calculate approximate differentiation of input signal Integrate To calculate approximate integration of input signal DoMatlab To connect signals to Matlab compile and run the Matlab code 3 3 1 Remove DC Hemove the signal direct
151. N ame C sine txt WriteN ow Write file now If it is true it would also write file when updating Related Functions Csv Writer TFA Writer Wave Writer and Text Writer 7 4 Writer Export multi channel data into tfa format Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular Audio which could be real number or complex number single channel or multi channel Regular Properties Module El Writer WribeMow False OGutputFileMame C Documents and Settings user s Br Ea csv Property Name Property Definition WriteN m Displays the default location of the files to be saved Note You can edit the default location Dictor from the main menu under Tools Preference Select the location to save the file With the file name and location entered the file is only saved when WriteNow is set as True OutputFileName Example TFA Wwriber updated Auto Q Q Output a Sine Wave signal to a tfa file Create a Source Sine Wave and connect it to a Writer TFA Writer to save the data into a tfa format Click on the Properties Writer OutputFileName field and a button appears at the right hand side of the field Enter the file name and the file will be stored in the OutputDirectory folder F iu z El Writer WriEeMow False GutputDirectary C Program FilessAnCAD Vi
152. Noise Viewer2 0 20 40 60 80 100 120 140 160 180 200 220 frequency Hz Properties lx El FIR FilterType HighPass Fl 100 FilterOrder 500 Module Module Mixer FIR 0 9 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 time sec 4 Repeat step2 and add one FIR filter Change the FilterType to BandPass F1 to 25Hz F2 to 100Hz and FilterOrder to 500 The frequency components between 25 100Hz would pass through while other components would be cut off Therefore the output is a sine of 51Hz Viewer2 0 20 40 60 80 100 120 140 160 180 200 220 frequency Hz Properties FilEerTvpe BandPass 3 Fi fo Fz 100 Filter Order 500 Module v FilterOrder The filter order Mixer FIR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Related Functions Noise Sine Mixer References http en wikipedia org wiki Finite impulse response http cnx org content m11918 latest 3 2 2 Median Filter Median Filter is a one dimensional non linear filter used to calculate the median in the range of filtering Filter Order Because it can reduce speckle noise significantly while retain good edge detection it is usually used in digital image processing Introduction Let X x x x _ be a N length input signal Y y y y be the output signal and M be the signal length for calculation The Median
153. O parameters c Retain Plot keeps the original plot when Viewer SFO is not connected d Auto Legend Name sets the legend automatically e Line Color Preferences sets the color of each channel in the Viewer SFO as shown the image below In the Plot Time Frequency Plot section we can set default values of CMin and CMax for the plot and they can be based on the percentage of the Absolute Maximum Value or Pencentile of the time frequency data p om lt gt Preference Keep the plot Plot width and height Show legend Keep plot range automatically Set the color of input signals Line Color Preferences Time Frequency Plot Set the CMin and CMax CMin Default 0 CMax Default 100 BEIM weer of Absolute Maximum Value or Percentile IP Line Color Setting 81 0 Line No Color Line 1 Line 2 Line 3 Line 4 Line 5 Line Lime 9 Line 9 C C C LL C C mum wt lose Ci Output Tab In the Output Writer section we can a set the default outout directory b the encoding format of the output file In the Output Graph section we can set the graph export format during the batch run In the Output Reporter section we can set the resulotion of the output The default number of decimal places shows the digits after the decimal point aan lt gt Preference System Plot Default output Writer directory location Output
154. Property Name Property Definition zii dn Value 5 types are provided which are LowPass Filter Type we LowPass HighPass BandPass BandStop and ByPass For LowPass and HighPass F1 represents the cutoff frequency For BandPass and F1 BandStop F1 represents the frequency 10 starting point Unit is Hz Varies Demonstrate the normalized F1 based onthe based on NormalizedF 1 sampling frequency of the input signal the input signal Eo The frequency ending point F2 for BandPass 50 and BandStop filters Unit is Hz The number of points in the discrete impulse FilterOrder response function of the filter N means N order Filter Example This example shows the process of using FIR Filter to remove different frequency components based on an input signal which contains 10 51 193 Hz sine waves plus white noise 1 In the Project window select Source Noise to create a white noise signal and set the Properties Amplitude as 0 3 Then use the Source Sine Wave to generate 3 sine waves and change their Properties SignalFreq to 10 51 193 Hz After that use the Compute Mathematics Mixer to mix the above signals and plot them using the Viewer Channel Viewer by dragging the Output of every signal to the Input of Mixer Projecti X Viewer updated Auto gt SS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSS SSE SEES d Properties Properties El Noise LH Source 4 NoiseT ype Wh
155. SFO Conversion provides the Source SFO a variety of options to change or convert such as change its x axis unit convert signal data format to playable audio data format and convert index format data to regular format data etc Conversion type SFOs can be created to manipulate the data of the Source SFOs without editing the original data Source Source is represented as a green colored SFO You can load an external data file or generate a customized wave noise wave sine wave triangle wave and square wave from this type 7 Viewer Viewer is represented as a yellow colored SFO It is used to display graphs and images from source signals or manipulated signals such as the ones that have gone through changes from Compute and Conversion types Writer Writer is represented as a light blue colored SFO It is used to output the calculation and data from a SFO to a file with specified text or sound formats 2 2 Components of a Signal Flow Object Image below is a Signal Flow Object and the explanations of each component Switch Name Input gt r Update Status 2 2 1 Input Output and Name 1 Input Shown in the image above is a SFO The blue triangle to the left of the SFO is the input port The EEMD SFO will receive data from other SFOs The number of input ports varies depending on the SFO e g Merge To Complex SFO has two input ports 2 Output The red triangle to the right of
156. SamplingFreg DataLength SignalFreg Amplitude aAmplitudeofFset Phase Symmetry TimeStart Property Name Property Definition eeu Value Set the time in ps ns us ms sec minute TimeUnit P oec hour day month or year TimeLength Set the value of time selected in TimeUnit Set the number of Sampling frequency the SamplingFreq 1000 amount of data values to be sampled Set the length of the data SamplingFre et the length of the plingFreq x 10005 TimeUnit 1 Set the maximum displacement of a periodic AmplitudeOffSet Set the amplitude offset Set the time in ps ns us ms sec minute TimeUnit 1 hour day month or year DataLength TimeUnit Set the value of time selected in TimeLength TimeUntt set the Phase in degree When the phase is Phase non zero the entire waveform appears to be shifted in time by the entered amount Symmetry set at 0 5 is equal symmetry where the left of the inflection point takes up 0 5 half oymmetry of the period E g Symmetry 0 2 means that 0 5 the left of the inflection point takes up only one fifth of the period TimeStart Set the start time for the data S Example Create a Triangle wave 1 Create Source Triangle Wave Viewer Updated Triangle 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 Set the Properties Source SignalFreq to 4 Amplitude to 1 AmplitudeOffSet to 0 3 Phase to 0 Symmetry to 0 7
157. Significantly reduce impulsive noises 3 Moving Average Filter Used to remove the random noise 4 Iterative Gaussian Filter Efficiently remove aperiodic components from an input signal 5 Trend Estimator Simplified version of Iterative Gaussian Filter Used to extract aperiodic components from an input signal 3 2 1 FIR Filter Finite Impulse Response Filter is the fundamental filter prototype in digital signal processing which can remove high frequency low frequency or a given band frequency components The term of finite means that the filter impulse response is finite Introduction Assume an input signal is given as shown below test2 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec The Fourier Transform is shown below It is desired to remove the high frequency components and preserve the low frequency components Viewer2 0 5 10 20 30 40 50 60 70 frequency Hz eo The thin black curve represents the Fourier Transform of the original signal and the bold red curve represents the desired filter Therefore define a function representing the filter above in Fourier Space and multiply it with the Fourier Transform of the original signal Multiplier ToComplex 0 2 0 1 10 20 30 40 50 60 70 frequency Hz eo Next conduct Inverse Fourier Transform to remove the high frequency component The result is shown below Multiplier ToComplex IFFT 0 5 eo 0 5 0 2 0 4 0 6 0 8 1 1
158. Square Wave and connect it to Compute gt Enhanced Morlet Transform and then connect it to a Time Frequency Viewer SFO Select the ValueType as Properties Representation Magnitude Square EnMorlet 500 400 H wo e frequency Hz 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Set the Properties Hepresentation CMax to 0 197772704820884 This value is the maximum value of the signal strength and it is also the maximum color value on the Colormap A user can set the value of the CMax variable to show the signal strength below this value Since the colors on the Colormap keep the same a better resolution of the signal strength can be presented if CMax becomes smaller oet CMax to 0 1 the graph uses this as the maximum color value for Colormap All signal strength below 0 1 is remapped to the Colormap and the graph is redrawn to focus on the region that was unclear when CMax was 0 197772704820884 Properties auto 0 Colormap Show Title Show Axis Max Colormap range maximun Square EnMorlet 400 H 09 e frequency Hz N 100 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 Set the Show Color Bar to True will display a color bar legend on relationship between the color and its values frequency Hz Pro perties Colormap Shows Tithe Show xAxis Show axis Show Color Bar Show Color Bar Show Color Bar Square EnMorlet
159. Time and the unit is in second i e the period corresponding to Hz Module EO xXAxisUnit Abscissa Unik Convert to period Convert to period Convert bo period Axis sine FFT 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1 time sec 3 he time frequency analysis module TFA is not able to pass the result to Change X Axis Unit for frequency unit modification directly since the frequency is located on the y axis fo the time frequency diagram However the conversion can be achieved by changing the unit of x axis first and then performing time frequency analysis Connect Change X axis Unit to the source signal of sine wave change the Properties Abscissa unit to msec use Compute TFA Enhanced Morlet Transform to perform time frequency analysis and then use Viewer Time Frequency Viewer to plot the result It shows that the y axis i e the frequency axis has been changed to KHz i e 1 msec Properties Module El 0 Abscissa Unik yt Abscissa Unik Covert En Time Unit Sine EnMorlet frequency KHz 0 100 200 300 400 500 600 700 800 900 1000 time ms Related Functions Import Data from File Viewer Fourier Transform Enhanced Morlet Transform 4 2 Convert to Audio This component changes the type of signal data from Signal to Audio Introduction The output data format of Convert to Audio follows the Microsoft Wave Format The Microsoft Wave Format co
160. ToM View Matrix Display the correlation coefficients matrix Correlation Matrix for ToNWtiuiti Correlation Matrix Channel CH1_ Sine CH2 CH2 CH1 Sine 1 7 926 14 1 CH2_Sine 7 G2E 14 1 94 1 4 CH3 Sine 1 94 14 1 Create new signal with Source Triangle Wave it to Compute RCADAEEMD to calculate its IMFs The results are displayed using Channel Viewer oet Properties Multi channel Display in the view to List and set Viewer Height to 350 There are 9 channels in the signal Triangle RCADA EEMO 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Connect HCADA EEMD SFO to Compute Statistics Correlation Matrix for calculating correlation matrix among IMFs General Correlation Matrix for RCADA EEMD Correlation Matrix Channel IMF hi1 IMF h2 1 h3 IMF h4 h5 IMF h amp MF hz IMF h8 MF residual h1 1 0 0743 0 00447 0 012 0 00459 0 00491 0 00583 0 00332 0 0196 IMF_h2 0 0743 1 0 0267 0 00578 0 00371 0014 0 0133 0 0145 0 0106 h3 0 00447 0 0267 1 0483 0 07 0 0482 0 000593 0 000782 0 0209 IMF_h4 0 012 0 00578 0 493 1 0 125 0135 1000549 000429 0 068 IMF_h5 0 00459 0 00371 0 07 0 125 1 0 229 0 185 0 193 0 098 h6 0 00491 0 014 0 0482 0 135 0 229 1 0 141 0 0868 0 116 h7 0 00563 0 0133 0 000593 0 00549 0185 0 141 1 0 981 0 418 IMF h8 0 00332 0 0145 0 000782 0 00429 0 193 0 0868 0 981 1 0
161. Toolbox are explained below Basic Operation Function Definition Add plus operation to Expression field can be typed in directly can be minus operation to Expression Field typed in directly Add multiply operation to Expression Field can be typed in directly divide operation to Express Field can be typed in directly Special Function Definition Operation Set group operation type By Channel or By Input By Channel channel by channel calculation for selected multi channels the output is a single channel such as By Channel Y 1 X1 1 X1 2 X2 1 X2 2 By Input input by input calculation for selected input signals the output is multi channel signal such as Y 1 X1 1 X2 1 Y 2 X1 2 X2 2 TT Add rr pi value to Expression field Add vertor of time axis t to Expression field It is corresponding to the time axis of the selected input signal These two tools work as a group The pull down menu gives the internal functions After selecting internal function press ih button to add selected function to Express field The function can also be typed in directly such as sin X1 1 abs X1 1 Common internal funtions are listed below Function Description Function Description Round to the nearest integer abs Absolute value ceiling AM toward infinity Hound to the nearest floor integer towards minus round Round to the nearest integer infi
162. Viewer Trend Estimator Data Viewer 4 9 Convert to Matrix Professional Only Convert the signal to Numeric matrix and carry out matrix operations Properties This module accepts input signals of real complex single channel or multi channel regular indexed Audio and spectra Property x El Convert To Matrix iCalumn IMajor True Module Property Name Property Definition Default Value Column Major Time series of input signal is the column of the matrix True Example Using Source Noise and Sine Wave to create two signals connect them to Compute TFA ShortTerm Fourier Transform separately then convert the signals to matrix with Conversion Convert to Matrix as shown below Next connect these two matrixes to Compute Matrix Matrix Operation with default parameters Then connect Matrix Operation A B to Coversion Covert from Matrix and set DataType to TimeFrequencySpectra display result with TF Viewer Mop FromMatrix 500 400 300 200 frequency Hz 100 p 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Related Functions STFT Convert from Matrix 4 10 Convert from Matrix Professional Only Convert Numeric matrix to various signals such as time series spetra time frequency data Properties This module accepts matrix with real complex regular or indexed numeric value Property Column Majar True DataType TimeFrequency5pectra SkartDate Time
163. a length would be less than the length of input data Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The input signal format and the output signal format are identical Moving Average Filter has two properties which are FilterType and AverageLength AverageLength represents the number of data points M for average calculation The unit is time FilterType sets the type of filters which include LowPass HighPass and ByPass LowPass is the calculation result using the theory introduced above HighPass is achieved by subtracting the LowPass result from the input signal Because the original signal is equal to HighPass LowPass the output of ByPass is equal to the input signal The default values of properties are shown in the table below Properties prapertyarid nes E El Moving Average AverageLengath Average lount FilterType Result park Lawpass means the averaging part Highpass means the compensation part Bypass would be the same as the input Property Name Property Definition Default Value To set the filter to remove high frequency or low frequency components The Filter Type l P LowPass available options are LowPass HighPass and ByPass The signal length for calculation of AverageLength TP 0 05 of
164. aType It has been changed to Complex El Module Mame ToComplex InputPort Side Left OutputPortSide Right AcceptableDataTvpes Real Multi Channel Signal of Rank 1 Regular Data OutputDataType Output Data Connect Viewer XY Plot Viewer to ToComplex The viewer uses the real part of input signal as X axis value and the imaginary part as Y axis value to plot the signal following the time order 2 duc 0 0 180 180 Therefore the signal can be plotted in the complex plane ToComplex Im 0 ToComplex Re The figure above is obtained by making the Properties ViewerHeight to be the 519 same as the ViewerWiath in the XY Plot Viewer So the X axis and Y axis have identical scale For detailed introduction about XY Plot Viewer operation please reference to chapter of XY Plot Viewer With Channel Viewer timing diagrams with different computation cost can be obtained by modifying the Properties YValueType The figure below shows the Magnitude of this complex signal Viewer updated Auto gt E OOCL Sine ToComplex 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Multi Channel signal 1 In Network Window select Source Noise to generate a white noise signal and SourceSine to generate a since Wave with default settings Then use Computer Conversion Merge to Multi channel to merge these two signals into a 2 channel signal Follow the same procedure to merge a square wave a
165. al points consisted of zero crossings and local extrema The quarter period is the time duration between neighboring critical points the half period is the time duration between three consecutive neighboring points and the full period is the time duration covering five consecutive neighboring critical points Image of a sine wave demonstrating the physical relationship between the above variables and the signal The time frame of q is for which the frequency is being calculated An advantage of the GZC algorithm is that it can avoid negative frequency in calculating instantaneous frequency found in the Hilbert Transform Also since GZC relates directly to physical phenomenon in the data it is clearer how more local frequency values can be obtained in relation to the traditional definition of frequency The primary disadvantage GZC has over using the Hilbert Transform is that the resolution of the frequency values is limited to a quarter of the wavelength Nevertheless the clear physical meaning of the GZC made the frequency definition the true value in the mean Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The output is real number single channel or multi channel Regular signal OutputType Specify type of output Ex InstantFreqency _InstantFregency or InstantAmplitude
166. al red lines displayed in Graph A Note Depending on the configuration it is possible for the vertical red lines to span across the entire Graph A The field From indicates the starting position of the left vertical red line the starting position begins at From 0 the field Step indicates the counting increment that will be shown from Graph A to Graph B e g having Step 2 will have Graph B showing every second value of the points in Graph A The field N indicates the sampling area of Graph B Note The maximum value of N allowed is relative to the value of Step and the Sampling Frequency of the SFO Bele Gh Data Fiewer Channel Information Histogram Channel 1 E Data Channel Channel CHI 83568 70198721 0 062790519529 0 125333233564 0 187381314555 0 248689997104 In the image above Graph B s first point begins at 0 contains 500 points has not been down sampled Graph A 0 3 5 From mien N Graph B You can move the horizontal scroll bar which is located below Graph A to reposition the two vertical red lines in Graph A Project Selection 0 3 0 4 0 5 5 From H 0 1 0 2 Table of Data is located at the bottom left half of the Data Viewer window The table is column based each row represents a different point in time The first column is the Ind
167. alculate its spectra and show that its frequency varies with time Click button in Network tools or use Source Open data from file to read signal from a file The file is chiro1000 tfa and it is located at demo directory of the installation The default location C Program Files DynaDx DataDemon demo Basic then show the data with Viewer Channel Viewer Chirp 10000 0 02 0 4 0 8 0 8 1 12 14 1 6 18 2 tima iset Do the transform with Compute TFA Enhanced Morlet Transform and show the result with TFA Viewer It shows that the result looks better than Morlet Transform at high frequency chirp 1000 EnMorlet frequency Hz he e 0 2 0 4 0 8 0 8 1 12 14 18 1 8 2 time sec Related Functions Short Term Fourier Transform Morlet Transform References 1 A Wavelet Tour of Signal Processing 2nd 2 Y N Jeng C T Chen and Y C Cheng The Enhanced Morlet Transform via Iterative Filter to Study Turbulent Data Strings The 6th Aslan Computational Fluid Dynamics Conference Taiwan August 2005 3 5 4 Hilbert Spectrum Hilbert Spectrum is a time frequency matrix outputed from Hilbert Transform Its elements are instaneous frequency and instaneous amplitude For HHT EMD method extracts IMFs from the input signal Then Hilbert Transform can be applied to each IMF for Hilbert Spectrum results The output of Haar Transform can directly apply to Hilbert Spectrum also Introduction
168. ale Entropy It analyzes the complexity of time series of the system The complexity value represents the adaptability of the system to the environment The higher is the complexity the healthier is the system This method has shown good results in biological systems earth science and mechanical vibration Introduction MSE is different from traditional Entropy method In traditional Entropy theory the more chaotic is the system the higher is the entropy value For the theory of MSE method the complexity represents the heath of the system If the system is too uniform or too chaotic the system deems to be unhealthy MSE is the entropy value at every scale level The complexity represents the entropy changes under different scales Conventional entropy measure entropy Expected complexity measure complexity disorder This module uses Sample Entropy to calculate the entropy value It is an improved version of the Approximate Entropy It requires less data points than Approximate Entropy does x For the concept of the scale we can define the scale of the time series i as x i N gt lt j T i j l1x l x fo T Ax AW P Every point in the series is the average value within each scale We can calculate Sample Entropy for every scale T N m m I i Hy 5 scale m r N In In N m ng I where sat
169. all existing m files DoMatlab can run an existing Matlab m file Assume there is a m file round2 m which is saved in file Its content is B round 10 A 10 which rounds off A to 1 decimal place Editor CAM File Edit Text Go Cell Toole Debug Desktop x Hem IB 111 x 256 DoMatlab Example B roundi 10 4 10 Now substitute the 1 listed below channel of X2 with A for calculation The procedures are 1 First type in cd CM file in the Editor change the current directory to file and set the 1 channel of X2 DATA as A DoMatab Editor Matlab script file file X2 DATAI1 2 Enter round2 in DoMatlab Editor to run this m file Notice that because the output variable of round2 is B while the output variable of DoMatlab is Y the B needs to be substituted into Y DoHatlab Editor 5 Matlab script file cdi CAM file xz DATA Il rounde Close Editor use Viewer Channel Viewer to plot the DoMatlab result The rounding result of the data in the EEMD 1 channel can be observed Project1 x Sine DoMatlab 0 5 0 6 0 7 0 8 0 9 1 0 1 0 2 0 3 0 4 time sec Use DoMatlab to generate new Source 1 2 Use Computer Mathematics DoMatlab to create a DoMatlab SFO and change the Properties AsS
170. alse SystemCopy False DliProperties Info Demo 1 v1 2 2 0 Multiplier 1 1 Multiplier 1 amp utlo name True Connect both Noise and Sine Wave signal to demo1 SFO then view the results using Channel Viewer Demat 2 0 d 0 1 4 time SEC Open another ExternalDIl In ExternalPath directory open ExternalDllIDemos dll C Program Files DynaDx DataDemon External External ExternalDlIDemos dll And select YahooStocks in the Module This DLL can download stock data from Yahoo website Property ExternalPath Module LocalCopy System op DllProperties company EndDate IsImportDake Time StartDate 4ubo name In DilProperties set Company to 2330 TW And connec it to Channel Switch and select open price close price volume etc then display the data using Channel Viewer 0 ancad test bin External Exte ahooStocks False False Info ahooStocks 1 2 2 0 GE 010 1 10 False 005 01 01 True Property lx External ExternalPath test bin External Exte Module Yahoo Stacks LocalCopy False SystemCopy False OllProperties Info YahooStocks 1 2 2 0 Company 2330 TW Endate 2010 1 10 IsImportDateTime False StartDate 2005 01 01 True YahooStock 2330 TW Ch CH 0 iW X au 50 Be c S 1000 1100 1200 150 time day Helated Functions ExternalViewer 3 10 2 External Viewer This module helps u
171. ame Select OutputFileName Save in Dell9100 C BJPrinter Le Documents and Settings MyRecent jextra Documents Matlab 3 output Program Files _SRECYCLER iC3sleep housekeeper DJ System Volume Information temp tmp WINDOWS 48 G Yanhui Bullfrog Desktop My Documents My Network Save as type CSV files csv Cancel since Properties Writer WriteNow is set as False the file has not be saved yet Now change the WriteNow option to True and the file will be saved in C directory Properties True OulputDireckary C Program Files AnC AD Yi OQutputFileMame C sine cs WriteNow Write File now IF it is true it would also write File when upda Related Functions Text Writer TFA Writer Wave Writer 7 3 Text Writer Turns signal data and audio data to text file Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular Audio which could be real number or complex number single channel or multi channel Regular Fro 5 Module E Writer False v OutputFileMame C Documents and Settings user f IBI Ea csv Default Value Select True to write the data to file Ld Displays the default location of the files to be saved Note You can edit the default location from the main menu under Tools Pr
172. ame input as following Properties Motice the connecting order This module accepts input of Multiple Channel Regular Signal and Audio Notice that error message will show if the channel number of the input are not equal to 3 Other adjustable parameters are Appearance Channel Font and Colors gt Module Representation Module Representation Title They are almost the same like the parameters of other Viewer only Error Bar Plot Element Editor under Representation is unique to this module b Appearance gt Channel gt Fonts and Colors o Grad 5 Module Representation Tine U int Legend Postion D ataV alue Hold Flot Range XMin Date Time Format show Title ehow Exi show Y Axis gt Title day None False LinearA xis PlotEditor m Magnitude False auto 2008 04 01 00 00 00 auto 2008704730 00 00 00 auto 4 15616313190199 auto 5 16524462035515 Auto Time Time Time Open Error Bar Plot Editor the dialog below will show a Plot Element Setting Display Ene 1 ErrorBar Line ErrorBar Line Color Line Width Line Style Marker Style i m CH1 You can choose whether to display error bars in the for channel adjust marker style of the data point and so on Currently the color of error bar and line can not be set separately Chapter
173. annel Regular Chanel Viewer can accept multiple input data sources 1 Appearance The Appearance property contains the options to set the appearance of how the graph of the Channel Viewer will be shown on the Visualization Window El Appearance BackColor white ViewerWidth default 750 ViewerHeight default 180 ListOrder El Channel Channel Count 1 Module A Title Plat x Title Propert Property Definition Default Value Name oet the background color of the BackColor graph displayed in the White Visualization Window Set the width of th hi pixels set the height of the graph in pixels ViewerHeight The default position on Set the order of the graph to be the Visualization Window ListOrder shown on the Visualization is based on the order that Window the Channel Viewer is created 2 Channel Properties O Channel Channel Count 3 Multi Channel Display Overlapped Show value Channel Channel 2 ListOrder List order of the plot black Property Default Property Definition Name Value Displays the number of input signals currently Cannot be _ Channel Count E i y connected to the Channel Viewer edited Select from the option Overlapped to display Multi Channel the graphs of the input signals on the same A Ed Overlapped Display graph overlapping each other or List to display the graphs on top of one another When there are multiple inputs select the channel
174. antiles Quartiles and Quantiles for Quantile Method Linear Quantile Fractions 0 01 0 1 190 25 0 5 0 75 0 3 Quantile Fractions Specify the quantile fractions The second method is to click button to the right of Quantile Fractions to pop up the quantile edit window below If you need to add or remove a number of quantile values you can take this approach On the left is the Quantile Member panel User can use the Add Remove button to add remove members Additionly in the right panel you can edit each member s quantile ratio For example 0 01 Representative 196 quantile when the editing is complete press the OK button to complete the setup After setting up these parameters the result of the Quantiles calculations will appear in View Quartiles and Quantiles window Double Collection Editor 21 0 01 properties a E E Double Value Members There are five Quantile Methods namely linear next mean weighted mean and nearest Their methods of estimation are distailed in the Introduction section Parameter name Parameter Definition Default View Quartiles View results for Quartiles and n a and Quantiles Quantiles Quantile Linear Next Mean Weighted Linear Method mean Nearest Quantile Can set the percentage of multiple 0 01 0 1 0 25 0 5 0 75 Fractions Quantiles 0 9 0 99 Examples Use one group of Brownian Noise as input signal calculate Quartiles and Q
175. argas A Ram irez Rojas and F Angulo Brown Multiscale entropy analysis of electroseismic time series Nat Hazards Earth Syst Sci 8 855 860 2008 2 Costa M Peng C K Goldberger AL Hausdorff JM Multiscale entropy analysis of human gait dynamics Physica A2003 330 53 60 3 Costa M Goldberger A L Peng C K Multiscale entropy analysis of biological signals Phys Rev E 2005 71 021906 4 Costa M Goldberger A L Peng C K Multiscale entropy analysis of physiologic time series Phys Rev Lett 2002 89 062102 3 8 10 PCA Introduction The PCA Principle Component Anaylsis decomposes k mixing signals of X to q signals of Y where k and q are the numbers of signals and Y are un correlated signals In this case the mixing signal could be expressed by fewer signals Descriptions in mathematics We assume that the input mixing signals X include k signals and the length of the signal is n the output signals Y include q signals and the length of the signal is n The purpose of the PCA is to find a matrix which meets i where X is the mixing signals The DC value should be removed firstly W is named the principle component Y is named the reconstructed signal It could be certified that W is the eigenvector of the covariance matrix of X The eigenvalue decides the contribution of each principle component to X We could remove lesser eigenvalues to express the mixing signals by fewer signals NOTE The PC
176. as given in the linear system Marginal Spectrum The amount of energy in the signal for each frequency Noise Data that is either without meaning or relevance to the information of interest Normalized Hilbert Transform A method of normalizing the amplitude of the data before applying the Hilbert Transform in order to satisfy the condition stipulated by the Bedrosian theorem Orthogonality Defined as the inner product of the two vector is identical zero Here we use it to check how linearly dependent the generated IMFs are Values closer to zero are better Residual A signal that is the result of a series of IMFs being subtracted from the original signal A residual which is created when all possible IMFs being subtracted from it has the property of having no more than 2 extrema Riding Wave Any occasion when there are multiple extrema in between to consecutive zero crossings Sifting Criteria The number of times a signal needs to pass the test for an IMF in the EMD sift process before it can be considered an IMF Spectrum A two dimensional plot of frequency verses time with color intensity used to illustrate the amount of energy at each point of the signal Stationary Demonstrating a lack of change Stopping Criteria The rules used to determine when to stop sifting when generating an IMF This includes a test to see if the signal meets the definition of an IMF as well as the sifting criteria Threshold The nu
177. ase refer to the Trend Estimator Based on the computer with the CPU 2 8 GHz Intel E6300 points by computing time figure for computing signals with Brown noises of different lengths by the standard fast version Trend Estimater is shown as below Iterative Gauss timiersec 1 05 2 05 3e 05 4 05 05 05 7T e 5 SetO5 B e 05 1 0 Miptsi Helated instructions Fast Iterative Gaussian Filter Trend Estimater Iterative Gaussian Filter Heferences Yih Nen Jeng Diffusive and Fast Filter Using lterative Gaussian Smoothing Department of Aeronautics and Astronautics National Cheng Kung University YIH Nen Jeng P G Huang You Chi Cheng 2007 Decomposition of one dimensional waveform using iterative Gaussian diffusive filtering methods Proc R Soc A doi 10 1098 rspa Yih Nen Jeng You Chi Cheng 2006 Accuracy Comparison between Two Sharp and Diffusive Filters Proc R Soc A doi 10 1098 rspa 3 8 4 Fast Iterative Gaussian Filter The algorithm of the Fast Iterative Gaaussian Filter is faster than the standard version consuming less memory and presenting more accurate results especially on the boundary Introduction Please refer to the introduction of the Iterative Gaussian Filter Properties This module accepts real numbers single channels regular signals and audio inputs the format of the input signal is the plural and single channel spectra data Properties are set up as the below table El
178. ata Apply FFT to get the spetrum of the input data Determine and b Attenuation Factor and calculate two parameters of Iterative Gaussian Filter Smoothing Factor and Iteration Number m First calculate two over parameter ki and 2 In 1 2 Use iteration method to solve this equation and determine value P 0zP exp amp X In 1 exp na From value to calculate Gaussian Smoothing Factor v and Iteration Number m In 1 5 jh St ee In Q 1 a EDT 75 n p Then multify the FFT spectrum with this factor I g jm Sampling Frequency and repeat this filtering m times So the frequency below and the frequency above Fx are completely filtered out and the distribution between F and is Gaussian Use Inverse FFT to get the filtered input data _ __ b Attenuation factor N e g b 0 01 N f Low frequency fu High frequency f fH For LowPass the frequency below is filtered out For HighPass the frequency above F is filtered out The frequency in the middle shows Gaussian distribution the distribution is determined by b value Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio The formats of input signal and output signal are identical E Iterative Gaussian
179. ault parameters for the program It contains three sections oystem Plot and Output q Preference System Plot Output start up options must restart F Start Matlab Engine at Start up if installed Auta Llpdate checked at Start up Help Language English Pre Collapsed Property Categories EMTER ta separate Module Misc Forced Garbage Collection System Tab In the System Start up Options section we can a select to start Matlab Engine if Matlab is installed when DataDemon starts b select to check upgrades automatically c select language interface for DataDemon currectly only English and Traditional Chinese are supported The program must restart after the changes of these options In the System Pre Collapsed Property section we can set the Properties content format of each SFO the default value is Module It means that the Module property in Properties of each SFO is in collapsed status when initial displayed as shown below Default is to collapse tree display of Module Froperties lH x Convert To Audio Sample Rate 44100 Hz Forced Garbage Collection sets when to do the gargabe collection None Per Project and Per Module It helps to release memory space Plot Tab In the Plot Default Plot Size section we can a set the default width and height of the plot in the Visualization panel b Hold Plot Range determine whether to keep XY range of the plot or not when setting Viewer SF
180. average of each series are standard deviation For unbiased moment estimator the definition of Correlation Coefficient Is N i 2 x 1 l xy N DEN v where is the correlation coefficient of the two series Y are standard deviation of each series Correlation coefficient is the ratio between covariance and standard deviation of two series If there is a multi channel series the total channel number is M correlation coefficient matrix can be represented by Ri 7 where 1 are channel number Properties This module accepts input of real number multi channel and regular signal The output is a MxM matrix where M is the total channel number And the output is in Indexed format The result can be viewed in Reporter windown by clicking Properties View Matrix View Matrix Correlation Matrix For EMD Unbiased Moment Estimation False Correlation Matrix Default Property Name Property Definition Ben al value Unbiased Moment Calculate the covariance using Estimation unbiased moment estimation method False Example Calculate covariance matrix for sine waves with different phase and frequency Create a since wave in Netowrk panel using Source Sine Wave and its default frequency isi0Hz Then add two more sine waves One is set with Properties SignalFreq 5Hz and the other is set with Properties SignalFreq 10Hz and Properties Phase 180
181. between two points of input signal If ImpulseShape Decay one more property is Property Property Definition Default Name Value Set the width of square waves If width is 0 the actual width Width 0 is the time distance between two points of input signal h f th li Th Decay Set the decay time of the amplitude The smaller the value 0 005 the faster the decay Example Create and analyze a signal Create a pulse signal with the Source Advanced Impulse and viewing its results with the Viewer Channel Viewer Impulse 0 0 1 0 2 0 5 0 4 0 5 0 7 0 9 0 9 time Sec Connect the Impulse to the Compute TFA Short Term Fourier Transform and view the result with the Viewer Time Frequency Viewer Impulse STFT 500 0 005 400 0 004 P aly AA 0 003 e 1 r E 0 002 D 4 co 0 001 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Set the properties of the Impulse Set Sigma 0 0001 The smaller is the value of oigma the better is the pulse The pulse is almost perfect as shown in Channel Viewer It clearly shows that frequency band is quite large in TFA Viewer Properties El Impulse ImpulseShape Gaussian Stare 0 Sigma 0 0001 SingleImpulse False Interval 0 2 PasitiveImpulse True Impulse 5 0 0 0 1 0 2 0 9 0 4 0 5 7 8 0 9 1 time sec Impulse STFT 500 400 C c e bh c frequency Hz 10
182. buted noise added to the original signal for ensemble computation the seed would be set according to current time opecify the initial value of the noise seed Hidden when UserDefineSeed is False Selected mode for BP Hidden when Auto is True Selected mode for BFV 1 Hidden when Auto is True opecify the control of noise seed If false Selected mode for BFV 2 Hidden when Auto is True Minimum frequency of the dominant oscillation range in Hz 0 02 Maximum Maximum frequency of the dominant quA Frequency oscillation range in Hz Auto Specify True for automatic IMF mode selection Output Select output for MMPF results IMF or ALL both of them You can click the Excel button to export data of all results or selected results to a file for futher analysis Metwork x 4x Project1 The tables below explain the meaning of each column in the output Excel file Define NBP total number of IMF modes of BP including residual NBV1 total number of IMF modes of left BFV including residual NBV2 total number of IMF modes of right BFV including residual If there is no BFV2 input for MMPF analysis NBV2 0 and there will be no columns related to the right BFV in output file NT NBP NBV1 NBV2 1 Select output for IMF CH NBP each mode for BP Mode 1 is the raw input data CH1 CH NBP 1 CH NBP NBV1 each mode for BFV1 Mode 1 is the raw
183. cerebral autoregulation is useful under many clinical conditions Impairment of vascular reactivity to regulate cerebral perfusion has been found in many syndromes associated with aging hypertension stroke diabetes dementia and traumatic brain injury TBI For example autoregulation estimates based on BFV and direct measurements of cerebral perfusion pressure CPP have shown predictive value for determining outcomes in TBI patients Therefore the MMPF analysis may play an important role to assess and monitor dynamic cerebral autoregulation in a wide range of clinical settings 1 3 4 References 1 Novak V Yang ACC Lepicovsky L Goldberger AL Lipsitz LA Peng C K Multimodal pressure flow method to assess dynamics of cerebral autoregulation in stroke and hypertension Biomed Eng Online 2004 3 39 2 Huang NE Shen Z Long SR et al The empirical mode decomposition method and the Hilbert spectrum for non stationary time series analysis Proc Roy Soc London 1998 A454 903 995 3 Hu K Peng C K Huang NE Wu Z Lipsitz LA Cavallerano J Novak V Altered phase interactions between spontaneous blood pressure and flow fluctuations in type 2 diabetes mellitus Nonlinear assessment of cerebral autoregulation Physica A 2008 387 2279 2292 4 Hu K Peng C K Czosnyka M Zhao P Novak V Nonlinear assessment of cerebral autoregulation from spontaneous blood pressure and cerebral perfusion pressure fluctuations Cardiovasc Eng 2
184. channel Regular and Audio which could be real number or complex single channel or multi channel Regular El Data Sampling Frequency Module El Time Shift ShiFtMode Shift StartTime shifty alue Sampling Frequency Sampling Frequency Property Name Property Definition Displays the number of channels connected to the SFO Channel Count Sampling Frequency Data Length Displays the data length of the SFO Displays the sampling frequency of the SFO Data Unit Displays the data unit of the SFO Displays the unit of the SFO Variable Option Property Definition Default Value Select the type of shift method to ShiftMode ShiftStartTime apply to the graph Shift Value Shift the start time of the raph to the entered value the time ShiftStartTime 9 9p I9 ShiftValue 0 shift will either add to or minus from the original start time Start Value Set the start time of the SetStartTime StartValue 0 graph to the entered value Start Date Start Time Set the start StartDate 2000 1 1 setStartDate date and the start time of the graph to the entered value StartTime 00 00 00 Example Create a sine wave SFO and shift its time value 1 Create Source Sine Wave and set the Properties TimeStart to You can see that the first point of the sine wave will begin at the 3 sec mark E propertytrid Time Writ TimeLength samplmgFreq DataLeneth signalPFreq Amplitude
185. cient to update them automatically every time they are edited If you do not want to automatically update SFOs you can un check the Auto box and click on Q to update a selected SFO manually 2 Qupdate Calculation When Auto is not checked click on Q button to update a SFO that has been edited A SFO which require updating will have a sky blue line near the bottom of the SFO Once a SFO is updated the sky blue line will turn into a dark blue line that indicates an updated SFO 3 Qstop Calculation During an update of a SFO you can click on Q button to stop the update 1 3 4 Data Viewer Data Viewer can be created so that the calculation result of a SFO can be quickly viewed examined and analyzed through an information browser Select a SFO and click on the Data Viewer button and the Data Viewer window will pop up Depending on the type of selected SFO Data Viewer will display data based on the different signal types such as signal source spectrum numeric and spectra The following will be a brief introduction to the interface of the Data Viewer and how it displays information depending on the different types of SFO selected The interface of the Data Viewer is divided into three sections as shown in the image below the upper left half is the Graphic Information where the graphs are displayed the bottom left half is the Table of Data which contains the values of the graph which is displayed in a table format and the ri
186. cified at a level of DecibelPoint The unit is pi radians per sample The phase correction function is enabled when the PhaseCorrection is set to true vice versa PhaseCorrection Example 1 Build an Impulse source Impulse Shape is set as Square and Singlelmpulse is set as True Then connect Computet Transform Fourier Transform Lastly the distribution of frequency is shown by Channel Viewer Property El Impulse Impulseshape Square Start 0 width 0 SingleImpulse True Positivelmpulse True Module El Source TimeUnit TimeLength 1 SamplingFregq 1000 D acaLength 1001 Amplitude 1 AmplitudeOfFsetk TimeSEarE 0 Irpulse FFT 0 002 0 001 0 0 50 100 150 200 250 200 350 400 450 500 Frequency Hz 2 Connect Impulse Source with Compute Filter CombFilter Connect Comb with Compute Transform Fourier Transform FFT s Max value is set to 1000 which is equal to sampling frequency The frequency is filtered with equal interval when it is viewed by Channel Viewer Impulse CombF ilter FFT 0 002 0 001 0 0 100 200 300 400 500 B00 FOO B00 900 1000 Frequency Hz 3 Change the Filter Type of Comb Filter as CombPeaking and NotchNum of it as 11 The result is going to be a series of frequency The rest of them are going to be removed Property rix Comb Filter FilterType CombPeaking NotchNum 11 DecibelPoint 3 BandWidth 0 01 Impulse CombFilter F F T 0 002 0 001
187. ck to select the column representing the time information NOTE Unchecked After checking the box the data will be displayed in the Indexed format Specify Time Column Field Format Contains the options to set how data values are read Separate the data values by the white space White spaced character Separate the data values by the comma or the Delimiter TAB character Customize your own rules to read the data values NULL Value Handle Contains the options to deal with NULL or NaN values missing values Select the calculation method to fill in the missing values please look up Chapter 3 1 4 Linear Interp Fill NULL Value for further details NULLFilledMeth od the option to set the date and time nsec msec Time Unit sec minute hour day week month 30days sec and year 365 days Time Shift Set the starting time of the data Sample Set the Sample Frequency 1000 Frequency Set the Down Sample rate With every increment of the value the sample data will be shortened to save time during calculation Note The Sampling Frequency value will be Down sample by automatically recalculated depending on the 1 down sample value E g Sampling Frequency 1000 with Down sample 2 will result in creating an imported Source SFO wtih Sampling Frequency 500 Date Axis Enable Select to enable the date and time option Unchecked Disa bled Start Date Time
188. culation for signals The components are Basic Statistics basice statistics for the signal such as maximum minimum average standard deviation Covariance Matrix calculate covariance matrix among signals Correlation Matrix calculate correlation maxtrix among signals Equiphase Statistics calculate equiphase statistics for the signal Kernel Smoothing Density calculate the probability density function of the signal using special kernel function and smooth the result Orthogonality Matrix calculate the orthogonality matrix among multiple signals Quartiles and Quantiles calculate different quartiles and quantiles of the signal Rolling Statistics calculate rolling statistics for the signal Hypothesis Test build the hypothesis for the signal select the test method and validate hypothesis 3 4 1 Basic statistics Basic statistics is a quick way to get basic statistical values for a signal Introduction Let the signal series be 9 1 w 1 is the length of the signal It is not limited to time series Basic Statistics gives following calculation Statistics Formula Description N 1 Sumation of all the Sum 2 Xj elements i Q Min Minimum value Max Maximum value N 25 Xi Average value Geometric mean mainly used in Geometric exponential change Mean series such x 70 for all i population growth raio calculation N Harmonic average Harmonic Y I
189. current component i e to remove the signal shift along Y axis Introduction Let the signal source be X x x x _ its average is x i e DC Hereafter X x X xy X is said to be Remove DC Properties This module accepts input of Signal which could be real number single channel Regular and Audio which could be real number single channel Regular The property is DC type which includes four types of calculation methods to compute the shifting along the Y axis where the default option is Mean The detailed meaning of these methods is given in the table below Module Ej Remove DC Channel Count DC Value 0 DC type DFTZerothTern Trapezoid Inte gration UserSetting DC type Property Property Definition Mean To calculate arithmetic average After performing Fourier Transform on the original data define X axis as zero point which has the DFT First Amplitude Y lUe a 1 x DC DC P zO dt 0 0 TIERS ien tu Divide the result of Trapezoid Integration by the did total number of points The result is the DC User Setting The users can set the desired shift value manually Example Create a sine wave which is shifted along Y axis and then use RemoveDC to remove the shift 1 Create a sine wave using the Source Sine Wave and then adjust the Source AmplitudeOffset to 1 2 to shift the signal along the Y axis in positive direction for 1 2 unit Next us
190. d Viewer updated Auto gt DoMatlab 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 4 n this step let s use the Matlab internal function peaks to create a matrix of 49 x 49 and change its signal format to Spectra output Open a new Project create a DoMatlab signal source following the step 2 then open Properties MatlabEditor First create a peaks as output signal Y ES DoMatlab Editor Matlab script file Y peaaks DER Script Help amp Examples Matlab script file peaaks n m sizeiY PEARS Spectra lengths n m starts 0 intervals 1 1 mits sec Hz tormats Reqularc Reqular name of output This signal is named Y DESC name PEAKS data PEAKS Type of output The signal type is set as us P Y DESC type Spectra 9 signal opectra Item Code Comment The number of discrete points in X axis Y axis Y DESC lengths n m Because Y is a 2 dimensional array the lengths of row and column need to be set in order Corresponding to the axis definition in Spectra row represents time i e x axis column represents frequency i e y axis The starting point of x and y axis Y DESC starts 0 0 Set the starting points of two axis to zero The interval in x and y axis Y DESC ntervals 1 1 Set
191. d Up sampling interpolation method Resample 1 0 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 4 Now create a Square wave SFO and connect it to two Resampling SFOs and set one Resampling SFO s NewSamplingFrequency to 100000 and UpSamplingMethod to Spline and the other Resampling SFO s NewSamplingFrequency to 100000 and UpSamplingMethod to MonotonicCubic and connect both Resampling SFOs to the same Channel Viewer SFO Resample o o 2 o w o A 0 5 0 6 0 7 0 8 0 9 1 time sec Notice the slight different around the corners of both wave signals Now lets zoom into the graph for a closer look Resample 0 048 0 0485 0 049 0 0495 0 05 0 0505 0 051 0 0515 0 052 0 0525 0 053 0 0535 0 054 time sec Overshooting The thin black line is created through the Spline method and the thick blue line is created through the MonotonicCubic method From the graph you can observe that Spline method has a tendency of overshooting whilst MonotonicCubic method has no such problem Related Functions Filling NULL Value Reference Numerical Recipes 3 Edition The Art of Scientific Computing by William H Press Saul A Teukolsky William T Vetterling Brian P Flannery http en wikipedia org wiki Monotone cubic interpolation 3 1 8 Time Shift Shift the graph along the x axis time Properties This module accepts input of Signal which could be real number or complex single channel or multi
192. d must be set in the final step and then use Viewer Channel Viewer to show it in the window as shown below project Viewer updated 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 To show every points clearly click PlotEditor in the Properties Representation Plot Elem Editor which in turn is in the Viewer 1 In the popped up Plot Element Setting window select in Marker Style to mark every time points as symbol of in the curve Properties El Representation Timelint LegendPosition Mone DrawSEvyle Line Axis LinearAxis Plot Elem Editor PlotEditor YVWalueType Magnitude Hold Plot Range False Plot Elem Editor Setting plot element H Plot Element Setting loj x Display Channel Mame Line Color Line Width Line style Marker Style Display All Hide All Sine 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 3 Perform numerical integration Compute Mathematics Integrate on the sine wave and change Marker Style to x as what has been done in step 1 and 2 The figure plotted is the integration result viewerz Updated Auto gt Sine Int 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 4 Change Properties StartPosition of the Int SFO to 0 3 the new calculation result is shown below Next use DataViewer to observe the signal output from Int SFO It can be seen that the original value of 21 in DataCount has been changed to 15
193. d to pass through the lower the value the higer frequency smaller period to pass through Related Instructions Iterative Gaussian Filter Reference 1 Diffusive and Fast Filter Using lterative Gaussian Smoothing Yih Nen Jeng Department of Aeronautics and Astronautics National Cheng Kung University 2 http www ancad com blog AnCADSupport wp connent uploads 2008 05 it gauss 3 2 6 Comb Filter Comb filter can be used to remove or retain a series of frequencies with equal interval Introduction The Frequency Response Function of Comb Filter is shown below Irnpulse CombFilter FF T 0 002 0 001 0 100 200 300 400 500 600 800 900 1000 Frequency Hz Properties This module accepts real number single channel or multi channel regular signal or audio signal as input signal The formats of input signal and output signal are identical Property IX El Comb Filter Filter Type CombNotching 4 DecibelPoint 3 Bandwidth 0 01 Property Name Property Definition Default Value Filter types consist of CombNotching and Filter Type P er CombPeaking Set the number of notch whichis betweenOand sampling If the filter type is set as CombNotching the actual notch number NotchNum 1 Set the decibel point The smaller value we set _ the sharper notch we will get BandWidth BandWidth Specify the ra the of which is DecibelPoint spe
194. degree unit is in Degree Finally merge three signals into a Multi channel signal using Conversion Merge to Multi channel n this case three sine waves are generated 10Hz 5Hz and 10Hz with phase shift of 180 degree Using Viewer Channel Viewer the signals can be displayed Black curve is Sine blue curve is Sine2 and red curve is Sine3 Sine2 Properties Properties El Source TimeLIni TimeLength SamplingFreq DatalLength SignalFreg Amplitude AmplitudecOfFsek Phase SignalFregq The Frequency of the to be generated signal Sines Properties Properties El Source TimeLlIniE TimeLength SamplingFreg DataLength SignalFreq Amplitude AmplitudeOfFset 0 Phase The phase in degree Sine TaMulti 0 0 1 02 0 3 0 4 0 5 0 6 07 08 08 1 time sec Connect ToMulti SFO to Compute Statistics Correlation Matrix and click Properties View Matrix to show the result in the pop up window The matrix element Ki along the diagonal is self correlation value which is 1 Ki correlation between Sine and Sine2 Since the value is very small it means there is no correlation between these two signals 32 23 are also very small It means that there is no correlation between Sine2 and Sine3 Signals Sine and Since3 mirror along X axis and the correlation is 1 it shows that two signals are totally negative correlated Properties El Correlation Matrix View Matrix Correlation Matrix for
195. der to show the plots Keep the plot If True the plot is kept even if the HetainPlot ChanneViewer is removed if False the plot is deleted Show Title Show the title in the plot Title Title name Example True None White False default 750 default 180 Follow the order of Viewer creation False True default Start Compute External ExternalDIl and open ExternalDlIDemos dll in ExternalDLL path C Program Files DynaDx DataDemon External External ExternalDllDemos dll There are many modules in the Property Module as shown below Property 1 El External ExternalPath C Program Files AnC AD Visual Signal E DIlPraperties Auba name Module select demo6 in Module Path property is shown in DllProperties Select an image and display it using ExternalViewer E External ExtemalPath C Program Files AnC AD isual Signal Extermal Ext Module demo06 LocalCopy False SystemCopy False 3 DllProperties Info Demo06 v1 2 2 0 Path Select Path coe 5m RAILI 77 ABS _ Ti SE XSAUCT Image files jpg png gif bmp wmf w Run 49 Yisual Signal 1 3 Professional RC File Edit View Layout Tools Help 5 T PN NN gt np Pm 7l _ Project Title Externalviewer2 updated Auto Q Q blc Mmmm mmm m m m mmm meee ed Property AX Related Functions ExternalDIl 3 11 MMPF Multi
196. ds Finally link these two signals to Viewer Channel Viewer to plot figures Viewer2 updated Auto Properties El Source TimaeLlInil TirneLength SamplingFreg DataLength SignalFreg Amplitude AmplitudeOfFsek Phase Symmetry TimeStart Module SEC 333 1333 10 0 5 0 33 4 Viewer 2 0 5 1 1 5 2 5 3 3 5 4 time sec Pass these two signals to Conversion Merge to Multi Channel and use Channel Viewer to plot figures Viewer Updated Auto E El Merge To Multi Channel ReferenceInput Module ReferenceInput I Sine bl Select From connected inputs to be the merging reference Sine ToMulti 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Click on the ToMulti Because its Properties Referencelnput is set as Sine the time axis setting of the output is identical to those in the Sine Wave i e the time starting point is 0 sampling frequency is 1000Hz time length is 1 second and the number of data point is 10001 The contents of Sine are copied to the CH1 in the ToMulti completely For the input signal of Triangle the original time axis would be replaced by the time axis of Sine The number of data point in Sine is 1001 while it is 1333 in Triangle This module would place the first 1001 data points of Triangle to the CH2 in the output signal and delete all other 3 Change the Properties Referencelnput to 1 Triangle the time axis setting of the output
197. ds to fill the NULL value oplinelnterpolation Variable Option Property Definition new FixedValue variable option appear in the FixedValue Properties Window Enter a value to replace all the NULL values to the value entered PrevValue The NULL value will be replaced with the previous value in the signal The NULL value will be replaced with the next available NextValue value in the signal Using Linear Interpolation to calculation the value of the Linearlnterpolation NULL uL La Using Spline Interpolation to calculation the value of the Splinelnterpolation Ji Monotone cubic interpolation is a type of cubic interpolation that preserves monotonicity of the data set MonotonicCubic being interpolated MonoticCubic method is better than Splinelnterpolation method when the slope of the signal is large e g Square wave Example To fill in the missing values using Fill NULL Value SFO 1 Open demods in the directory C Program Files DynaDx DataDemon data From the graph in the Visualization Window you can clearly see the missing values on the graph tests Nah j NULL Value 0 2 0 4 0 8 a a 1 1 2 1 4 1 6 1 5 2 time i sec 2 Connect the source signal data to Compute Channel Fill NULL Value and select Spline Interpolation in the Properties FillMethod of the Fill NULL Value SFO Fillethad SplineInterpolation al Module i FillMethod The Filling null value
198. e Based on a computer Intel dual core E6300 2 8 GHz the graph of computing time vs data points for both the standard and fast MSE is shown as below The test signal is the pink noise other properties are all default values MSE run time amp Brute CH1 mmm Sliding K D tree CH3 e ce ce e ce timets ec 1000 10000 1 05 1 06 lagcM points Related instructions Noise Viewer References 1 Pincus S M Approximate entropy as a measure of systemcomplexity of the National Academy of Sciences USA Vol 88 pp 2297 2301 2 Costa M Goldberger A L Peng C K Multiscale entropy analysis of physiologic time series Phys Rev Lett 2002 89 062102 3 Costa M Peng C K Goldberger AL Hausdorff JM Multiscale entropy analysis of human gait dynaiics Physica A 2003 330 53 60 4 Costa M Goldberger A L Peng C K Multiscale entropy analysis of biological signals Phys Rev E 2005 71 021906 3 8 6 Peak Detection The Peak Detection can be used for intercepting the position of the peak signal or calculating the time difference of the two peak signals Introduction 1 Ihe peak is defined as the maximum value in one cycle This maximum value is the mathematical Local Maximum 2 The judgement could be disturbed by noises To eliminate this disturbance the user could firstly filter the signal by the FIR the IIR or the EMD and then intercept the peak In this module
199. e Map to Real 6 4 Time Frequency Viewer Time Frequency Viewer uses images to display three dimensional time frequency signals time frequency and signal strength The x axis represents the time the y axis represents the frequency and the color represents the signal strength Properties This module accepts input of Spectra which could be real number or complex number single channel Regular Time frequency Viewer and Channel Viewer are very similar with the difference being that there are more variable options for Time frequency Viewer Properties Representation ValueT ype Magnitude Min auto 0 s Max auto 1 Y Min auto 0 YMax auto 500 Min auto 0 Max auto 0 438519166195455 Colormap Eg Jet Show Title True Show xAxis True Shaw VY Axis True Shaw Calar Bar False ValueType The data representation of the result Property Name Property Definition HALLO SUY Value Set the minimum value of the time frequenc CMin color Set the maximum value of the time freguenc CMax 57 d y Auto Show Color Bar There are four types of color representation Jet n Hsv Rainbow and Gray select whether or not to display the color bar at M the right side of the graph Example Create a Square Wave SFO and connect it to an Enhanced Morlet Transform SFO and then connect it to a Time frequency Viewer SFO Then change some configuration to the Time Frequency Viewer 1 Create Source gt
200. e Matrix A View Matrix Covariance Matrix for EMD Unbiased Moment Estimation False View Matrix Display Ehe covariance matrix zm Report for Covariance Matrix for Z lE e E m Covariance Matrix for ToNIult Covariance Matrix Channel CH1_ Sine ER CH1 Sine 0 5 3 95E 14 CH2 Sine 3 95E 14 0 5 CH3 Sine 0 5 3 87E 14 Create a new signal with Source Triangle Wave and connec it to Compute HHT RCADAEEMD to calculate its IMFs The results are displayed using Channel Viewer oet Properties Multi channel Display in the view to List and set Viewer Height to 350 There are 9 channels in the signal Triangle RCADA EEMO 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Connect RCADA EEMD SFO to Compute Statistics Covariance Matrix for calculating covariance matrix among IMFs Report for Covariance Matrix for RCADA EEMD General Covariance Matrix for RCADA EENID Covariance Matrix Channel IMF h2 IMF h3 h MF h5 MF hB IMF h7 IMF h8 residual IMF h1 IMF h2 IMF h3 IMF h4 IMF h5 IMF_h6 IMF_h IMF h8 0 000115 7 8E D6 2 69E 05 4 03 06 4 38E 07 1 35E 07 1 76E 08 4 15 09 IMF residual 3 83E 07 7 08E 065 7 8E 05 0 000133 1 61E 06 2 94E 07 3 18E 07 3 46E 08 1 5E 08 1 72bE 07 2 58E 05 0 000133 0 316 0 00849 0 00035 6 94E 05 9 74 08 5 1 3bE 08 2 13E 05 4 03E 06 1 61E 06 0 0084
201. e accepts input of Signal which could be real number or complex number single channel or multi channel Regular and Audio which could be real number or complex number single channel or multi channel Regular Enter the selected range of the signal by defining the Properties StartPosition and Properties EndPosition time unit El Data El Data Selection StarkPasition 2008 01 701 00 00 00 EndPosition end 2008 01 04 00 00 DownSamplestep 1 Module 4 DownSampleStep Down sample step Data Property Definition Property Name s the sam juency of the input SamplingFrequenoy 4 d the sampling count of the input data Data Count Data Selection Property Definition Default Value Property Name The original start time for the input data Enter the value of the start position of the input data StartPosition The original end time for the input input data data Enter the value of the end position of the EndPosition Example 1 Create Source Sine Wave and connect it to Viewer Channel Viewer Project Viewer updated cine B 0 1 0 2 0 3 0 4 0 5 time sec In this Sine Wave SFO the SamplingFreq is 1000 and the SignalFreq is 20 2 In DataSelection SFO set the Start Position to t 0 2 and End Position to t 0 4 and the new graph will be show the range between t 0 2 to t 0 4 original range Timelength is between 0 1 so the new range has t
202. e domain is the starting time of the pulse signal and is the sharpness of the pulse signal t 1 jr Gaussian This signal is approximate to a square Tu c to lt w wave with tiny width is the starting time of the pulse signal W is the width of the square pulse wave oquare This signal is approximate to a square 4 z1 Wave with tiny width and decays the Decay 7 exponential ratio is the starting time of otherwise the pulse signal and W is the width of the square pulse wave Properties Properties x El Impulse ImpulseShape Gaussian Stare 0 Sigma 0 005 SingleImpulse False Interval 0 2 PasitiveImpulse True Property Name Property Definition Default Value ImpulseShape The shape of the pulse Gaussian Square Decay Gaussian otart The starting time of the pulse 0 Singlelmpulse To create a single pulse False Interval The interval between two pulses 0 2 Positivelmpulse Set pulse to be positive True If ImpulseShape Gaussian one more property is Property Default Property Definition Name Value Set the width of the Normal Distribution The smaller of Sigma 0 005 sigma the sharper of the shape If ImpulseShape Square one more property is Property gw Default Property Definition Name perty Value Width Set the width of square waves If width is 0 the actual width 0 is the time distance
203. e input signal is at least 3000 points in length Actually the first 3000 points are not used for computing but for reference This module accepts real numbers DeltaVoltages TwoElectrodes The Regular type of the output data is the index DeltaVoltage Properties are set as below Module El R R interval Type TwocElectrode Umit milli olt main 200 Dc value Property pl Default Mame Property Definition Valve Setting the type of the input data DeltaVoltage or TwoElectrode DeltaVoltage Unit Setting the unit of the input data Volt or milliVolt milliVolt Gain The ratio of changing the ADC unit to the physical unit 200 DCvalue DC value of the ECG reference value 0 taking the 100 MITDB http Awww physionet org physiobank database mitdb for example The format of the input data is a hea file When the data is imported we can find that the data is a TwoElectrode signal with the unit of mV ai WFDH WaveForm DataBase Importer WFDB Signal Information Mame Ms Channel Count 2 sample Freg 360 fewelessec Magnitude Unit mv Time Umit sec Data Range From To Down sample bw 1 s Count 650000 Range 1805 6 sec 0 1605 6 Date Axi Fe Det Axis 92 9 selected Channels v 1 v 2 Y5 The result is viewed with the Channel Viewer LI LII 400 AOE gon wee 1700 14 00 1600 time sec mV 79
204. e of Stationary with NASA Hilbert Spectrum and then display the result of NASA Degree of Stationary in the Channel Viewer Set the Properties XaxiaType as LogAxis LOD S NASA ENLD NA SA Hilbert Spectrum NASA Degree of Stationary Frequency cycles day References 1 N E Huang Z Shen and S R Long et al The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary Time Series Analysis Proceeding of Royal Society A vol 454 pp 903 995 1998 2 Semion Kizhner Thomas P Flatley Dr Norden E Huang Karin Blank Evette Conwell On the Hilbert Huang Transform Data Processing System Development 2004 IEEE Aerospace Conference Proceedings Big Sky Montana March 6 13 2004 3 N E Huang Z Wu S R Long K C Arnold K Blank and T W Liu On instantaneous frequency Advances in Adaptive Data Analysis Vol 1 pp 177 229 2009 4 Wu Z and N E Huang Ensemble Empirical Mode Decomposition a noise assisted data analysis method Advances in Adaptive Data Analysis Vol I No July 24 pp 1 41 2008 Glossary Analytical signal A complex valued signal the results from applying the Hilbert Transform The real part is the original signal the imaginary part is the complex conjugate Cauchy principal value The value of the integral evaluated with the contribution from the singular point within a neighborhood of a vanishing radius excluded The internet encyclo
205. e the Viewer Channel View to observe Viewer updated Auto gt a El Source TimeLIni Sec TimeLength 1 SamplingFreq 1000 DataLength 1001 a SignalFreq 10 d Amplitude AmplitudeOfFset Phase ag TimeSEarE 0 Amplitude ffset Sine 2 1 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 Connect the original signal to Compute Mathematics RemoveDC and set the method as Mean in DC Type It can be seen that the shift is removed El Remove BC DC type Mean Module sine RemoveDC 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 3 The DC Type can be chagned also e g DFTZerothAmplitude However in this example the result would be identical Sine RemoveDC 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 4 Connect the signal to Compute gt Transform Fourier Transform to perform Fourier Transform Without the RemoveDC in Fourier Transform it can be seen that the amplitude at OHz is 2 times of 1 2 Project1 x Viewers updated Auto gt a RemoveD Min Max Resolution Window E Module Class Name RemoveDC Remove DC component 2 4 Sine FFT e 10 15 20 25 30 35 40 frequency Hz For horizontal shifting along time axis please reference to Channel TimeShift module Related Functions Source Fourier Transform TimeShift 3 3 2 Mixer Mixer is used to mix several signals Introduction Assume N gro
206. e the second SFO all the available SFOs will be shown and the ones unavailable will be grayed out Network gk m RU M uu Prajeckz x Compute Conversion Source Data Viewer Box plot Viewer Channel Viewer Properties Histo gram Viewer Module El Source You can also create two SFOs and use the mouse to drag them together In the example below a connection is established by dragging the red triangle of the Sine SFO to the blue triangle of the EEMD SFO Direction of mouse drag The advantage of this method is that you can connect any SFOs at will without going through the menu to find a second SFO to connect to This method gives you more freedom and control but it also leaves rooms for error If you try to connect two SFOs of different input to output data then an error message will pop up not allowing you to connect them together shown in the image below MTime does not accept Signal data with Eank 1 Eegular coordinates e Connection fails due to data mismatch Mixer updated Auro gt When trying to connect multiple SFO output to a single SFO input the order you drag the connection from the output port to the input port will be the order it is shown on the input port The first connection will be listed at the top followed by the second connection and so on rag the connection to the d middle af the viewer SFO It is
207. e we can see that there is a Bump between t 22 77 and t 41 27 but when we zoom in this area it is not a Bump Bump Remave Bump dq S32er07 Z4 S25etr 7 41 27 41 272 41 274 41 276 41 278 41 28 41 282 41 284 41 286 41 288 41 29 41 292 time i day The Bump is in the time range of t 37 to 38 Bump Remove Bump 4 831e 07 4 8305e 07 36 8 3T 37 2 37 4 37 8 37 8 38 time i day We can find that the Bump is removed in this area Bump Femave Bump Femowe 4 2307 e 07 4 530Ge 07 4 5305e O 38 8 37 37 2 37 4 37 5 37 8 38 time day The second method Setting the Jump Threshold Ratio and the Slop Threshold Ratio to be 0 1 and remaining the StartPosition and the EndPosition unchanged m The output is 4 Sz20er 7 gq S288er07 20 22 24 Helated instructions Data Selection Diff 28 28 Bump Remave Bump Remave 30 32 34 38 time i day 38 qz 3 8 3 Fast Trend Estimater The Fast Trend Estimater is the same as the standard Trend Estimater but the fast version and consuming less memory Introduction Refer to the algorithms of the chapter Iterative Gaussian Filter Properties This module accepts real numbers single channels regular signals and audio inputs the format of the input signal is the plural and single channel spectra data Properties are set up as the below table Property lix El Fast TrendEstimater Filter Type LowPass TrendBasis Frequency
208. eTo The new replaced value Square Replace 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Important You can only replace one value at a time If you want to replace multiple values then several Replace Value SFO will have to be created Related Functions None 3 1 7 Resampling You can set a new sampling frequency value to a signal data Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular and Audio which could be real number or complex number single channel or multi channel Regular El Data EJ Module El Resample Step Downsampling False ReSamplingMethod Linear HewSamplingFrequency 1000 E Module Resample Property Definition Property Name NewSamplingFrequency Set the new sampling frequency value 1000Hz Set the sampling frequency method nearest ReSamplingMethod Linear linear spline and mono tonic cubic Display the ne i t of the dat play w sampiing count of the data Nore output Variable Option Property Definition The NULL value will be replaced with the next available value in the signal NextValue Nearest Using Linear Interpolation to calculation the value of the Li Int lati inearInterpolation UTI Using Spline Interpolation to calculation the value of the linel lati oplinelnterpolation NULL Monotone cubic interpolation is a type of cubic interpolatio
209. ean Median etdDev Variance Variation aef Skewness kurtosis SemistdDey Semivariance 0 162 Add a Sine Wav the Noise using Conversion Merge to multi channel and display both signals with Viewer Channel viewer Then connect to Stats and display the result using Properties View Statistics in Basic Statistics Noise Toluit j i 0 0 1 0 2 0 5 0 4 0 5 0 7 0 8 0 9 1 time sec Basic Statistics for To Multi E E Basic Statistics for TolvIul t Basic Statistics Mean i5enrmetricearn Harmonichlean TrimmedmMean Median StdDey Variance wariatianccoaef Skewness kurtosis Semistdvey Semivariance set the parameter in Basic Statistics toolbox to Scientific and set the digits to 5 after decimal point Click Refresh button to update the result za Basic Statistics for ToNIul Basic Statistics for ToMulti Basic Statistics Channel CHT Moise CH2 SUM Min Mean Geametrichean HarmanichMean Trimmedhtearn Median Stdbey Variance Variation oat akewress kurtosis SsemistdDey Semivariance 20 0 996 0 997 0 0279 0 565 0 754 0 0309 0 04 0 564 0 319 20 2 0 0499 1 12 0 403 0 162 2 44E 15 1 1 2 39 16 0 55 1 82E 13 3 33E 15 1 84E 15 D 707 0 5 2 95 15 4 38 16 1 5 0 5 0 295 Create another white noise signal using Source Noi
210. elated Functions Writer 7 2 csv Writer Export the data to csv format the data is separated by commas Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular Audio which could be real number or complex number single channel or multi channel Regular Properties Module El Writer WribeNow False OutiputFileMame C Documents and Settings user m Br Ea csv Default Value Select True to write the data to file Displays the default location of the files to be saved Note You can edit the default location from the main menu under Tools Property Name Property Definition OutputDictory Preference Select the location to save the file NOTE With the file name and location entered the file is only saved when WriteNow is set as True OutputFileName Example Projecti x CevWriber Iv Auto Create a Source Sine Wave SFO and connect it to Writer CsvWriter to save the data to csv format Click on the Properties Writer OutputFileName field and a button will appear at the right hand side of the field Click on the button to enter the name for the file and the location to save the file Enter the file name as sine and save the file to the location C directory P r El Writer WriEeMow False OutlputDireckary C Program Files AnC AD Mi QutputFileWamne OutputFileName The output Filen
211. elated Functions oine Wave Merge to Complex Channel Viewer 4 5 Merge to Complex This component merges two real signals to form a complex signal The real part of the complex signal is the 1 input and the imaginary part is the 2 input signal Instruction Let X bo to be a multi channel signal where cx represents the channel j is the signal time axis Also let Y 1 to be another signal where is the signal time axis The number of channels and the data lengths of these two signals may be different The output signal of Merge to Complex for these two signals is c_ref m a p 9 4 i y where c ref and mrepresent the number of channels and data length respectively If the reference signal is X we have c ref cx m j The sampling frequencies of the resulting complex signal is identical X Properties This module accepts input of Signal which could be real number single channel or multi channel Regular or Indexed Audio which could be real number single channel or multi channel Regular and Numeric which could be real number single channel or multi channel Regular or Indexed The property of Reference Input is used in case when the number of channels of input signals is different or the time axis is different The users need to select one input signal as time axis reference for the output signal The default value is O which means that the output reference is the 1 input signal
212. ent of the hypnic physiological signal including the EEG the ECG and the EOG etc is shown as below The hypnic EOG signal is shown as below 0 5000 10000 15000 20000 25000 time sec Processing the EOG signal by the Rolling MSE and watching the variation of the MSE over time EOG rolling MSE scale n 0 5000 10000 15000 20000 25000 time sec The upper figure of the Rolling MSE is similar with the lower figure of the doctor s judgement result Sleep stage 0 5000 10000 15000 20000 25000 time sec Turning on the demo73_1 C Program Files DynaDx DataDemon demo Enhanced demo73_1 RollingMSE vsn we can see an acceleration signal which measures the vibration of the elevator from the start to the stop Processing the vibration signal by the Fast STFT module the result is viewed by the TF Viewer We can find that there is a stable 20 Hz frequency between the 25 second to the 65 second which are the time points of the vibrations of the elevator Acceleration FastS TFT 200 0 006 150 W 0 004 ax 100 aq D 0 002 50 Ma AAAA A AAA DANA nr E d D d 10 20 30 40 50 60 70 time sec 7 J af S And then processing the signal by the Rolling MSE we can find that the MSE value is lower during this time Acceleration Rolling MSE 10 20 30 40 50 BD 7D time sec Related instruction Fast MSE Heferences 1 L Guzm an V
213. eparated by white space character and there are three groups of data one column is one channel CO CO D DO CO CO D CO CO CO 1 Click on the 4 Import data from file button in the Netowork Window Toolbar or open it from right mouse clicking on the Network Workspace to open up the Network Workspace Menu and select Source Open Data The Text Importer will pop up when you have selected the text file to import lets assume the multi channel text file was selected as describe above If you want to import all three data columns then leave the Column option as 1 end TIPS oet the Column option as 2 2 if you only want to import the second data column Data Range Rows to Columns to Data direction Column based Concatenate to one channel Specify Time Column 2 Because the imported data does not contain any time information the Time Unit will be set to seconds and Sample Frequency set as 1000 Time Coordinate Click on the Import button to import the data 2 1a 0331 0 2 4 6 8 10 12 14 16 18 20 22 24 time sec 2 Import a data file which has time information and some missing data values This example demonstrates how to import a data file which has time information included but contains some missing data values Data Range Data direction Column based Specify Time Column B Field Format White spaced Delimeter Mull Value Handle U
214. equality below 0 lt J R R If the two input signals are independent events statistically then R The procedure of calculating the cross correlation of a signal itself i e R is the Auto Correlation Properties This module accepts input of Signal which could be real number single channel Regular and Audio which could be real number single channel Regular Two input signals are required The output format is real single channel Regular signal The lengths of the two input signals could be different However the sampling frequency and time unit of these two signals must be identical Example First create a white noise as original signals and then use part of the data to create another noise signal Next perform Cross Correlation on these two signals and observe the relationship between them 1 Select Source Noise to create a noise Change the Properties TimeLength to 5 sec and use Viewer Channel Viewer to plot the result Project1 X Viewer updated Properties El Noise Noise Type El Source TimeUnit SamplingFreq DaktaLength Amplitude TimeLength Time length in unit Noise 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 time sec 2 Click on the icon of the Noise and then press right mouse button to select Compute Channel Data Selection Change Properties EndPosition field to 3 5 Projecti x Shift updated v Auto gt MN P TOPE Samplin
215. er Replace the Noise signal where the amplitude is between 0 and 10 with a Sine wave The equation of the calculation is written in the Expression field Expression A 1O0 Sin 2 pi 10 D 10 X gt 0 TU Display the output of Math in the same viewer as the input Noise signal and compare the curves Viewer 10 r Au 0 P du Vw A 10 0 1 0 2 0 3 0 4 1 5 0 6 0 7 0 8 0 9 time Sec Related Functions Viewer Mixer Multiplier Source 3 3 5 Diff This component performs subtraction or differentiation operation on two signals Introduction Let X x x xy_ be a length N signal the various difference differentiation is defined as below e Forward difference AS a sex i 1 1 i Divided by the sampling period h the approximate differentiation value is given by e Central difference Dividing the central difference by sampling period the approximation of differentiation can be obtained as follows Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular and Audio which could be real number or complex number single channel or multi channel Regular Settings of related properties are given below Differentiate False m Module The differentiation methods include oimple and Symmetrized Simple is 2 points forward difference while oy
216. er Prajeck1 WavelWriter updated I Auto gt Related Functions Noise Sine Merge to Multi channel and Convert To Audio Chapter 8 Macro and Container oignal Flow Objects 8 1 Macro Professional Only Macro allows user to save all current Signal Flow Objects SFOs and their network relationship with each other into a macro file so that the same SFOs can be recreated in other projects by opening the saved macro file By utilizing this feature available in the professional version users can save a lot of time without repeating the same process of recreating the same SFOs over and over again Example Evaluating a Noise Wave 1 The Signal Flow Diagram between the SFOs is shown below Viewers updated Q Q S SS RS SES SS SSS SESS SES SESE SEES ESSE EEE EEE EEE EE EE 2 user can save the current SFOs setup into a macro file without the need to save the project Go to the main menu and click on File and then click on Save Macro to save it to a file In the example the macro file is saved as testMacro TIPS It will be easier to locate macros if you save macros into the Macro folder directory or save the file with a macro prefix or suffix in its file name GAH D Macros o 2 tai Sura hoch A Suec ar BAEN E aue FB A Layout Ctlt N Chl Cili Chr 1 1 ATF o Visual signal Network ven Tras
217. er Viewerz updated Auto gt TestData ToMulti 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 time sec Related Functions Noise Sine Channel Viewer 4 7 Split Complex This component splits the real and imaginary part of a complex signal or numeric data Introduction Let 7 zo be a multi channel complex signal where n represents channel j represents the time axis x Lbh i represents the real part and represents the imaginary part Therefore z is denoted as VA x The output signal of Split Complex is S777 RAZ X S Im Z zY 1 lt n where the odd channels in output signal S save the real part X and the even channels save the imaginary part Y All channels are real data Properties This module accepts input of Signal which could be complex number single channel or multi channel Regular or Indexed Audio which could be complex number single channel or multi channel Regular Numeric which could be complex number single channel or multi channel Regular or Indexed The output is real multi channel data Example With sampling frequency of 1000Hz length of 1 second and amplitude of 1 a sine wave and a white noise are chosen as input signals to generate a complex signal by FFT Then perform Merge to Multi channel and use Split Complex to split it into real and imaginary parts 1 In Network Window use Source Noise and Source Sine to generate a
218. ercome problems related to nonstationarity and nonlinearity Novak et al 1 recently developed a novel computational method the Multimodal Pressure Flow MMPF technique to analyze the BP BFV relationships during the Valsalva maneuver Unlike conventional approaches that are based on the Fourier transform and thus require linearity and stationarity of the signals the MMPF analysis does not rely on these assumptions Instead the MMPF technique evaluates autoregulatory dynamics based on instantaneous phase analysis of BP and BFV oscillations The MMPF analysis applies the Empirical Mode Decomposition EMD algorithm proposed by Huang et al 2 to decompose complex BP and BFV signals into multiple empirical modes Each mode represents a frequency amplitude modulation in a narrow frequency band that can be related to a specific physiologic process As a result MMPF analysis not only can be applied to protocols such as the Valsalva maneuver and sit to stand conditions where large BP and BFV oscillations were induced by the interventions but can also be used to study spontaneous oscillations of BP and BFV under resting baseline conditions 3 Blood pressure Blood flow velocity 80 150 F F S 120 5 E gt a 90 0 30 60 90 120 0 30 60 90 120 Time sec Time sec 80 150 T 60 g 120 5 E 40 a 90 T e e 0 0 30 60 90 120 0 30 60 90 120 Time
219. ere a he k d f aft UIN du CUP 181 wA N D 2 4 B 8 10 12 14 16 18 time sec And then decomposing the mixing signal by the ICA the result is shown below Switch ToAudio 0 2 4 b B 10 12 14 16 18 time Sec Switch ToAudia B 10 time Sec References 1 Independent Component Analysis by by Aapo Hyvtirinen Juha Karhunen and Erkki Oja A Wiley Interscience Publication 2 E Bingham and A Hyvarine A fast fixed point algorithm for independent component analysis of complex valued signals Int J of Neural Systems 10 1 1 8 2000 3 A Hyv arinen A family of fixed point algorithms for independent component analysis In Proc IEEE Int Conf on Acoustics Speech and Signal Processing ICASSP 97 pages 3917 3920 Munich Germany 1997 4 A Hyv arinen Fast and robust fixed point algorithms for inde7endent component analysis IEEE Trans on Neural Networks 10 3 626 634 1999 5 Z Koldovsky P Tichavsky and E Oja Efficient Variant of Algorithm FastlCA for Independent Component Analysis Attaining the Cram r Hao Lower Bound IEEE Trans on Neural Networks Vol 17 No 5 Sept 2006 3 9 Matrix Professional Only 3 9 1 Matrix Operatoin This module does calculations between two maxtrices A and B 4 Ba h Matrix Addition A and B have same dimensions M a j b Matrix Subtraction and B have same dimensions M i B gt dis hy Matrix Multip
220. ernal api cs VSignalExternalDllIDemo Properties ExternalPath C Program Files AnC AD Visual Signal Module demo0 LocalCopy False SystemCopy False DllProperties Info Demo 2 v1 2 2 0 Multiplier 1 1 Multiplier 1 Propert Default Property Definition Name Value External Path The directory to the external DLL None Module Select module in the external DLL None LocalCopy _ If True copy DLL file to local project False SystemCopy True copy DLL file to DataDemon special folder False C Program Files DynaDx DataDemon External Auto name Set the name for the external modue automatically True Properties of DLL which implemented by the user or API Version etc DIIProperties None Example Start Compute External ExternalDIl and open ExternalDlIDemos dll in ExternalDLL path C Program Files DynaDx DataDemon External External ExternalDllDemos dll There are many modules in the Property Module as shown below Property Ix El External ExternalPath C Program Files AnCAD Visual Signal Ne DIlProperkies Module YahooSkacks Select module demo1 In the DilProperties Multiplier1 is the weight factor for the 1 signal and Multiplier2 is the weight factor for the 2 signal The sum of both weighted signals is the output Property ExternalPath C Program Files AnCAD Visual Signal External Module demoli LocalCopy F
221. esis or the maximum of High the confidence interval Run Count Refer to Introduction this value represents the R in Runs Test Above Threshold The amount greater than the bound threshold Below Threshold The amount smaller than the bound threshold z Value This only appears in Runs Test the value for Z Z Test Properties Hypothesis Test View Test Results Hypothesis Tests TestType z Test Mean Sigma 1 igniFicanceLevel 0 05 Hypothesis Mull Module Property Name Definition Default Mean Set the average 0 Sigma Set the standard deviation 1 oet the criterion to reject the null hypothesis the proportion under normal distribution The most commonly oignificanceLevel used values are 0 1 0 05 or 0 01 The smaller the 0 05 significance level the harder it is to reject the null hypothesis Test methods Null two tail RightTail right end where the average input data must be greater than the sample Hypothesis Null mean LeftTail left tail where the average input data must be less than the sample mean T Test Properties il x El Hypothesis Test view Test Results Hypothesis Tests TestType E Test Mean 0 SigniFicanceLevel 0 05 Hypothesis Mull Module Property Name Definition Default Mean Set the average 0 SignificanceLevel Set the criterion to reject the null hypothesis the 0 05 proportion under normal distribution The most commonly used values are 0 1 0 05 or 0 01 T
222. etting m Efx Channel Nane Line Color Line Width Line Style Marker Style SineCHI Seco v v x Zoom in the result in Chanel Viewer as below Viewer 2 Add these two signals to form a new signal As shown below in the Network use Compute Mathematics Mixer to perform the signal mixture The first input to Mixer is Sine the second input is Square and the corresponding properties are Gain 1 and Gain 1 respectively Both have default value of 1 Next use Viewer Channel Viewer to plot the Mixer wave Viewerz updated Auto gt Properties x El Mixer i3ain1 1 s Gains 1 aain 1 2 Module Mixer 2 0 2 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 time sec 3 Now use Data Viewer to check the sampling frequency and duration of the output signal from Mixer The sampling Frequency is 300 Hz The signal starts at 0 second and ends at 1 63333 second The computation method in Mixer uses the duration of mixed input signal as the total duration selects the minimum sampling frequency from the input signals and adds all signals after they are multiplied by corresponding weights Therefore to use Mixer special attention must be paid to the sampling frequency of input and output signals Viewer updated Auto gt Bc Project Mirer Channel Information Histogram Channel 1 Notice that more than 3 groups of data can
223. ex a number indicating the point on the graph the second column is the X Value and followed by the different channels CH1 Channel 1 CH2 CH3 etc In the image below there is only CH1 available 6 203185303045 0 000251327409 0 Dnn5654856547 The values in the Table of Data are dependent on the configuration of Graph B in Graphic Information As the position of Graph B is moved the changes will also be updated in the Table of Data Channel Information is located on the right hand half of the Data Viewer window Channel Information displays the statistical information of the SFO The Histogram is a bar chart representing a probability distribution and the information is divided into 21 bars Histogram Channel 1 Data sampling Frequency 1000 Data Count 2001 Time Length 2 Init SEC E Data Channel Channel Count 1 Channel Channel 1 0 99999792 Max 1 0 01407522879077036 SIL Deviation 0 71090 0992466514 Below the Histogram graph there is the Data and Data Channel information The information shown here cannot be edited TIPS If you wish to edit this information you will have to go back to the Network Workspace to select the SFO and edit the values in Properties In the Channel field you can select the Channel to be displayed through the drop down menu 2 Spectrum Click on a Spectrum source SFO and click on the Data Viewer button will open a Data Viewer with 6 additional b
224. f Signal which could be real number or complex number single channel or multi channel Regular or Indexed Audio which could be real number or complex number single channel or multi channel Regular XY Plot Viewer and Channel Viewer are very similar with the difference being that there are more variable options for XY Plot Viewer Default Property Name Property Definition dnd Value MaxPointCount number of points tobe drawn Example Example 1 Sine Wave is drawn on the axis and Triangle Wave is drawn on the y axis and then use the XY Plot Viewer to display the graph 1 Create Source Sine Wave and then create Source Triangle Wave and connect both signal data to Viewer XY Plot Viewer Project Project2 Project Project x X Y Plot updated Sine e a 0 8 0 6 0 4 0 2 0 0 2 0 4 0 6 0 8 Sine Example 2 Create a Brownian Noise and a CustomWave and calculate them using Kernel Smoothing Density Now connect both signal data to a XY Plot Viewer to display the graph 1 Create Source Noise and change its Properties Noise NoiseType to Brown Then create Source Custom Wave and set its Properties Source Expression to sin 2 pi 10 t 3 t t Connect both signal data to a Conversion Merge to Multi Channel and then connect it to Viewer Channel Viewer to display the data Projecti Viewer updated Noise ToMulti time sec 2 The
225. f the input output data Module El Teager ype TEO he Property Name Default Property Definition Value setting the type of the output TEO Teager Energy Operator InstantAmplitude or InstantFrequency OutputType TEO Example Generating the signal with the Source Custom wave setting the sampling rate to be 1 and the TimeLength to be 200 the Expression is 1 0 25 cos pi t 100 cos 0 2 pi t pi POW t 100 2 4000 EH Module O Source TimeLIniE Sec TimeLength 200 SamplingFreg 1 DataLength 201 TimeSEarE Expression 1 0 25 cos pi E 100 cos 0 2 pi E pi pow E 100 2 4000 CustomvVave 0 20 40 60 80 100 120 140 160 180 200 time seg Analyzing the signal with the Teager module setting the output type to be the TEO the result is viewed by the Channel Viewer as below Viewer 0 20 40 60 BO 100 120 140 160 180 200 time seg If the output type is the InstantAmplitude the result is viewed by the Channel Viewer as below Viewer D 20 40 60 100 120 140 160 180 200 time sec If the output type is the InstanceFrequency the result is viewed by the Channel Viewer as below Viewer 20 40 60 80 100 120 140 160 180 200 lime seri 3 8 9 Rolling MSE The Rolling MSE is the analysis method that makes the MSE computation for the signal transplates the watch window of the MSE to repeat this computation and draws 3D Time ScaleEntropy Plot
226. ful to determine which is which when there are multiple signals on one graph You can change the Channel Name Line Color Line Width Line Style and Marker Style to improve the presentation of the graph and customize the looks according to your need F Plot Element Setting ioj Display Channel Name Line Color Line Width Line Style Marker Style Sine CHI gH iv Sine CHI m F Display Hide All Done Cancel Apply 4 Title P r m El Title m ern Title default YTitle detault Title Flot Title Property Default Property Definition Default Title Change the title of the graph name of the input SFO Xtitle Change the title of the x axis Ytitle Change the title of the y axis Example None A demonstration of how to use the Audio Player 1 Create Source Sine Wave and connect the Sine Wave SFO to Conversion Converter To Audio to turn the Sine Wave signal to an Audio file Then connect the Converter to Audio SFO to Viewer Channel to display the graph and the audio component on the Visualization Window Viewer updated Sine ToAudio ii a B 0 002 0 004 0 006 0 008 0 01 0 012 0 014 0 016 0 018 0 02 0 022 time seci 2 Change the Properties Source TimeLength of the Sine Wave SFO to 10 Properties Module Source TimeLlIniE TE io 1 SamplingFredq 1000 DataLength 10001 SignalFreq 10
227. g dialog ad MMPF Auto Macro x Data Files EF D Hork DataDemon LiGong clMPF Baseline EP_O1 txt BFVI D Work Dat aDlemon LiGong cMMPF Baseline BF_O1 txt 2 WorkhatallemonhLiGonghcMMPF Bazeline BF 01 txt ua Farameters Sampling Frequency Hz Down5ample Step Output Output C Wsers LuiDesktop Directory Cancel Continu BFV1 is the input of left BFV If there is no right BFV you can use BFV1 as the input of the right BFV Set the parameters and the Output Directory and then click Continue The Signal Flow Diagram between the SFOs is shown below By selecting Viewer m SFO the wave of signal is shown If DataWriter m SFO is selected data is written in the Output directory The parameters of RCADA EEMD m SFO can be modified and the corresponding IMFs can be selected Related Functions RCADA EEMD Hilbert Transform FFT Chapter 4 Format Conversion Signal Flow Object 4 1 Change X Axis Unit After reading in the signal data the time unit of the data usually needs to be changed In this case Change X Axis Unit can be used to convert time directly In addition to time unit conversion this module can also convert the spectrum axis i e the X axis from frequency to period Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular and Audio which could be real number or complex n
228. g i il oi A on NM UA 10 time sec By modifying the Frequency Resolution to 75 the original value is 225 the result is as below sound003 FastSTFT frequency Hz 0 2 4 6 8 10 12 14 16 18 time sec We can find that the frequency resolution is better the seismometer data The seismometer signal has 8 million points If the signal is processed by the standard STFT the 3G memory is not sufficient Execution of STFT has consumed too much memory Please use Resample or Dataselection to reduce input data After the interpolation and the RemoveBump process the result is as below bumpedDARBseason1CHO 4 56948 0 Aa 4 6942e 07 25 30 35 40 45 50 55 time day After linking this signal to the Fast Trend and then the Fast STFT using the default setting the result is shown as below bumpedDARBseason1CHO FastlGaussFilter F astS TF T 40000 30000 25000 20000 15000 10000 sume L lt 17 LELLI NEDINTIIDLTTLIJUALSLISS frequency cycles per day 0 25 30 35 40 45 50 55 time day We can find that the low frequency is not filtered off completely so the trend frequency of the Fast Trend is tuned to 3000 The result is shown as below bumpedDARBseason1CHO FastlGaussFilter F astS TFT 0 25 30 35 40 45 50 55 time day We can get the signal in the range of 10000Hz to 40000Hz by resetting the FreqMax and FreM
229. g period Ar output signal and replaces the time axis T with 7 The formula for T is jxAUD 1S ja N 1 Therefore the output signal from RemoveGap has the same number of data points as the input signal However uneven intervals in the input signal are changed to even intervals Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Indexed The outputs are Regular signals which are real or complex single channel or multiple channels E Convert To Regular CConvertMethad FillGap FillMethad LinearInterpolation sampling Period 1 37199000900909005775 Unit sec AutoDetect True Module Sampling Period specifies the sampling period Default is automatically determined from the input data Property of AutoDetect provides the option to set Sampling Period of the output signal manually If it is set as True this module would detect the minimum sampling period of the input signals automatically and use it as the Sampling Period If AutoDetect is set as False user can set the Sampling Period manually Because a large sampling period would cause discrepancies between the output signal and the original one the manual setting of the Sampling period must be less that 1 5 times of the sampling period obtained by AutoDetect Property of IConvertMethod allows users to select FillGap or RemoveGap to calculate the time axis of the input signal If FillGap i
230. gFrequency Dakar aunt Data Selection StartPosition EndPasitian Mew aunt Module Select the Compute Channel Time Shift to connect with the Selection SFO Change Properties Shift Value to 1 5 which shifts the data in 0 3 5 seconds to 1 5 5 second Projeck1 x Shift updated Properties Sampling Frequency Data Length Datalnit Umit Module Time Shift ShiftstarktTime 5hiFEvalue 1 5 Selection Shift 2 5 3 time sec 3 5 4 4 5 5 4 Create another noise signal that the TimeLength is 1 5 seconds Use Compute Channel Mixer to mix the original noise and the one processed by Time Shift to obtain the second signal And then use Channel Viewer to plot the result Mixer 2 2 9 3 3 5 4 4 5 5 time sec 5 Perform Cross Correlation on the Noise signal and the output signal from the Mixer Then use Channel Viewer to plot the result crosscorrel Noise Mixer Corr 1000 500 5 4 3 2 1 0 1 2 3 4 5 time sec The above figure shows that the strong correlationship between siganl 1 and signal 2 at 1 5 sec Essentially the data of 1 5 5 second in the 2 signal and the data of 0 3 5 second in the 1 input signal are identical Therefore this result is consistent with the characteristics of these two input signals Related Functions Auto Correlation Data Selection Mixer Time Shift 3 6 7 MSE MSE is the abbreviation for Multisc
231. ght half is where the Channel Information is shown e g sample frequency data count time length and unit All three sections will show different information based on the type of SFO selected Graphic Information Channel Information M Channel Information Histogram Channel 1 0 99999989 0 99999822 0 99999101 0 99997158 0 99993061 m Table of Data On the top left corner of the Data Viewer there are two buttons 9 Close Tab and 3 Close all tabs A Data Viewer can open many SFOs and the multiple Data Viewer profiles will be displayed as tab menus under the Close Tab and 99 Close all tabs buttons Click on X Close Tab to close the current Data Viewer profile and click on Close all tabs button to close all Data Viewer profiles Note Data Viewers content will not change with a new update of a SFO To view the latest update of a SFO in Data Viewer you must close the Data Viewer profile and reopen it again in the Data Viewer The following will explain the different types of Data Viewer interface based on the different types of SFOs 1 Signal Graphic Information is where the graphs are drawn and the graphs are drawn based on X axis time and Y axis There are two graphs the top Graph A displays the whole graph that is plotted along the X axis The bottom graph Graph B can be a detailed zoomed in version of the top graph and the area shown in Graph B is the section between the two vertic
232. gnal Mixer 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 3 Perform Compute Transform Discrete Cosine Transform on the output generated by Mixer and plot the result using Channle Viewer It is shown that the signal spectrum mostly concentrates in the low frequency range Mixer DCT 0 50 100 150 200 250 300 350 400 450 500 frequency Hz Projecki x Viewers W Auto gt m 4 Final perform Compute Transform lInverse Cosine Transform to convert the signal back to the original wave Ec Hi 9 9 Projecti Mixer DCT IDCT 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 time sec Related Functions Fourier Transform Viewer Reference http en wikipedia org wiki Discrete cosine transform 3 6 3 Haar Wavelet Transform Haar Wavelet is the first published Wavelet function proposed by Alfr d Haar Harr wavelet is the simplest orthogonal wavelet which is the fundament of binary wavelet transfrom However because it is not a continuous function its performance is not the best as a fundamental wavelet Introduction The mother wavelet of Haar Wavelet can be denoted as follows w t 4 1 otherwise Haar 0 5 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec The FFT of Haar is E pens 2 qug plo Haar FFT 0 6 0 0 5 10 15 20 25 30 35 40 45 50 frequency Hz Properties This module accepts input of Signal which could be real number single channel Re
233. gnal When AutoDetect is set to True show the Based on input Unit signal time unit detected signals When AutoDetect is set to False besides showing the signal time unit set the signal time unit by using Sampling Period together Property Name Property Definition Default Value Determine whether to detect sampling Period AutoDetect and Unit automatically If ConvertMethod is set as FillGap and FillMethod set as FixedValue this property would be provided to set the fixed value for data filling NullValue Example 1 Read one set of signal data which are in Indexed format First generate one set of simple data as shown below where the first column is time while the second column is data c2 mom m om Com E E E oco gb oco e 00 ZM Then press the i in the Network tools or use Source Open Data to read a signal file TestData txt Check the Specify Time Column in Text Importer and then press OK Data Range Rows to Columns to Data direction Specify Time Column After reading the signal use Viewer Channel Viewer to plot figures And select TestData to verify the OutputDataType in Properties Module It can be seen that the time axis format is Indexed Viewer updated Auto El Module Name testData Qutpuk Port Side Right Output Data Type landexed 3 hA Output Da
234. gnals DoMatlab defines two variable groups of X1 and X2 where X1 is the sine wave of the signal channel and X2 is multi channel output signal created by EEMD The default variable X is the 1 channel of the input signal We can use the plot in Matlab script editor to plot X and X1 15 DoHatlab Editor Sets Help amp Exemples Matlab script file figure plot x b r hold on plotix ra After typing in the command press l directly or turn off the editor the DoMatlab will start to run As shown below the two signals overlap completely o Figa o2 D m HS AS PEO Dqpoqdeedqeqepqo SHPSS PEE D debra EEE EEE Q wapa dq eqq SEPP SPER AAI D Dp G Qpqppdpppapanes quaqua e Pea E EAER P QI b Hoh p OHSS SPSS EE PORE Qopqppppqeppqpamg PHP PED pE ppa Ea PE eS E p eb Gch bip papae qupd p e Ep EE AA EB D Q Bebb epa PRPS pE pp Eep Eaa qu 3 get the basic information of the input signal enter X2 DESC the command window and press Enter the information of input signal X2 is displayed MATLAB Command Window Signal channelCount 8 channelHames 8812 char lengths 181 starts intervals 68 6818 units sec Formats Regular coords 141001 double
235. gniFicanceLevel 0 05 Hypothesis LeftTail Hypothesis Tests for Noise Lj 2 x Hypothesis Tests for Noise var Test Rejected True aignificanceLevel 0 00468 Cl Loi 0 CI High 8 38 Related Functions Noise Square Basic Statistics 3 4 10 Linear Regression This function is used to compute two groups of signal s linear regression line similar to trend line function in Excel Introduction we can cite linear regression equation y ax b to illustrate the physical model between X and Y The experiment to verify the Hooke s law for instance always measures two kinds of data which are the weight of balance weight and the length of spring Then use these data to compute the elastic coefficient Hooke s law Oo Spring length cm J 2 12 14 16 18 20 9 The black dots represent the data derived from the measurement The blue line is derived from the linear regression computation The linear regression s formula is Spring length 0 0907 Force 4 99 This is the relationship between the spring length and force Compared with Hooke s law the formula can be shown as Force 1 0 0907 Spring length 4 99 Therefore we can figure out that the spring s length is 4 99 cm and its elastic coefficient is 11 02 g cm From this example we can know that it is easy to get the relationship between two groups of data by using linear regression formula A
236. gular and Audio which could be real number single channel Regular Detailed properties are given as follows x Haar Filter Bank Levels 1 Resampling Method MonotonicCubic ARE Resampling Method Choose a resampling method The resultng DWT components will have lengths equal to that of the original Default Property Name Property Definition ai Value The number of orthogonal basis starting from 0 1 means 2 basis 2 means 3 basis and so on Filter Bank Level Resampling Resampling Approximation method Please Linear Method reference to Resampling Example 1 Using all default values to create a square wave and then use Math Mixer to mix one white noise which has amplitude of 0 2 Finally use Viewer Channel Viewer to plot the result Projecti Viewer updated gt Mixer 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 Connect the mixed signal with Compute Transform Haar transform and set the Filter Bank levels to 3 and then connect Channel Viewer to plot the calculation result Project1 x El Haar Filter Bank Levels Resampling Method Linear Module Filter Bank Levels Specifies the number of filter bank levels single level Filter bank Change the Viewer Height in Viewer 2 to 300 for better observation Mixer Haar 8 6 4 2 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Obviously t
237. he signal file chiro1000 tfa in the data folder of installation directory which has a default location C Program Files DynaDx DataDemon data Look in e data My Recent Documents Desktop gt My Documents 48 Bullfrog My Network 100 atr 100 hea 111 E 111 6 fea chir 11000 tfa ej chirp10000 tfa f hello wav multi tfa smile tfa si test1 tfa 9 test2 tfa ei test3 tfa 8 test3_NaNe2 tfa test3_NaN tfa 9 test4 tfa File name ea testS tfa lj test6 tfa i test7 tfa test mat tide tfa uf Windows XP mp3 uf Windows XP wav Ed chirp1000fa Files of type Data updated All Suppot Files In Properties it shows that this signal has the SamplingFrequency of 10000 the DataLength of 20001 and the Unit in second Properties El Data C Program Files Channel Count 1 Sampling Frequency 10000 Data Length 20001 DatalUnit Unit Sampling Frequency Sampling Frequency In addition open the Module type in the Properties where the OutputDataType shows the signal format and type of this module output Since the OutputDataType is Real Single Channel Signal of Rank 1 Regular Data the data type of Chirp1000 is Signal Refer to the introduction of Properties in Chapter one for more details TimeFormat Regular O Module n Class DataSource
238. he averaging part Highpass means the compensation park Bypass would be the same as the input Mixer MA 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec Related Instructions oquare Noise Mixer Reference http Awww dspquide com ch15 htm 3 2 4 Iterative Gaussian Filter Professional Only Iterative Gaussian Filter is used to efficiently remove aperiodic components from an input signal Introduction Due to finite observation there usually exists an aperiodic signal in the data If the data is processed directly e g using FFT the resulting spectrum could be wrong Here is a typical example The input data is a Sine Wave FFT gives a single peak spectrum Sine 0 1 2 J E 3 7 a 3 10 time sec cGinge FFT 0 5 hi frequency c Hz However if there exists an aperiodic signal emedded in the Sine wave FFT gives two peak of this data The power at the very low frequency could be larger than the characteric frequency of the Sine wave 20 0 1 2 3 4 5 B 7 8 g 10 time Sec Mixer FFT 1 2 3 4 5 B 8 g 10 frequency Hz If simply remove the low frequency components from the data the spectrum gives the wrong result And the inverse FFT is not correct either There is a better way to achieve this Assume the data can be represented as the sum of a periodic signal and aperiodic signal n 2 1 b sinu pit gt t k i Follow these steps to filter the d
239. he characteristic of square wave is mainly shown in the 4 curve At the discontinous points of the original signal the jump characteristic is also perserved in the 2 and 3 curves significantly In addition noises are mainly shown in the 1 9 curves 3 To preserve the square wave characteristics in the 1 3 curves and reduce the effects caused by noises use Mathematics Math to multiply the 1 2 ang 3 signals and then plus the 4 signal The result is shown below Prajeck1 x Expression A1 UEM 2 1 3 81 4 Input List 1 Mixer Haar X1 1 DWT a1 X1 2 DWT C116 DWT_a3 X1 4 DWT con Math 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Processed in this way the visible noises have been eliminated while the characteristics of the original square wave is preserved 4 Similar to the EEMD the result of Haar Transform could be processed by Hilbert Spectrum to obtain spectra diagram Projecti X Mixer Haar Hilbert Spectrum 180 160 140 frequency Hz AR O Co o e 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Related Functions Mixer Multiplier Fourier Transform Hilbert Spectrum Reference http amath colorado edu courses 4720 2000Spr Labs Haar haar html 3 6 4 Hilbert Transform 1 Hilbert Transform executes convolution on an input signal x t and i e zt el X T part is the in
240. he data contains the titles of the columns so the data has to read beginning at second row Data Range 2 z nne 1 to ena Data direction concatenate to channel Field Forma C White spaced Delimeter Fixed field 1 Mull alue Handle Use Mull Value Handle Linear Interp Time Coordinate sample Frequency 1006 Cycles sec D own sample by 1 Date Axis Enable Start DateTime 20010 i r fos Jos 04 File Conte 15625000 159 59796080 6 229000 3 91603427 3 M3000 2 75641173E 3 10 2 64790928E 3 5 2008 08 20 18 31 11 156410 0 1 11530865 3 2008 08 20 l8 31 11 1564500fB 281 66348551E 6 2008 08 20 l8 31 11 15649008 932 67962356E 6 2008 08 20 l8 31 11 15653008 1 35312781E 3 2008 08 20 l8 31 11 1565700fl 1 86851533E 3 i 2008 08 20 18 31 1566100 3 00101225 3 9000 1 75954332E ae 573000 z 451z4798E 3 Import Cancel LZ If the data is too large then you can increase the Down Sample number to 5 so for every 5 data only 1 will be read Data Range Rows 2 to end coms 1 to end ES Data direction based concatenate to one channel Iv specify Time Column 1 Field Format wire spaced Delimeter Fixed field Mull value Handle v Use Mull Value Handle Linear Interp Time Coordinate
241. he first column to be the time column for the data Data Range Rows to Columns to Data direction Field Format White spaced Delimeter Mull Salue Handle Use Mull Value Handle Time Coordinate Time Unit sec hal b hoo Down sample by 1 2 Date Axis File Contents 001 0 0 625029011 002 0 001 1 01969833 003 0 002 1 089426309 E 004 0 003 0 951247108 005 0 004 1 01094514 006 0 005 0 921051052 007 0 006 0 582346454 008 0 007 1 37403913 009 0 008 1 42303473 l 0 009 1 12348247 011 0 01 0 703217927 012 0 011 1 29116472 O13 0 012 35694005 z Reporter Window Reporter Window is only available when the output data type is numeric Signal Flow Objects such as Basic Statistics Correlation Matrix Covariance Matrix Orthogonal Matrix Qurtiles and Quantiles can open the Reporter Window to displays statistical information based on the data calculation The Reporter Window can be accessed through clicking on the button on the Properties View Statistics Basic Statistics View Statistics Basic Statistics for Noise C Unbiased Moment Estimation True Trim Fraction 0 05 Trim at Ceiling False lt View Statistics Display the basic statistics There are two options and a refresh button at the top of the Reporter Window The first option is the way the decimal numbers are displayed The default is General decimal display and
242. he format of the output is real single channel spectra of regular data The properties are defined below Properties propertyGrid igz E Hilbert Spectrum FregMin 0 FregMax auto 500 FregCount 256 TimeCount 1024 Inst Freq Method Simple Smoothing True Module Fregktin The minimum frequency of the hilbert spectrum Propert Property Definition Default Value Name FreqMin Set display minimum frequency of Hilbert Spectrum 0 FreqMax Set display maximum frequency of Hilbert 0 5 Sample Spectrum frequenca FreqCount Set grid count of Hilbert Spectrum along frequency 256 axis TimeCount Set grid count of Hilbert Spectrum along time axis 1024 Inst Freq Method to calculate instaneous frequency Simple Simpl Method or Barnes Please refer to Hilbert Transform Smoothing Apply Gaussian function to smooth the curve True Example Click S button in Network tools or use Source Open data from file to read signal from a file The file is chiro1000 tfa and it is located at demo directory of the installation The default location C Program Files DynaDx DataDemon demo Basic then show the data with Viewer Channel Viewer Chirp 10000 0 2 0 4 0 6 0 8 1 1 2 1 4 1 8 18 2 time sec Connect Chirp 1000 to Compute HHT RCADA EEMD for calculating IMF Intrinsic mode function and display the results using Viewer Channel viewer EMD Jut Ul TI AM Eu ec Ij VM j vi
243. he next window are signal position 1 to 10 0 3 0 4 0 5 0 6 D 0 8 0 9 1 time sec 9 And there are 9 elements overlap between the 2 windows If p 7 then 12 2 y 0 5 time sec J p 7 The window has 7 position ovelap with the previous range And so on the output length of the series is N p K M p Please note that when m p gt 1 the length of output series K may not be an integer One solution is to round the remainder and keep the result for the complete window N We P floor M p Rolling statistics can be used to calculate statistical values similar to the functions in Basic statistics module and will not be repeated here Properties This module accepts input signals in the formats of real number complex number single channel or multi channel and regular The properties are defined as follows Properties Module El Rolling Statistics Type Window Overlap Type Select a statistics type Properties Definition Default Type Options for statistical calculation detailed list below Mean Set the window size the unit is the number of Window 2 elements for the signal Overla Set the number of overlapping elements for the Window width P rolling window E The options for Type are defined as follows it will calculate the statistics within the window Options Definition Sum Calculate sum Min The smallest number in the
244. he smaller the significance level the harder it is to reject the null hypothesis Test methods Null two tail RightTail right end where the average input data must be greater than the sample Hypothesis Null mean LeftTail left tail where the average input data must be less than the sample mean Var Test Properties x 5 Hypothesis Test View Test Results Hypothesis Tests TestType war Test variance 1 SigniFicanceLevel 0 05 Hypothesis Mull Module Property Name Definition Default Variance Set the variance 0 set the criterion to reject the null hypothesis the proportion under normal distribution The most commonly oignificanceLevel used values are 0 1 0 05 or 0 01 The smaller the 0 05 significance level the harder it is to reject the null hypothesis Test methods Null two tail RightTail right end where the average input data must be greater than the sample Hypothesis 9 E i P Null mean LeftTail left tail where the average input data must be less than the sample mean Runs Test Properties lx 1 Hypothesis Test View Test Results TestType RunsMethod IsExack RunThreshald SigniFicanceLevel Hypothesis Module Hypothesis Tests runs Test AboveBelow True Auto 0 05 Mull Property Name Definition Default RunsMethod AboveBelow UpDown AboveBelow To calculate if the P Value is calculated using the IsExact correct algorithm this parameter only exists when True RunsMethod
245. he starting element for the extraction 0 0 Length of the Vector Length The length of the extraction matix along a direction Example There is a 2 3 matrix A its elements are 0 270 950 15 0 54 0 96 0 97 oet Column Vector to True set Vector Direction to O row direction the starting point is 0 0 and the length of extraction is 3 The resulting vector is 0 27 0 54 References Gilbert Strang Linear Algebra and Its Applications 3rd edition 3 9 6 Diagonal Vector This module extracts diagonal elements from a square matrix and outputs as a vector Properties This module accepts real number complex number and Numeric data And the output has the same format as the input E Diagnal Vector Column Vector True H Module Property Name Property Definition perty Value If true the output vector is column based Column Vector True Otherwise the output is row based Example Use DoMatlab to create a 3 3 random matrix the elements are 0 03 0 67 0 39 0 84 0 75 0 65 0 93 0 74 0 17 Extract Diagonal Vector and get a vector of 0 03 0 75 0 17 References Gilbert Strang Linear Algebra and Its Applications 3rd edition 3 9 7 Reciprocal Matrix Condition Number Calculate 1 C where C is the Condition Number of the matrix Introduction For a given matrix A the Condition Number of matrix A is defined as qd C can be measured with or which are cal
246. hesis sample differences are true diffences and influenced by some non random cause gt 1 Z test In Z test is the average of the samples is the polulation mean 9 is the population standard deviation n is the sample size x u T EL 2 T test s yn In T test is the average of samples is the average of controls is the standard deviation n is the sample size During the testing if you repeat the tests many times the experiment results will show a normal distribution of the mean below To test whether the results of a particular experiment has random errors we can use Z test or T test to calculate the location of the mean in the normal distribution The researchers hypothesize the criterion to rejecte the null hypotheses based on the percentage of area under normal distribution or significance level then follow the test method of Null two tail RightTail right end and LeftTail left tail below to determine whether the results fall into the rejected experimental average range X u 2 S8 c lLo4sc u 1 645 __ 2 58 _ yr y x X 11 96 60 tau 190 Samples 95 Samples 99 Samples X H Hs Xp X Rejection 34 4cceptian t Rejection Low Bound High Bound fx X H x H H x Rejection Arcception Acception 3 Rejection Bound Threshold Bou
247. ide of the point has a different sign than that of the slope on the other side Creating an envelope Envelopes are generated by connecting a series of points with a smooth curve in this case the cubic spline interpolation is used Here envelopes come in two varieties an upper envelope in which the local maximum extrema are interpolated and a lower envelope where the local minimum extrema are interpolated Ideally the envelopes should encompass but do not cut into the data Assembling a local mean This mean is created by averaging point by point the upper and lower envelopes Creating an IMF candidate This is done by subtracting the local mean from the original signal The result is an IMF candidate it may or may not actually be an IMF otopping Criteria These rules are used to test if an IMF candidate can be considered as an IMF This consists of two checks first to see if the signal meets the definition of an IMF and seconaly if the signal has been sifted enough times Sift Completion of a set of all the steps above regardless if an IMF is found or not is called a sift Creating the residual If the stopping criteria are satisfied the IMF is subtracted from the original data to create an interim residual Then this residual is put through a subsequent sifting process These combine an EMD Flow Chart EMD Sift Step by Step as follows Input Data kesidual Parent Find Maximum Extrema 1n Parent
248. ile Number StdDev Standard Deviation Variance Variance VarianceCoef Variance Coefficient Skewness skewness Value Kurtosis Kurtosis Value semiVariance SemiVariance SemiStdDev SemiStdDev oome of the options may need to set parameters Quantile is explained in Quartiles and Quantiles section The rest of the options is detailed in Basic Statistics section Example Calculate different Equiphase Statistics values using a Brownian Noise Create a signal by right clicking Source Noise in Network panel and set Properties Noise Type to Brown Display the signal using Viewer Channel Viewer Properties MoiseType Source TimeLlIniE TimeLength 0 0 1 02 0 3 0 4 0 5 0 8 07 0 8 08 1 time Sec Connect Noise SFO to Compute Statistics Equiphase Statistics the default type is Mean Set Properties Period to 0 1 It means the period is 0 1 second The mean value of each element within the period is calculated Display the result using Viewer Channel Viewer Properties El Equiphase Statistics Perd 1 Period Start Time Unit Sec Type Mean Period Specifies the period The resulting output signal will have the Noise EquiphaseStat 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 time sec Change Type to Third Quartile The elements of the 3 quartile position in the period are calculated P In B The E Equiphase Statistics Period 0 1 Period Start 0 Time Uni
249. ime domain based decomposition and does not make assumptions on the stationary and linear properties of the signal By eliminating these assumptions and using the Hilbert Transform to obtain the instantaneous frequency sharper resolution in the frequency domain can be obtained compared to conventional methods In order to use the Hilbert Transform to obtain meaningful results it is mathematically necessary to have data that are locally symmetrical with respect to the y axis zero line In such data the rising side of a wave is relatively similar to its descending side and vise versa Applying the Hilbert Transform to unsymmetrical data yields several paradoxes that were defined by Cohen To avoid these issues the concept of an Intrinsic Mode Function IMF was developed which satisfies the necessary condition for obtaining the meaningful values of instantaneous frequency The technical definition of an IMF is a signal in which the number of local extrema and the number of zero crossings should be the same or at most differ only by one This rule implemented with the EMD produces IMFs with well defined instantaneous frequency Algorithms Empirical Mode Decomposition Algorithm The EMD process can be divided into several stages which consist of the following specific steps Finding local extrema Local extrema are sections of data that can be considered a local maximum or local minimum They are the points where the slope on one s
250. in The result is shown as below bumpedDARBseason1CHO FastiGaussFilter FastS TFT 40000 35000 MEA 1111 ELA HL UN Ai LUN i MI T 30000 F 25000 frequency cycles per day 15000 10000 time day We can find that the frequency resolution is not good By tuning the Frequency resolution to 500 the original value is 2500 the result is modified as below bumpedDARBseason1CHO FastlGaussFilter F astS TFT AUS SUN V a UM 1 VN iN i y VO f l v Aha m NER a NOR 0 2 mam Hey hi i ia MADERA Urn aUe of ud UM u Se a d ios REPE b TUM MA 3 EUM ALTER 0 1 2 time day Comparing the results of the First Order and the Second Order Generating the Sine signal by the Source Sine Wave and then linking it to two FastSTFT the result is shown by two TF Viewers The YValueType of the TF Viewer is set to Gain From the TF Viewer we can find that the computed amplitude of the Second Order is less the First Order in the high frequency 1st Order 500 400 200 200 frequency Hz 100 0 0 1 0 2 3 0 4 0 5 7 0 9 1 time sec 2nd Order 500 400 200 frequency Hz 100 0 0 1 0 2 0 3 0 4 0 5 0 7 0 9 1 time sec Analysing the data including Noise by the Fast STFT and the standard STFT Projecti x The
251. indow Properties Window and Visualization Window The positions of these three major sections can be customized You can drag and drop each individual window onto any part of the Ul or even combine the windows so they can be viewed through the display tabs To drag and drop a particular window move the mouse pointer to the top bar of the display window and left click and hold down the mouse button to drag During the process of drag and drop position icons such as Top Bottom Ld Lett Right Expand and r Tab will appear Drag and drop the mouse over to one of the position icons so the window will change according to the position icon selected 9 Data Demon 1 0 powered by Yisual Signal Beta File Edit Layout Tools Help P P PP A tal Al Project E EnMorlet updated Double click the top bar of a section display window to detach the window from its current position and it will appear in front of the other section windows as shown in the image below Double click the top bar of the section display window again to restore the detached window to its original position File Edit View Layout Tools Help 1 a oB PPD P 192 ES Project Bs Ax Project EnMorlet updated Q Q p
252. inear and Non Stationary Time Series Analysis Proceedings of the Royal Society Vol 454 No 1971 1998 Huang N E M L Wu S R Long S S Shen W D Qu P Gloersen and K L Fan 2003 A confidence limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis Proc Roy Soc London 459A 2317 2345 3 8 Enhanced Professional Only Fast Short Term Fourier Transform STFT s fast version with less memory requirement Hemove Bump Hemove bumps or jumps from the signal and connect them with smooth line for recovering the original signal Fast Trend Estimater Trend Estimater s fast version Fast Iterative Gaussian Filter Iterative Gaussian Filter s fast version Fast MSE MultiScale Entropy s fast version Peak Detection detect the peak position of the signal or compute the time difference between the peaks R R interval Compute time difference of two R waves of the ECG signal Teager Compute the instantaneous frequency and amplitude of the signal Rolling MSE Viewing the variation of the amplitude by different time and scales PCA decompose the composite signal to single signals ICA decompose a composite signal to a statistical independent signal 3 8 1 Fast Short Term Fourier Transform The Fast Short Term Fourier Transform has the same functions with Short Term Fourier Transform but is faster than the original version Introduction This module is the fast version of the STFT in terms
253. input data CH NBP NBV1 1 CH NT each mode for BFV2 Mode 1 is the raw input data If BFV2 input exists Row 1 NBP CH NT 1 Row 2 NBV1 Row 3 NBV2 If there is no BFV2 input 1 2 Select output for MMPF Column Variables Description CH1 IMFmodeBP Chosen mode for BP CH2 IMFmodeLBFV Chosen mode for left BFV CH3 IMFmodeRBFV Chose mode for right BFV If input BFV2 exists To testify whether there is huge CH4 annoT BP instantaneous frequency jump for BP 0 number of bad points gt 10 To testify whether there is huge CHS annot_LBFV instantaneous frequency jump for LBFV 0 number of bad points gt 10 To testify whether there is huge CH6 instantaneous frequency jump for REB RBFV 0 number of bad points gt 10 If input BFV2 exists CH7 cycleL sec Period or length of the cycle Estimated mean phase difference over each cycle for BP and LBFV CH8 phaseshiftL Estimated mean phase difference CH9 phaseshiftR over each cycle for BP and RBFV If input BFV2 exists The number of points of the phase difference berween BP and LBFV CH10 for consecutive two samples data points are over O 8pi or under 0 8pi The value should be equal to 0 The number of points of the phase CH 1 1 errorR pts difference berween BP and RBFV for consecutive two samples data points are over 0 8 or under 479 0 8pi The value should be equal to 0 If BFV2 input exists CH12 The ratio of
254. installation directory the default directory is C Program Files DynaDx DataDemon data 100 atr 8 test5 tfa 100 hea I testo tfa MyRecent 3 111 tfa 9 test7 tfa Documents 7 111 bxt test mat chirp1000 tfa fi tide tfa a chirp10000 tfa d Windows XP mp3 A hello wav uf Windows XP wawv multi tfa smile tfa s test1 tfa fi test2 tfa fj test3 tfa test3 NaN2 tfa j test3 NaN tfa 9 test4 tfa E File name ck My Network Files of type Al Suppot Files IM Cancel 2 Click on the Chirp 1000 SFO whose Properties show that the number of channels Channel Count is 1 and the sampling frequency is 1000Hz Next use Viewer Channel Viewer to plot this signal It can be seen that the signal frequency increases with the time increasing Projecti x viewer updated E Data File Mame C Program Files AnCAD Visual Sig Channel Caunt 1 Sampling Frequency 1000 Data Length 2001 Starkvalue D aballniE Unit TimeFarmat Chirp 10000 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec o gt X Select Compute TFA Short Term Fourier Transform to perform STFT on this signal and use Viewer Time Frequency Viewer to plot the result Observing the time frequency diagram it can be seen that the signal frequency varies lineally with time From the result the frequency at a given time point is available Prajeck1 X TF Viewer updated
255. ion visit www mathworks com zi Ready NUM 2 Note that MATLAB which is a product by MathWorks must be installed in the System before DoMatlab could be run If DoMatlab fails to run even after Matlab installation the reason most likely is that the MATLAB is not registered as COM server To solve this issue on WINDOWS systems type cmd in START RUN window to startup the command line console Run Ei Type Ehe name of a program folder document ar Internet resource and Windows will open it For vou Open snm Cancel Browse Next type matlab regserver in the command line and hit enter The issue should get fixed now cy C AWINDOWSAeystem 2wmid exe PERIERE UP T7 E12 m If the issue persists please try the following two steps e Right click Properties on My Computer System Properties window pops Choose Environment Variables at the bottom of Advanced tab Then click New button for User Variables and add New User Variable Variable name MATLAB RESERVE LO Variable value 0 Select Path under System variables panel then click Edit and add string C Program Files MATLAB R201 Oa bin win32 to Variable value entry The string is the installation path for Matlab please change it accordingly Properties in DoMatlab are shown in the figure below and the corresponding definitions are listed in the table below E DoMatlab MatlabEditor 09 Matlab script
256. is example below shows the procedure to mix a sine wave and a square wave with different time axis 1 Use Source Sine Wave to create a signal with frequency of 5Hz sampling frequency of 1000Hz and duration of 1 5 seconds And then create a square wave with frequency of 10Hz sampling frequency of 300 Hz duration of 1 3 seconds and time starting point of 0 333 second Next use Viewer Channel Viewer to observe the wave Sine properties are shown in the table below El Source Timel nik TimeLength SamplingFreg DataLength SignalFreg Amplitude Arniplitude rset Phase Symmetry TimeStart TimeLength Time length in unit Square properties are shown in the table below El Source TimeLlni TimeLenath SamplingFreq DataLength SignalFreg Amplitude Arnplitudecrrset Phase Symmetry TimeStart TimeLength Time length in unit SEC 1 3 300 391 10 0 5 0 333 sec 1 3 300 391 10 0 5 0 333 gt 4 gt 4 Viewer NTL time sec 0 0 2 Select PlotEditor in the Properties Representation Plot Elem Editor in Channel Viewer In the popped up Plot Element Setting window add o to Sine curve X to Square curve and use tool of Zoom X to enlarge the onverlapping point of these two signals It can be seen that the signal data point distributions along X axis time axis are completely different Settings of PlotEditor are given as follows ESI Plot Element S
257. is identical to those in Triangle Because there are 1333 data points in Triangle while there are only 1001 data points in Sine the CH1 of the output signal is filled with O in the corresponding points which have no data in Sine Properties El Merge To Multi Channel ReFerenceInput 1 Triangle hal Module s gt lt ReferenceInput Select From connected inputs to be the merging reference Triangle ToMulti 10 IN WIN TR 1 5 2 2 5 3 time sec 0 4 Next read in a set of signals in Indexed format First create a simple data set as shown in the figure below where the 1 column is time and the 2 column is data c2 e m m Gom om C 8 E A co e ee Next press 2 in the Network tools or use Source Open datafrom file to read in this data file TestData txt In Text Importer check Specify Time Column and then press the confirm button Data Range 1 gt to Columns 1 Y tola Data direction Column based Specify Time Column 1 B 5 Not only does Tomulti accept signals in formats of Regular and Indexed it also accept input signal of mixed Regular and Indexed Drag TestData to Tomulti and change the Properties Referencelnput to 2 TestData the original Regular format in the time axis of Sine and Triangle signals is replaced by the time axis of TestData This is clearer when observing the output of Channel View
258. is situation it is necessary to avoid generating it In this particular instance the solution is normalizing the signal Instantaneous frequency of signal Red indicates area where the result is negative frequency Normalized Hilbert Transform To compensate for the effect of the different amplitudes of the waves the HHT uses a preprocessing step on IMFs prior to applying the Hilbert Transform Initially the signal is normalized so that the maximum amplitude of each maximum extrema is exactly equal to one Additionally it also implements a step to neutralize the Gibbs effect by removing the discontinuity that often occurs at the signal s ends The following images demonstrate the process and its benefits 0 6 0 6 0 4 0 2 y cos t 2 75 cos t after normalization The analytic signal of the normalized y cos t 2 75 cos t The extra loops are due to sections of signal added to the ends of the data to help remove discontinuities The instantaneous frequency of the normalized signal Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The output is real number single channel or multi channel Regular signal opecify number of smooth point in 5 SmoothPoint median filter A value of 0 indicates that smooth should be used Example
259. isfies V 15 d is the distance of the Euclidean geometry df m fn maxt fG f 0 lt lt 1 Properties This module accepts input signals of real number single channel or multi channel regular and audio The format of the output is real number single channel or multi channel and regular The properties are defined below Properties i x El Multi Scale Entropy MinScale MaxScale ScaleStep MatchP aint MabchTolerance MarScale Maximun scale of the multi scale entropy Default Property Name Property Definition perty did Value MinScale The minimum scale 1 MaxScale The maximum scale 20 The increment step of scale during calculation ocaleStep from the minimum to the maximum increased 1 decreased by this step MatchPoint set the length of the pattern for comparing 2 Set the tolerance of pattern comparison This is r MatchTolerance P 0 15 in the original equation Example This example is for physiological signal In the Project panel load two data sets They are the recordings of the standing Center of Pressure COP along X axis from young and elderly subjects respectively Then use Viewer Channel Viewer to display the data time sec To understand the ability of the subjects to keep their balance we first take the differential values of the original data It is the velocity of COP which is shown below Young Velocity Elderly Velocit
260. it matrix is obtained p Proiecti Inv Proiectl Mop InvMatrx Mop o o gt From o Step E N 9 Channels 1 E Channel Information Histogram Channel 1 1 0000000000000002 2 2204460492503131E 16 0 8 3266726046886741E 17 0 99999999999999978 0 1 1102230246251565 16 0 m Data Channel 3 trn RO e 0 99999999999999989 Channel Channel 1 Related Functions Matrix Operation References Gilbert Strang Linear Algebra and Its Applications 3rd edition 3 9 2 Matrix Inverse 9 Calculate inverse matrix of A A must be a square matrix so 4 where is the unit matrix Properties This module accepts real number complex number and Numeric data And the output has the same format as the input Example Use DoMatlab to create a 3 3 random matrix the content is 0 86 0 63 0 37 0 22 0 66 0 69 0 99 0 56 0 78 Get the Inverse Matrix and the result is 3 44 8 05 5 49 3 09 0 87 0 69 1 79 0 39 2 47 Do the multiplication for these two matrices and a unit matrix is obtained i 1 If the input matrix is Singular such we get Warning message below Result of LAPACK funciton gett may be singular e Error computing RCond in channel Related Functions Matrix Operation 3 9 3 Transpose Calculate the transpose and conjugate optiontional of mat
261. ite TirmeUnit Sec El Source TimeLenath 1 TimeLlnil SEC SamplingFreq 1000 TimeLength 1 DataLenath 1001 SamplingFreg 1000 10 D ataLength 1001 Amplitude 1 Amplitude 1 Arnplitudecrrset 0 AmplitudeOfFsek B Phase 0 B TimeStart TimeStart 0 Module SignalFreq The Frequency of the to be generated signal Mixer 2 2 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec To facilitate the following FIR Filter design Mixer could be connected to FFT for frequency spectrum observation Mixer FFT 0 5 0 20 40 60 80 100 120 140 160 180 200 220 frequency Hz 2 On the Mixer icon select Compute Filter 5FIH Filter and change the Properties F1 to 25Hz The default FilterType is LowPass Then use Channel Viewer to show the processing result It can be seen that the frequency components higher than 25Hz are all removed and the output signal is similar to sine of 10Hz However because the Filterorder is only 101 the wave is partially affected Viewer2 0 20 40 60 80 100 120 140 160 180 200 220 frequency Hz Mixer Properties El FIR FilEerTvpe LowPass 25 FilEerOrder 101 Module F1 The First cutoff Frequency Mixer FIR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 3 Change properties of FilterType to HighPass F1 to 100Hz and FilterOrder to 500 As shown below the filter removes the frequency component lower than 100Hz and it leaves a sine wave of 193Hz with the White
262. ition of covariance IS NV 2 b i 0 V COV where x are average of each series For unbiased moment estimator the definition of covariance Is N Pa Xj y If there is multi channel series the total channel number is M covariance matrix can be represented by C i where 1 are channel number And the Diagonal terms of the matrix are covariance for each channel N 1 0 t g x x y y I b CO Pe N kK 275 CO N Properties This module accepts input of real number multi channel and regular signal The output is a MxM matrix where M is the total channel number And the output is in Indexed format The result can be viewed in Reporter windown by clicking Properties View Matrix View Matrix Covariance Matrix for Unbiased Moment Estimation False E Module a Covariance Matrix Default Property Name Property Definition Unbiased Moment Calculate the covariance using unbiased moment estimation method Example Calculate covariance matrix for sine waves with different phase and frequency Create a since wave in Netowrk panel using Source Sine Wave and its default frequency isi0Hz Then add two more sine waves One is set with Properties SignalFreq 5Hz and the other is set with Properties SignalFreg 10Hz and
263. iue window Hanning H 7 Viewer2 amp _ FFT amp Viewer3 amp TFViewer In the example 3 was clicked to be added to all four Run profiles After adding FreqCount click on button to hide the Parameter List and click on all the icon of every Run profiles to expand the details Now you should be able to see FreqCount value as 128 after clicking on all of the icons as shown in the image below Batch Run demo22 STFT PA B wd Output Directory C Program Files DynaDx DataDemon data Batch Runs Aunt unt Parameters for module STFT FreqCount Run2 Parameters for module FreqCount 256 Runs Parameters for module FreqCount 256 Rung Parameters for module FreqCount 256 lt is extremely easy to edit the value of FreqCount in any of the Run profiles Just double click on the value 128 of FreqCount to enter the new value TIPS You will need to double click the mouse on the value slowly because double clicking too fast won t allow you to edit the value Run demo22 STFT BRE P 4 X lo Output Directory C Program Files DynaDx DataDemon data amm Batch Runs Runt Parameters for module STFT FreqCount 256 Run2 Parameters for module STFT FreqCount 128 Runs Parameters for module STFT FreqCoun
264. k Properties Option Complex Magnitude Phase HealPart ImagPart PowerSpectrum Definition Integrate with respect to real part and imaginary part Re s r Re X t de Im x fmx G odo Re X t Im x o Im X t Integrate after performing norm operation on time frequency signal Re t Im t do oy J Im t oy dt Integrate after calculating the phase angle sie f Ek o to S fian il 2 Re t Integrate the time frequency signal with respect to the real part x t Re t oda x Re t Integrate the time frequency signal with respect to the imaginary part x t Im t odo x Im t Integrate after performing norm operation on time frequency signal x t o o do x Re t oy Im t oy Example In this example use audio signal hello wav as a signal source perform Enhanced Morlet Transform in DataDemon to perform time frequency analysis and then use Marginal Time to calculate the frequency distribution in time domain 1 Press the Jin the Network tools or use Source Import data from file to read the signal file hello wav in the installation directory default to be C Program Files DynaDx DataDemon data Next perform Compute TFA Enhanced Morlet Transform and then use Viewer Time Frequency Viewer to plot the
265. kness dot representation default etc Note User will need to click on the PlotElemEditor field for the button to appear Select different ways to display the y axis from a selection of Magnitude Phase Real Imagine Gain and Powerspectrum Normally YValueType this option is used for spectrum data When Magnitude there are multiple channels in the signal TIPS Please look up Chapter 4 4 Map to Heal for more information Conversion to Real If YValueType is set as Gain this option field will appear TIPS Please look up Chapter 4 4 Map to Heal for more information GainReference When HoldPlotRange is set as True after resizing moving and zooming into the graph HoldPlotRange False 9 the calculation done will still be based on the original range Xmin Set the minimum value of the x axis auto Xmax Set the maximum value of the x axis auto Ymin Set the minimum value of the y axis auto Ymax Set the maximum value of the y axis auto Select True to show the title on the graph and Show Title True False to hide the title Select True to show the x axis on the graph Show X Axis A are and False to hide the x axis Select True to show the y axis on the graph Show Y Axis y A and False to hide the y axis Clicking on the PlotElemEditor button will pop up the Plot Element Setting window Check the Display tick box to show the signal on the graph use
266. l Number Multi Channel Multiple Channels Signal Signal Data Data Types Audio Audio Data Numeric Numeric Data Spectra Spectra Data Regular Equal distance between points Information Types Indexed Irregular distance between points Regular Data and Indexed Data often cause the most problems for users so further explanation on these two types of data are required Regular Data means that the points on the x axis have the same distance between each other so the increment from one point to next point is always the same Data Range Rows to Columns to Data direction F Concatenate ta one channel Specify Time Column TE Field Format White spaced Q Delimeter Mull Salue Handle Use Mull value Handle Time Coordinate Time Unit sec wv Time Shift 0 sec sample Frequency 1000 E clez sec Down sample by C tn gt 22 82 8 File Contents 01 12z74 A 0022 1335 0003 1294 004 1265 005 1319 006 1359 007 1340 008 1379 009 1410 010 1401 011 1499 12 14 8 U13 1510 Tee In the Indexed Data type the distance between each point along the 5 is irregular If the imported file contains time information does not matter whether it is regular data type or indexed data type then check the Specify Time Column in the Text Importer and the Text Importer will assign t
267. l calculations will be saved and they will be restored when reopened next time If No is clicked when the project is opened next time all of the calculations need to be processed again Selecting Close will close the current working project or selecting Close All will close all projects currently opened in DataDemon Load Macro and Save Macro are new features only available in DataDemon Professional or above The implementation of the macro will allow you to quickly save and load the Signal Flow Diagrams that have been created The macro can be added to any project TIPS To get the feel of how to use the macro effectively create a simple project and play around with saving and loading macro files 1 3 Network Window Network Window contains the calculation steps for the program You can create execute and link Signal Flow Objects SFOs by using the mouse to click on or drag the SFOs to setup basic Signal Flow Diagrams for data calculation and manipulation Network gt Network Window be divided into three areas Network Window Toolbar Network Workspace and Network Control Area Network Toolbar Network Workspace Area Network Control Area Q 1 3 1 Network Workspace Area Network Workspace Area is the core of DataDemon DataDemon has implemented the object oriented design Under DataDemon object oriented environment it is simple to create and edit Signal Flow Objects and Signal
268. l mode decomposition and Hilbert spectral analysis Proceedings of the Royal Society vol 459 pp 2317 2345 London 2003 Kizhner Semion et al On the Hilbert Huang Transform Data Processing System Development Proceedings of the IEEE Aerospace Conference vol 3 pp 1979 2004 Poularikas Alexander D ed The Transforms and Applications Handbook Boca Raton FL CRC Press 1995 Weisstein Eric W Discontinuity From Math World A Wolfram Web Resource http mathworld wolfram com Discontinuity html Wu Zhaohua and Huang Norden E A study of the characteristics of white noise using the empirical mode decomposition method Proceedings of the Royal Society vol 460 pp 1597 1611 London 2004 HHT DPS Documentation Authoring This document was written and reviewed by Karin Blank Norden Huang Semion Kizhner Per Gloersen Tom Flatley David Petrick for the HHT DPS version 1 4 Copyright and Licensing Hilbert Huang Data Processing System Copyright Copyright United States Government as represented by the Administrator of the National Aeronautics and Space Administration KissFFT This software includes KissFFT which is released under the following license Copyright c 2003 2004 Mark Borgerding All rights reserved Redistribution and use in source and binary forms with or without modification are permitted provided that the following conditions are met Redistributions of source code must retain the above copyrigh
269. lder Click on Q to execute the Batch Run Paramater List From Project Project Batch Runs chirp T0000 Viewer m 111 8 chirp1 ODO amp TF Viewer After a Batch Run a Status Report will be generated telling you if the process has been a success or failure Batch Eun Status Report Batch Run Progress Output CAl 11 figures png Done Batch Eun Completed Executed a total of 3 runs U failed In summary Example 1 shows how to change the parameters of Batch Runs and Example 2 shows how to execute multiple files within the Batch Hun You can also run a Batch Run which changes the parameters of the variables while executing multiple files 1 3 6 Toggle Selection Mode Toggle Selection Mode helps user to scroll the view in the Network panel or group SFOs together for copying cutting pasting moving and deleting For scrolling display view of the Network panel i should not be pressed For example if there are many SFOs in the Network panel horizontal and vertical Scroll Bar can be used to change the display To move a single SFO select the SFO and hold the left mouse button in the Network panel then drag the SFO to the desired location and release the mouse button hal gt m For grouping SFOs button must be selected first then other editing operations can follow Toggle Selection Mode chirp 1000_m_m updated
270. le Default Property Definition Valde Setting the method of the ICA Symmetric Symmetric or Delfation y Setting the distribution function of the ICA hyperbolicTan hyperbolic Tan skewing or kurtosis yP Setting the maxmum time of the interation 100 Setting the criterion for judgement of the convergence 0 0001 Setting the eigenvalue threshold for the 1E 08 redundant signal setting whether the sign inversion function True is turnd on or not Setting the number of Independent components User defined Setting the interation time for the User defined computation Setting whether the eigenvalue and the User defined eigenvector are output In a report or not Opening the demo79 C Program Files DynaDx DataDemon demo Enhanced demo79 ICA vsn the user could find the original signal named Bird and Frog It is a recording of two mics for the sound of two different frogs One of the sounds is similar to the chiriping sound of the bird The user could hear these two sounds by pressing the Play button on the up left corner of the Viewer H E Fash TFT4 Switch ToAudia 0 5 0 5 2 4 b B 10 12 14 16 18 time Sec One sound is computed by the Fast STFT the result is shown as below Bird and Frog_Ch1 CH1 FastSTFT 0 01 5000 0 008 ri 4000 0 006 3000 D E 4000 0 002 0 LAN T fs a ILL x a A MW ali
271. led as and respectively They are corresponding to the Norm of A using different measurement The calculation of l ang lal are defined below which is different from Linear Algebra textbook A 2 max 2 a Ah max 2 M 3 j J where i j are the index of the row and column The meaning fo the Condition Number ni To measure the Stiffness of matrix A This is the distribution of the eigen value The round off error sensitivity of the solution for the linear quation 4 when b varies a little bit how x changes o brob Note A must be a square matrix If not SVD method can be applied However it is not supported in this version Properties This module accepts real number complex number Numeric data And the output is in the Reporter of the Properties TPP E Reciprocal Matrix Condition Number Condition Numbers Reciprocal Matrix Condition Numbers Reciprocal Matrix Condition Numbers for DoMatlab gt Sty Reciprocal Matrix Condition Numbers for DoMatlab Reciprocal Matrix Condition Numbers Condition CH1 1 norm 0 0579 infinity norm 0 0373 Example Use DoMatlab module to createa matrix A with random elements 0 86 0 63 0 37 0 22 0 66 0 69 0 99 0 56 0 78 If its Condition Number is close to 0 this matrix is Singular Its inverse matrix does not exist We can test it by General Reciprocal Matrix Condition Numbe
272. lication A s dimension is M N and B s dimension is N P Matrix Left Division 8 A s dimension is M N and B s dimension is M Matrix Right Division 6 00 A s dimension is M and B s dimension is P N Properties This module accepts real number complex number and Numeric data And the output has the same format as the input Property lx Matrix Operation Alpha 1 Beta 1 Operation addition True Propert Property Definition Default Value Name Input A A s name Reference only Input B B s name Reference only alpha A s weight factor detailed below 1 Beta B s weight factor 5 detailed below a Operator addition subtraction multiplication left division and right division aceon Operation If true the module name is A B for A B and it Auto name true depends on the operator Otherwise it is Mop If true calculation is for each element and not for By Element False the matrix Operation Operation expression Reference only statement 04 68 For matrix addition the output matrix is C S and are the weight factors for matrices A B respectively Example Use DoMatlab to create a 3 3 random matrix the content is 0 86 0 63 0 37 0 22 0 66 0 69 0 99 0 56 0 78 Get the Inverse Matrix and the result is 3 44 8 05 5 49 3 09 0 87 0 69 1 79 0 39 2 47 Do the multiplication for these two matrices and a un
273. line is the IMF after intermittency 0 12 0 1 0 08 0 06 0 04 0 02 0 02 0 04 0 06 0 08 50 100 150 200 250 300 350 400 450 1650 1700 1750 1800 1850 1900 1950 2000 2050 2100 Properties This module accepts input of Signal which could be real number single channel regular and Audio which could be real number single channel regular The output is real number multi channel Regular signal Method EMD method includes Standard _ Standard Intermittency Test and Ensemble m The prediction type of endpoint ex PredictionType PatternPrediction CopyEndpoint and Endpoint PatternPrediction _ A The number of times an IMF candidate siitCriteria must pass the test before considered an Maximum number of IMFs to generate MaxlmfCount Should be set high this is safeguard for dataset where it may run seemingly indefinetly Maximum number of sift to generate IMF Maxsitt It is intended mostly to prevent the EMD from getting stuck in an infinite loop IntermittencyTest The intermittency threshold which unit is samples represent the distance between Threshold 2 zero crossing points If the distances between zero crossings is greater than threshold the two zero crossing would be zeroed out Ensemble Ti EEMDNumber Ensemble number for the EEMD The amplitude level of the noise as a 0 1 EEMDEpsilon ratio to the standard deviation of input signal
274. lthough the data derived from measurement is discrete some data can be indicated by linear regression formula even if there is no measurement data For example from above we can know the spring length is 8 6cm when the weight is 20 g For those unknown xj within the data range we can get the yj by x a b For those data out of the data range we can also get them by using linear regression formula However the result is not that accurate since the linear formula is the simplest approximation module Example This function has two types to compute linear regression TimeSeries linear regression equation is x at b and XY linear regression equation is y ax b You can check which type you are using from Property Window Instead of being chosen by users the type will be changed automatically according to the formats of the input That means users have to connect this device correctly First of all make sure that what you want to know is 1 The relationship between a group of data and time 2 The relationship between two groups of data Then connect the device according to the following method 1 The relationship between a group of data and time The corresponding format is TimeSeries Connect signal and this device directly and view the result by Channel Viewer as the flow chart below Based on the flow chart above Viewer will draw two lines One of them is the original time series The other one is line after the regression
275. m on the top left corner displays the spectrum s probability distribution To view different channel and different value type in the histogram edit the Properties Data Channel Channel to change the channel and edit the Properties Data Channel Value Type to change the value type to view Histagram Channel 1 2000 ail h 0 0001 0 0004 0 0002 Data Data Count 31250 Time Length 312500 Unit Hz E Data Channel Channel Count 1 Channel Channel 1 Value ImagPart Min 0 0030456070388992021 Max 0 0052127150711840471 Mean 2 1905842525464665E 07 SIL Deviation 6 6143820857034655E 05 3 Spectra Another type of Data Viewer is spectra Spectra is created through wavelet transformation or other Time Frequency Analysis and it is a two dimensional complex array Data Viewer y EX Spectra Information Histogram 1021 3 738028190604 3 393738694256 3 006319148899 2 593645335757 12 275915859372 9 94000200940 2 0 5 1022 3 810650908790 3 409691804214 2 954093058935 2 478468354537 2 118182264356 9 ATN ENNIO aiu AAA eaten 4 X 0 900068027210884 Y 752 041176470588 Val 1 74921074438702E 05 1023 3 869262825722 3 412628454734 2 891385077156 2 356259864977 1 958575002584 1 MNOlAG1 AOL A 1024 3 915982616625 3 403955177257 2 818247876853 2 225839217012 1 795824007262
276. maily used in Mean s average speed calculation x 70 for all i Average with removing top and bottom percentile Set a percentile value sort X series remove top and bottom Trimmed Mean percentile average the remaining elements This removes the effect due to outliers Median Median Value Standard deviation estimate the deviation from the average This is Biased Moment StdDev Estimation toi Assume it is the true l Sample This is pur A 25 29 1 Unbiased Moment Estimatiom V 1 Variance square of StdDev This is Biased Moment Estimation 2 EY tes 2 o x N i 0 Variance N u gt p This is Unbiased 2 ERI N Moment Estimatiom i 0 The ratio between variance and average It used to X 100 show the discrete Coefficient of degree This is Variation Biased Moment Estimation 10097 This is Unbiased X Moment Estimatiom N to SERE ur y 2 Xj El x x i70 Ax 1 mA Skewness ET 2 x x 0 N N 1 27 V 1 X t v 3 N 1 2 dar s l Kurtosis i 0 N gt X 1 0 1 a l n 1Xn 2yXn 3 5 N 2XN 3 25 x i b 1 x lt 94141 semivariance x 2 i L x x bi N I J A measure of the asymmetry of the probabili
277. mat View Statistics Unbiased Moment Estimation Trimmed Fraction Trimmed at Ceiling Example For AcrossChannel setting calculate 15 statistical values for the data of all channels at the same time point The output signal contains 15 channels and its length is the same as the input signal Open Reporter window to view the result If the input is Sample it is True Unbiased Moment Estimation for calculating the statistics of Population If the input is Population it is False biased Moment Estimation for calculating the statistics of Population The percentile of the top and bottom segments to be removed If the position of specific percentile is not an integer include the previous point False or the next point True to be removed Calculate the basic statistics of white noise and square wave None True 0 05 False Create a noise using Source Noise default is white noise in Network panel connect this SFO to Compute Statistics Basic Statistics Select Properties View Statistics of Basic Statistics to view result HE El Basic Statistics View Statistics Basic Statistics for Noise Unbiased Moment Estimation True Trim Fraction Trim at Ceiling View Statistics 0 05 False Display Ehe basic statistics Basic Statistics for Noise Basic Statistics for Noise Basic Statistics GeametricMean HarmanicMean Trimmedht
278. merical value used during intermittency to determine if a section of signal between two zero crossings should be kept or discarded Distances between zero crossings less than the threshold are kept otherwise they are zeroed out Threshold is measured in number of samples without regard to the timescale of the signal Zero Crossing Where the signal crosses the x axis at y O 3 7 4 RCADA Instant Frequency RCADA Instant Frequency is a method for calculating instaneous frequency provided by RCADA This module uses the same algorithm as Instant Frequency function in MATLAB code from RCADA Introduction Please refer to http rcada ncu edu tw research1 htm Properties This module accepts input signals of real number single channel or multi channel regular and audio Instantaneous Frequency Normalizing Iterations 5 Module Property Name Property Definition Default Value Normalizing Iterations Number of times to obtain envelop maxtrima 5 Example Continue the analysis for the gsta dat after RCADA EEMD decomposition Using Compute Channel Channel Switch to get the 3 IMF and connect it to HHT RCADA Instant Frequency display the result with Channel Viewer Please refer to demo68 in C Program Files AnCAD Visual Signal demo HHT qsta ToRegular NHHT EEMD h 1860 1870 1880 1800 1900 1010 1820 1030 1940 1850 1860 1070 1050 1900 2000 Date Property IX
279. mm iil tima set oince the result of EMD is multi channel the above graph is hard to see For better viewing change the setting of Channel viewer set Properties ViewerHeight to 300 and set Multi channeldisplay to List EMD time sec Connect RADAC EEMD to Compute TFA Hilbert Spectrum and then to Viewer Time frequency viewer for displaying results This is how to show the instaneous frequency of HHT EMD Hilbert spectrum 500 400 e ce ce 200 frequency 100 0 0 2 0 4 0 6 0 8 1 12 1 4 1 8 1 8 time Sec Hilbert Spectrum can also show the instaneous frequency from Haar Wavelet Transform Connect Chirp 1000 to Compute Transform Haar Wavelet Transform and set Properties FilterBank levels to 9 set Resampling method to Spline Then follow steps 2 3 to do time frequency calculation Filter Bank Levels Resampling Method Filter Bank Levels Specifies Ehe number of Filter bank levels 4 single level Filter bank will produce two components al high Frequency and flow Frequency a two level Filter bank will produce three components al az and Chiro 1U00 Haar AAMVVAVAAMNMT SOAANMAM WA AW Ro ua LAVA CLL eta V Chirp 1000 Haar Hilbert Spectrum 500 400 LER c ce frequency Hz 100 0 0 2 0 4 0 8 0 8 1 1 2 1 4 18 18 2 time sec Related Functions RADAC EEMD IMF Propertie
280. mmetrized is central difference Divide the result by the sampling period Differentiate to obtain the approximation of differentiation Example This example shows the differentiation of a Sine Wave 1 Right click in Network Window to select Source Sine Wave to generate a sine wave and then use Viewer Channel Viewer to show it in the window 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 Right click on the icon of Sine select Computer Mathematics Diff and then use View Channel Viewer to plot the calculation result as shown below It can be seen that the Sine wave is changed to Cosine after Diff calculation However because the default value of Differentiate is False the amplitude is very small X oine Diff 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec The approximation of differentiation can be obtained by changing the Properties Differentiate in Diff to True Here the Source Sine Wave issin 2z ft where f is the signal frequency t is the signal time and the differentiation of this sine wave should be 2z f cos 2z ft In this example f is 10 Hz 2z is 6 28 therefore the maximum amplitude should be 2z f 262 83 The result can be verified by comparing with the result shown below Ed Simple Differentiate False Module Diff xj EB Diff a Method cine Diff 50 50 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec Related Functions Integrate Viewer
281. modal Pressure Flow Cerebral autoregulation reflects the ability of the cerebral microvasculature to adapt to systemic blood pressure BP changes by modulating the small vessel resistance to maintain relatively stable blood flow Noninvasive assessment of cerebral vasoregulation is important for medical diagnostics and acute care Recent studies have demonstrated that beat to beat measurements of BP and cerebral blood flow velocities BFV measured by transcranial Doppler ultrasound TCD during the Valsalva maneuver and head up tilt can identify impairment of cerebral vasoreactivity in various medical conditions indicating that a reliable non invasive index for dynamic cerebral autoregulation may be extracted from the BP and BFV signals Conventional approaches model autoregulation with BP as input and blood flow as Output e g Windkessel models and assume that signals are composed of superimposed sinusoidal oscillations of constant amplitude and period over a pre selected frequency range A transfer function is typically used to explore the relationship between BP and BFV by calculating gain and phase shift between their spectra However BP and BFV signals are often nonstationary and are modulated by nonlinearly interacting processes at multiple time scales corresponding to the beat to beat systolic pressure respiration spontaneous BP fluctuations and those induced by interventions such as the Valsalva maneuver and postural changes To ov
282. mported into the project and the DataSource is checked from the Parameter List Note DataSource parameter will only be available in the Batch Run window after a file has been imported into the project Clicking on the will open browser window to select files be added the Batch Run TIPS For multiple files selection hold the Ctrl key Paramater List From Project Hemo25 STFT mj FFT viewer E T1STFT TPViewer E Selection viewer3 hello Gt E Auo create batch runs from data files Look ir data P gt Er 100 atr 9 fft vsn L4 e 100 dat demo10 fir vsn My Recent 100 hea demoi1 fir vsn Documents demo12 fir vsn 12 1ii txt 1 14 Source vsn 3 ies chiro 1000 th 1 demoi6 MovingAverage vsn chirp10000 tfa 1 demo17 MovingAverage vsn amp demo01 basic vsn 1 18 DataSelection vsn 1 demoO2 basic vsn 1 demo19 WaveReader vsn demo03 basic vsn a demo20 SacReader vsn 9 demo04 basic vsn 1 demo21 Writer vsn 19 demo05 mixer vsn demo22 STFT vsn i demo06 resample vsn 1 24 STFT sn 09 1 07 naise vsn 25 STFT vsn D 1 8 fft vsn i demo26 Colormap vsn Desktop My Documents Bullfrog gt File chirp10000 tta 111 tfa chirp 1000 tfa My Network Files of type All
283. mpting to apply it directly for signal analysis few datasets processed would return meaningful information This is due to four paradoxes identified by Cohen see glossary p 95 The Hilbert Transform P is the Cauchy principal value The Hilbert Transform produces a complex signal that consists of the original signal as the real part and the complex conjugate as the complex signal 0 005 0 01 0 015 O02 0 025 0 03 0 035 0 04 0 045 The analytic functions from applying the Hilbert Transform to sin 2 Pi 60 x Solid line is the real part of the transform dotted line is the imaginary part of the transform In case of simple sinusoidal functions the Hilbert Transform will give a 90 Degree phase shift Once the Hilbert Transform is applied instantaneous frequency can be obtained by considering a polar representation of the analytic signal For this the real part of the analytic signal is plotted on one axis the imaginary part on the other The instantaneous frequency is then derived by calculating the instantaneous angular change of the analytic signal 011 1 tan cdit H Equation for instantaneous angular frequency Image of the complex analytic signal of sin 2 Pi 60 x Equation for instantaneous frequency Negative Instantaneous Frequency A problem with the Hilbert Transform when used to obtain the instantaneous frequency is that there are several situations where a signal will yield a negative f
284. n these IPs Introduction What is the HHT The Hilbert Huang Transform HHT method is composed of multiple algorithms intended to filter and analyze the data These algorithms include Empirical Mode Decomposition where data is broken down into Intrinsic Mode Functions IMFs Normalized Hilbert Transform which converts the IMFs to the time frequency domain Generalized Zero Crossing an alternative method for calculating local frequency from IMFs Degree of Stationary a method for ascertaining the amount of variation in a signal NASA HHT Module NASA HHT Module has multiple modules base on above mentioned algorithms NASA HHT Module includes NASA EMD which decomposes the signal into many Intrinsic Mode Functions IMFs NASA Hilbert Transform which converts the IMFs to the time frequency domain by Normalized Hilbert Transform NASA GZC using Generalized Zero Crossing method to calculate zero crossing rate from IMFs NASA Hilbert Spectrum converts all IMFs into spectrogram by Normalized Hilbert Transform NASA GZC Spectrum converts all IMFs into spectrogram by Generalized Zero Crossing method NASA Degree of Stationary which calculates the variation degree of s the ignal 3 7 3 1 NASA EMD Introduction Empirical Mode Decomposition EMD is a method of decomposing data into Intrinsic Mode Functions IMF Unlike many traditional filters which are based in the frequency domain the EMD is a t
285. n connect the ToMulti SFO to a Compute Statistics Kernel Smoothing Density and then connect it to a XY Plot Viewer Projecti mi KSDens ity f x 0 5 0 0 5 1 1 5 2 1 KSDensity x Example 3 Ihe x axis on the XY Plot represents the odd numbers of the Channel signal information and the y axis on the XY Plot represents the even number of the Channel probability density function A single channel multi data signal will be drawn by the XY Plot Viewer 1 Create two Source Sine Wave signals and change the second Sine Wave SFO s Properties Source Phase to 90 which will create a Cosine Wave Connect both signal waves to Conversion To Complex to combine the signal data to a single channel multi data signal and then connect it to a XY Plot Viewer to display the graph ToComplex Im Project Project2 Projecti Project pestDataSet X HY Plot updated Properties Module Source TimeLlni Hum TimeLength 1 SamplingFreq inn DataLength 1001 SignalFreq 10 Amplitude 1 AmplituideOfFsek Phase B Sine ToComplex ToComplex Re Set both the Properties Appearance Viewer Width and Viewer Height to 300 and have the XY Plot Viewer update the graph Properties X El Appearance 5 BackColor White ViewerMWidth 300 E ViewerHeight 300 ListOrder 0 Sine ToComplex ToComplex Im 0 5 0 5 0 ToComplex Re Related Functions Channel Viewer Kernel Smoothing De
286. n convert them to matrix using Conversion Convert to Matrix as shown below Next connect these two matrixes to Compute Matrix Matrix Operation with default parameters Then connect Matrix Operation A B to Coversion Covert from Matrix and set DataType to TimeFrequencySpectra display result with TF Viewer Mop FromMatrix 500 tt cC t 7 tT 300 AauanbaJl 100 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time 0 1 SEC Set DataType to TimeDomainSignal with default parameters and show the results with Channel Viewer Frornhlatrix meee i m C a P H Pom ie y ih SEC time Related Functions STFT Convert from Matrix 4 11 Convert from Spectra Convert Spectra data to single multi channel time series or single multi channel frequency distribution signal Introduction We can extract one row or all rows from the Spectra which is the amplitude time series at a fixed frequency We can also extract one column or all columns from the opectra which is the frequency distribution at a fixed time point Properties This module accepts spectra with real complex single channel or multi channel data Property El Convert From Spectra ExtractionMode SingleRow v 0 Default Property Definition Name perty Value Extract Row or Column options MultiChannelRows ExtractionMode leR
287. n could be the Tanh the kurtosis Fourth Order Moment the skewness 3rd Order Moment Usually the tanh could give reasonable accuracy c In the formula the and the S are both unknown so the formula could ne o oc be rewritten as where amp is any nonzero constant the isa solution This is the ambigiosity of the ICA So a function named the Flip signal sign is provided in this module which adjusts every element of the A to be non negative values 0 d When ames there is redundancy in the signal the eigenvalue of the Covariance Matrix shows the connection of the original signals When the eigenvalue is zero there is linear dependency in the mixing signal and the ICA will remove that signal The user could specify a threshold to remove a signal Because the eigenvalue of the noise is much smaller than that of other signals the ICA could be used for removing noise Properties This module accepts real numbers multi channels regular signals and audio signals Property x El ICA Parameters ICA Method Symmetric Cost Function hyperbolicTan Max Iteration Steps 100 Epsilon 0 0001 Neglect Small Eigenvalue 1E 08 Flip Signal Sign True El ICA Property Report ICA Property Report Property Name ICA method Cost function Max iteration Steps Epsilon Neglect small Eigenvalue Flip Signal Sign Number of Independent Components Computedlteration Steps Heport Examp
288. n that preserves monotonicity of the data set MonotonicCubic being interpolated MonoticCubic method is better than oplinelnterpolation method when the slope of the signal is large e g Square wave Example Create a sine wave SFO and apply Resampling SFO to it 1 Create Source Sine Wave and edit the Properties Source SamplingFreg to 100 and Properties Source DataLength to 101 Connect the Sine Wave SFO to Viewer Channel View to see the graph You can clearly see from the graph that the wave signal is not as smooth anymore M Viewer updated Auto gt Properties property rrid lx Regular Real Single Channel Signi DataLength AmpliudeOtiset I DataLength Data leneth of the generated signal 3 Sine 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 2 Connect the Sine wave SFO to Compute Channel HResampling and edit the vale of Properties Resample NewSamplingFrequency to 51 and Properties Resample UpsamplingMethod to Linear to compare the difference between the two Module Resample Hew SamplingFrequency 51 UpSamplingMethod Linear E e Mew sampling Frequency Resample 1 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Now try with changing the UpsamplingMethod to Nearest Properties Module El Resample Hew SamplingFrequency 51 UpSamplingMethod Nearest nnm M UpSamplingMetho
289. n the Expression can edited directly Example The usage of different calculation method and functionality is shown below Create a triangle signal using Source Triangle Wave connect to Compute HHT RCADA EEMD for calculation The goal is to get a Multi Channel signal Show the signals using Viewer Channel Viewer Change Properties Multi Channel Display in Channel Viewer to List And each channel is displayed separately E Appearance E Channel Multi Channel Display List v E Show value Channel RCADA EEMD CH1 9 Fonts and Colors Grid EJ Module Triangle ROCADA EENLD 0 1 0 2 0 3 0 4 0 5 7 8 1 time sec Do the same as step 1 however change Triangle Wave to Square Wave ie S RCADA EEMD2 Square RCADA EEMO 10 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Connect RCADA EEMD and RCADA EEMD2 to Compute Mathematics Math expand box before Expressions in Math Property Window and click Properties Expression Editor at the end of the line to open the interface Property El Math ReferenceInput 0 RCADA EEMD E Expressions 9 Expressions E Module In Multi Channel Expression Editor open the tree map in the Input List by clicking sign in front of the signals Please note the default output signal is the 1 input signal 21 Multi Channel Expression Editor 7 3 By Channel 24 abs pression S Inp
290. ncy Example This example shows the multiplication of a sine wave and a triangular wave 1 Use Source gt Sine Wave and Triangle Wave to generate a sine wave and a triangle wave Change the Properties SignalFreq of the triangle wave to 5 and use the Viewer Channel Viewer to observe the original wave Project1 x TimeUnit TimeLength SamplingFreq DataLength SignalFreg Amplitude AmplitudecOfFsek Phase Symmetry TimeStart SignalFreq The Frequency of the bo be generated signal MM Viewer Y time sec M 2 AN 6 4 8 Multiply these two signals using Compute Mathematics Multiplier The output signals are shown as below Multiplier 0 5 0 5 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 As Mixer the Multiplier allows the sampling frequency and time length of the two signals to be different The sampling frequency of the output signal is identical to the minimum sampling frequency in the input ones On the time axis the overlapping parts of the input signals are multiplied together while the other part is intact Change the SignalFreq of the triangular wave to 100 TimeLength to 2 Then in the output signal the Signal Frequency would be 100 and the Time length would be 2 seconds Properties TimeLlni TimeLenath SamplingFreg DataLength SignalFreg Amplitude aAmplitudecfFsaet SamplingFreq Sampling Frequency Multiplier 0 0 2 0 4 0 6 0 8 1
291. nd Threshold 9 n 1 s 2 3 Var Test Chi square variance test In Var test 5 size is the sample variance 9 is the population variance n is the sample 4 Runs Test Runs test of Randomness Geary test T 4 T T T T 2T TAT T T E R V R T T 1 R E R In Runs Test is the number of samples greater than the sample mean I is the number of samples smaller than the sample mean H is the number of times that a and b appear alternatively For example aaabbaaba then R 5 Properties Hypothesis Test There are 4 types of One sample tests currently We will introduce these four types of testing methods individually and the default values for all parameters are defined as follows Property Name Definition Default View Test Results Use Hypothesis Test to examine test resutls n a TestType z Test t_Test var lest runs Test z Test If you press the View Test Result you will see test result as shown in the following table Property Name Definition To show that test results fall within the range for rejection True Hejected means we can reject the null hypothesis and vice versa we can only accept the hypothesis Demonstrate where the sample mean falls within the population ianifi L SIGMA SEVEN The minimum of the scope of null hypothesis or the minimum of Cl Low the confidence interval The maximum of the scope of null hypoth
292. nd a triangular wave into a 2 channel signal And set the Properties TimeLength to 2 seconds And use Viewer Channel Viewer to show the result oignal diagram in ToMulti2 square wave and triangle wave Click on any ToMulti and open the Module in Properties It shows that the OutputType is Real which means that the signal data are real numbers ReFerenceInput 0 Sine gt El Module Mame ToMulti InputPortside Left OutputPorESide Right J AccepbableDataTypes Real Single Channel Signal of Rank 1 Regular Dat OutputDatal ype EA OutputDataT ype Output Data Use Merge to Complex to convert two multi channel signals ToMulti and ToMulti2 to a complex signal According to the order of channels this component uses the 1 input signal Tomulti in this example as the real part the 2 input signal Tomulti2 in this example as the imaginary part to make a multi channel complex signal In ToComplex the data of 1 channel is Sine Wave i Square Wave and the data of 2 channel is Noise i Triangle Wave Viewerz updated Auto gt E E E S S S SS SE S SE ES S E S S E E E E E S E E S E E E E S S E Adjust Reference Input to decide the time axis of the ToComplex It uses the 1 channel as the default Connect Channel Viewer to the ToComplex Because the Reference Input is set to ToMulti it shows that time axis length is 1 second and the data between 1 second and 2 sec
293. ne Wave creates a sine wave with default frequency of 10 Hz Next create two sine waves One wave set properties SignalFreq 5Hz and the other wave set Properties Phase 180 degrees Lastly use Conversion Merge to Multi channel to combine three waves into a Multi Channel signal The above steps create a sine wave with frequency of 10Hz a sine wave with frequency of 5Hz and a sine wave with 180 degree phase angel Use Viewer Channel Viewer to graph result with the black line representing the Sine the Blue line representing Sine2 and the red line on behalf of Sine3 Sine2 Properties Source TirneLIniE TimeLength SamplingFregq Dakalength ignalFreg Amplitude nmplituidecofrrFaset Phase SignalFreq The Frequency of Ehe bo be generated signal Sine3 Properties F TOPe x El Source TimeLlniE TimeLength SamplingFreq DataLength SignalFreg Amplitude AmplitudecOfFset Phase Phase The phase in degree Sine 0 0 1 0 2 0 3 0 4 0 5 0 8 07 0 8 0 8 1 time Sec Connect Compute Statistics Orthogonality Matrix after ToMulti select Properties View Matrix to show calculating results The diagonal entry of the matrix is the inner product of its own signals The value is 1 O12 are the comparision between Sine and 5 2 If the value is extremely small meaning that the two signals are orthogonal If 32 23 are also extremely small then Sine2 and
294. ng 2007 Decomposition of one dimensional waveform using iterative Gaussian diffusive filtering methods Proc R Soc A doi 10 1098 rspa Yih Nen Jeng You Chi Cheng 2006 Accuracy Comparison between Two Sharp and Diffusive Filters Proc R Soc A doi 10 1098 rspa 3 8 5 Fast MSE In the algorithm of the standard MSE the time for computing a Scale is proportional to the sqare of the length of the signal Properties This module accepts real numbers single channels regular signals and audio inputs the format of the input signal is the plural and single channel spectra data Properties are set up as the below table Property IX Fast Multi Scale Entropy Algorithm Auto MinScale 1 MaxScale 20 ScaleStep 1 Match Points 2 Match Tolerance 0 15 Default Value Property Name Property Definition The options of the algorithm include the Auto the Brute the Sort and the K D tree The Brute is the Algorithm algorithm of the MSE When the length of the signal is larger than 5000 points the K D tree is chosen otherwise the Sort is chosen The minimum scale is the scale s lower limit of the MinScale dimensional analysis The maximum scale is the scale s upper limit of the MaxScale dimensional analysis scaleStep The increasing decreasing step of the scale MatchPoint Setting the series length of judging the similarity MatchTolerance Setting the tolerance of judging the similarity Exampl
295. ng period It is intervals mee Required None meaningless for Numeric The unit of signal time or units quan Optional sec or Hz frequency The time axis format of signal formats Currently Regular and Indexed are Optional Regular available Required The X axis value of input signal For coords signal and spectra it is time For uf the Indexed spectrum it is frequency Format is Indexed Example The three examples below show the DoMatlab operation The basic variable structure in DoMatlab 1 Use Source Sine Wave and Square Wave to generate two groups of signals Connect the square wave to Compute HHT EEMD to create a multi channel signal Then connect both of Sine and EEMD to DoMatlab Matlab updated Auto gt r1 2 Automatically a Matlab command window pops up after DoMatlab component is generated Firstly enter whos in the Matlab command window or press the Workspace browser button in the window tools to check the current Matlab variables available MATLAB Command Window File Edit View Window Help Size Bytes Class 1881x1 1881x1 1x1 1x1 1x1 1881x1 1x8 1x1 1x1 100151 1 1 S868 n 868 0322 9 3888 64544 9566 9 S868 9888 double array double array cell array struct array double array double array cell array struct array double array double array struct array Grand total is 16235 elements using 132568 bytes Because there are two set of input si
296. ng replaced To make things easier for yourself create a Channel Dup SFO that connects to the rest of the networked SFOs So the next time you load the macro just connect the new Source SFO to the Dup SFO and you are ready to view the results without having to drag and connect the new Source SFO to other SFOs every time Viewers updated Auto Q Q SERBS RE SESS S RE SSSR SES SERS SEES SS The above macro example is quite simple but most of the time macros contain a lot more Signal Flow Objects In DataDemon there are several predefined macros and one such macro is the HHT SplitView macro HHT SplitView macro will turn a signal into EEMD and calculate and display the graph for each of the channel Compute Conversion source Viewer Writer mme eee 0X Network Channel Projecti 0 4 0 5 time iseci channel Viewer m updated n 5 time sec Channel Properties Macro saves time when there is a need to repeat certain processes within different projects So saving complicated macros and reuse those in different projects can increase work efficiency 6 Macro file and DataDemon project file are both saved as vsn file The only difference is that when you load a vsn file through Load Project the file will be opened as a project and when you load the same v
297. ngPeriod to 0 149 Dragging the output result to Viewer 1 to compare with the original signal where the black curve is the original signal and the blue curve with x is the ToRegular signal It shows that the signal with bigger sampling frequency is distorted lt Viewer updated Auto gt El Convert To Regular ConverkMethad FillGap FillMethod LinearInterpolation E Sampling Periad 0 1 49 Sampling Period Specifies the sampling period Default is automatically dete Viewer 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 time sec 5 Next try to change the Sampling Period to 0 15 An error message is popped up for not allowing to enter a value which is bigger than 1 5 times of the minimum sampling frequency of the input signal The sample period of 15 ts too and may result in less data porte than the oriemal data inaccruate conversion E Convert To Regular ConvertMethod FillGap FillMethad MonotonicCubic Sampling Period 1 5 Unik SEC AutoDeteck False Module Sampling Period Specifies the sampling period Default is automatically determined From the input data Related Functions Convert to Audio Filling Null Value Resample 4 4 Map to Real This component converts a Complex signal to a specific Real Signal Introduction Let X 0 0 0 yO yO yo to be the real part and the imaginary part of a complex signal respectively
298. nity sin Sine asin Inverse sine COS Cosine acos Inverse cosine tan Tangent atan Inverse tangent sinh Hyperbolic sine cosh Hyperbolic cosine tanh Hyperbolic tangent exp exp x equals log Natural logarithm log10 Base 10 logarithm pow pow x a equals x sqrt oquare root oignum function Returns 1 if square Equals sign greater than zero 0 if equals zero and 1 if less than zero Round to the nearest integer toward zero If lt 0 truncate x equals truncate ceiling x If x220 truncate x equals floor x Complex conjugate For a complex x conj x Real x i Im x In addition there exists gt lt gt lt zz and conditional signs If the condition is satisfied return 1 If the condition is not satisfied return O There are examples below to show the usage Output Channels Output Channels display all output channels and defined math equations in Expression The order of the channels in the output gives the sequence number of the signal The sequence number order of the channel can be changed using the button to the right of the panel moves up and B moves down t deletes channels The name of the channel and the equation can be modified Double clicked the channel to modify the name if the math equation needs to be modified select the Express of the target channel click the mouse left button once similar to double click but with a slower speed the
299. nsity 6 6 Histogram Viewer Professional Only Histogram Viewer is a graphical display SFO which will draw rectangular bars on the graph It is included in the DataDemon Professional Introduction Histogram is used frequently in probability X axis represents the category of the data and the y axis represents the probability of the data and the graph is drawn as rectangular bars Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel Regular or Indexed Audio which could be real number or complex number single channel or multi channel Regular Histogram Viewer and Channel Viewer are very similar however there are more variable options for Histogram Viewer Properties Active Channel Channel 1 Binicaunt 25 Color 1 3 Gray Colorz _ Transparent BrushStyle Horizontal Percentage False TValueTvpe Magnitude IsDrawLine False Property Name Property Definition Default Value Specify the Channel to be drawn when there are multiple channels connecting to Active Channel the viewer NOTE This option will only Channel 1 appear if there is a multi channel data connecting to it 25 set the number of rectangular bars on the graph Set the first color of the bar Bincount Set the second color of the bar Set the direction of the brush stroke for BrushStyle Horizontal the color on the bar Select True to change the y axis to Perce
300. ntStyle 5 False percentage select different ways to display the y axis from a selection of Magnitude Phase Real Imagine Gain and Powerspectrum YValue Type Normally this option is used for spectrum data When there are multiple channels in the signal TIPS Please look up Chapter 4 4 Map to Real for more information Magnitude Select True to draw lines connecting the IsDrawLine False top of the rectangular bars together Example Create a Gaussian Noise and a CustomWave and use Merge to Multi channel to turn both signals into one multi channel signal and output it to a Box Plot Viewer 1 Create Source Noise and change its Properties Noise Noise Type to Gaussian and set the Properties Source TimeLength to 5 Now create Source Custom Wave and change its Properties Source TimeLength to 5 Connect both signal waves into Conversion Merge To Multi Channel and then output it to Viewer Channel Viewer Project1 Viewer updated v Auto gt Noise ToMulti 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 time sec 2 Connect ToMulti SFO to Viewer Histogram Viewer and the graph of Channel 1 will be displayed Project1 i Histogram updated v Auto gt Histogram CH1 Noise 3 Edit the Properties Hepresentation lsDrawLine to True and a red line will be drawn through the top of the rectangular bars Properties lx Percentage False VY WalueType Magnitude IsDrawLine True
301. ntains 3 data blocks RIFF FMT and DATA The details are given as follows RIFF defines the file format file size and other information The format is WAVE FMT contains the related properties of audio signal such as code type sampling frequency number of audio channels byte rate etc DATA The original data which contains audio information Properties Acceptable input data sources are real single channel or multi channel Regular signal or audio signal Note that this component only accepts double channels for multi channel The output format is real single channel or double channel Regular audio signal Available properties are Sample rate and Bits per sample Convert To Audio sample Fate 44100 Hz Bits Per Sample 16 bps Module Module Default Property Name Property Definition id Peur Value The number of sampling points in every second It affects the resolution of voice Sample Rate frequency The available options are 1000 44100 2000 4000 8000 11025 22050 44100 48000 and 96000Hz Define the value of every saved data which could affect the resolution of sound intensity The available options are 8 16 24 and 32 bps Bits Per Sample Example Convert a signal data file Chirp1000 tfa to audio signal using Convert To Audio 1 Press 2 in the Network tools or use Source Import data from File to read t
302. number or complex number single channel Regular Numeric which could be real number or complex number single channel Regular or Indexed In this module Heference Input selects an input signal used as reference of the number of channels and time axis of the output signal The default value is O which means that the output references the 1 input signal The time axis settings of other input signals would be copied directly from the 1 signal The principle of copying time axis setting is that the time points of missing data are filled with O and time points of exceeding the time reference are discarded In order to avoid the operation confusion it is recommended to use signals with identical settings such as SamplingFreq time starting point and Time Length Definitions and default values of properties are given below ReferenceInput 0 Square Module Merge To Multi Channel Default Property Name Property Definition md Value To set the reference signal its time axis is The 1 Referencelnput used as the time axis of the output signal input signal Example This module accepts Regular Indexed input signals The examples show the operation of input signals with identical and different time axis setting 1 Use Source Sine Wave to generate a Sine Wave and use Source Triangle to generate a triangular signal Change the Properties SamplingFreq of Triangle to 333 TimeStart to 0 33 and TimeLength to 4 secon
303. numbers of SFOs reconnecting a new Source SFO back to the network relationship can be tedious So the easy way is to create a Compute Channel Dup in place of the current position of the Source SFO and connect the Source SFO to the Dup SFO viewer m updated Whenever a new macro is loaded just connect the Source SFO to the Dup SFO without having to reconnect the Source SFO to the rest of the network relationship since the Dup SFO is already connected to the rest of the network relationship Related Functions Macro 3 1 4 Fill NULL Value Use mathematical method to fill any data that is missing with the NULL value Introduction To fill in the data signal X x x xy_ which contains NaN Not A Number or NULL Properties This module accepts input of Signal which could be real number single channel or multi channel Regular or Indexed and Audio which could be real number single channel or multi channel Regular In the Properties Fill NULL Value Fillmethod there are 6 methods to fill in the missing values Properties lx Fill Null Value Fill Methad Fixed alue ull alue Fixedwvalue Module Frew alue FillMethod didi aid LinearInterpalatian SplineInterpolation MonotonicCubic The Filling null value method There are the FixedValue PrevValue NextValue Linearlnterpolation oplinelnterpolation and MonotonicCubic metho
304. nvergence test Specifically when the normalized squared difference SD between two successive sifting operations defined as below is less than a predetermined value h SD hi t 0 2 A number S is pre selected The sifting process stops after S consecutive times or when the numbers of zero crossings and extrema are equal to or differ at most one The two criterions above are used simultaneously and the sifting process will be terminated when either is satisfied DataDemon outputs the decomposing results in the order of high frequency to low frequency i e the channel 1 is the highest frequency the channe2 is the next and so on until the last channel which outputs the Residue There are several functions associated with HHT module 1 RCADA EEMD EEMD method from Research Center for Adaptive Data Analysis RCADA at National Central University in Taiwan 2 RCADA Instant Frequency A method to calculate instant frequency from RCADA 3 RCADA Spectrum Hilbert Spectrum method from RCADA 4 IMFProperty List properties for each IMF including the number of zero crossing the number of maxima average frequency of zero crossing orthogonality among IMFs power ratio of each IMF etc 3 7 1 RCADA EEMD RCADA EEMD is the latest 2009 algorithm from Dr Norden Huang which is published at Research Center for Adaptive Data Analysis RCADA at National Central University in Taiwan This module has
305. o Frequency the parameters are as following in Iterative Gaussian Filter FL 22 TrendPeriod FH 24 TrendPeriod Default Value If the frequency is lower than this value then it is considered as trend Corresponding parameters Trend in terative Gaussian Filter Frequency FL 22 TrendFrequency FH 24 TrendFrequency Frequency Unit Set the unit for TrendFrequency Default The original unit of the FFT on input signal Hz Frequency Unit Example Property Name Property Definition Use Trend Estimator to process trend in noise signal Create Source Noise signal and set NoiseType in Properties to Brown The signal looks like Moise 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time serj Connect Noise SFO to Trend Edtimator and set TrendPeriod in Properties to 1 0 DE E TrendEstimater FilterT ype LowPass Time Unit sec Trend Period 1 0 The output shows below Moise IGaussFilter a a E a a fs 0 5 0 6 0 7 0 8 0 9 time serj Set Trend Period to 0 2 the output looks like Moise IGaussFilter a hJ a a 0 5 0 6 0 7 0 8 0 9 time sec oet Trend Period to 0 05 the output looks like Moise IGaussFilter 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 time sec It shows that the setting of Trend Period becomes small signal shows more details Because rend Estimator set the lower bound of the perio
306. o be within the original range Project X Viewer updated Selection 1 D 1 0 2 0 22 0 24 0 26 0 28 0 3 0 32 0 34 0 36 0 38 time sec Related Functions Channel Switch Viewer Source 3 1 3 Dup Duplicate a signal data Properties Dup can take input from any type of data input and it does not require to configure anything Example To duplicate a Sine Wave SFO using Dup 1 Firstly create Source Sine Wave can connect it to Viewer Channel Viewer Project X Viewer updated 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec In this Sine Wave SFO the SamplingFreq is 1000 and the SignalFreq is 10 2 After connecting Sine Wave SFO to a DUP SFO you can see that both signal data looks the same through the Channel Viewer SFOs Viewerz updated Auto gt Sine 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Below is an example of saving a DUP scenario into a Macro Connect Source Sine to Compute Transform Fourier Transform and Compute Transform Hilbert Transform and view each result through Viewer Channel Viewer save this Signal Flow Diagram as a macro file Now load the macro file into a clean project and the result will be as shown Now you want to change the Source SFO to another source After deleting the old Source SFO create a new Source SFO and connect it back to the other SFOs If the macro contains numerous
307. of envelop to use outer differetial Envelope True calculation Endpoints Use Guassian Use Guassian Noise otherwise use White Noise Fasle Noise Boundary Condition The 3 derivative of points on the boundary the closest is equal This is the same condition as in the MATLAB code at NotAKnot RCADA However the final results may differ due to different random noise added NatureCubicSpline The 2 derivative of the points on the boundary is 0 ClampedSpline The 1 derivative of the points on the boundary is fixed 20 Example This example uses the data gsta dat from RCADA It is the annual average temperature on earth surface You can refer to demo68 in C Program Files DynaDx DataDemon demo HHT gata N AKA JANI 980 1880 1800 1820 1840 1860 1980 2000 time year Connect the signal to Compute HHT RCADA EEMD for decomposition With default parameter setting the results are shown below Note the last curve in light blue is the Residual and it shows the temperature trend 0 5 18509 1860 1870 1860 1890 1900 1910 1920 1930 1940 1850 1850 1970 19890 1990 Date Let us compare the running speed with MATLAB code from RCADA using a same signal The signal IS vint S 2Ttt sin 30 2TI1 sin 50 2TT14 1 100 27 and the length of this signal is 20 000 The result of RCADA EEMD calucation is Mix Sine 0 0 1 0 2 0 5 0 4 05 06 0 7 00 09 SEC
308. of the same size data the module consumes less time and memories It shows hundreds times speedup in terms of 3Gb memory the upper limit of the Windows XP 32bit the computation upper limit of the standard STFT is about 4 million data points as for the fast STFT the limit is about 22 million data points Properties This module accepts real numbers single channels regular signals and audio inputs the format of the input signal is the plural and single channel spectra data Properties are set up as the below table Property lx El FastSTFT Method SlidingFFT Freghin 0 FreqmMax auto 500 FregqResalutian auto 25 Freqcaunt 40 TimeCount 00 Removebt True Window Hanning Display Type Downsample Order First rder Property Name Property Definition Default Value Setting the method of computations including FFT olidingFFT FFT provides the 1st Order Solution SlidingFFT provides the 1st 2nd Order Solution olidingFF T moves one point for each computation Method so the computation grid is at high densities but not SlidingFFT be presented fully on the screen If the FreqCount or the TimeCount is set less than the number of the time frequency grid of the data the users need to set the DisplayType In the results of the SlidingFFT if the FreqCount or the TimeCount is less than the computation grid of Display Type Downsample the data the sampling points are reduced by the Downsample the Maxima the Minima and the A
309. oine3 are orthogonal Sine and Sine3 are series symmetrical to the X axis so its result is the 1 T Properties El Orthogonality Matrix View Matrix Orthogonality Matrix for H Ortho zonality Matrix for l lol x Orthogonality Matrix for ToMulti Orthogonality Matrix tt em p Teak e CH2 sine 7831554938505844E 14 1 7 35855524205 5BE 14 CH3 ime 1 7 0358556524203 5BE 14 1 Related Function Covariance Matrix Correlation Matrix Merge To Multi Channel Channel Viewer Reference Probability Random Variables and Stochastic Processes McGraw Hill Page 211 3 4 7 Quartiles and Quantiles Quantile is the element value at certain percentage position of a sorted series while the quartile is the element value at 25 position 50 position and 75 position of the sorted series Introduction Let 9 1 v1 be a serie with N elements the quartile can be expressed as P X lt lt 1 4 More specifically the quartile of a series is the value at cumulative distribution function equal to 2596 position q at N 2596 1 The median and three quarters of the median follows the same concept Quantile is more generalized and use percentage as standard For example 17 quantile represents values with the cumulative distribution function equals to 17 If the location of quantile is between 2 points q N 1 is not an integer we need to estimate the location The e
310. omponents at the ends So the resultion of the signal gets improved The transform equation is shown below Y a l f id X a b Til IG G9 b tdt a o 4T O h 40 where 9 9 is the Gussian function At high frequency the parameter a of the Scale in Morlet wavelet becomes smaller this reduces the resolution at high frequency Before the transformation Morlet Wavelet multiplies Gaussian Window 9 9 9 to improve the resolution at high frequency Properties This module accepts input signals of real number single channel regular and audio The format of the output is real single channel and the spectra of regular Properties are defined below Module E Morlet Linear Axis vi FreqMin 0 FreqmMax auto 0 CwerlappedFackor 1 Freqcaunt 128 TimeCount 2048 RemoveD True FreqAxis Frequency axis type Property Name Property Definition Default Value FreqAxis The frequency distribution of spectra can LinearAxis be in Linear scale or Log scale 0 FreqMin Set the frequency range minimum and FreqMax maximum 0 5 Sample Frequency The overlapping factor when moving Overl dFact 1 Tego tm Gaussian window it is 9 in the equation FreqCount Set grid count in frequency axis 128 TimeCount Set grid count in time axis 2048 he D f Bises Remove the DC component before True performing Morlet Transform Example The input signal is chirp sound of birds We c
311. ond are discarded in ToMulti2 Sine ToMulti ToComplex 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec If the 2 signal is selected as Reference Input for ToMulti2 the signal diagram will be altered as the figure below The time axis length is 2 seconds Because there are no data between 1 second and 2 second in ToMulti signal this part is cleared to be zero automatically And the imaginary part and Magnitude are preserved Square ToMulti ToComplex 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 time sec Related Functions Noise Sine Triangle Square Map to Real Merge to Multi channel 4 6 Merge to Multi channel This component merges several single channel signals into a multi channel signal Introduction Letx to be a signal whose time axis is y to be a signal whose time axis is k then the merged signals z is Lm x i Jm j Reference Input x where 5 Reference Input y m represents the signal time axis If the Heference Input is set to x the time axis output signal z is identical to the one in x i e m and the time axis of y would be replaced by the time axis of x Note that this module replaces the coordinates of the time axis and more attention is needed for the lengths of input signals Properties This module accepts input of Signal which could be real number or complex number single channel Regular or Indexed Audio which could be real
312. operty Name Property Definition OutputDictory Preference Select the location to save the file NOTE With the file name and location entered the file is only saved when WriteNow is set as True OutputFileName Example Text Writer v Auto gt Output a Sine Wave signal to a txt file Create Source gt Sine Wave to Writer Text Writer to save the data into a text format Click on the Properties Writer OutputFileName field and a button will appear at the right hand side of the field Click on the button to enter the name for the file and the location to save the file Pro z E Writer WriEeMow False OutputDirectory C Program Files AnCAD Mi OutputFileMame OutputFileName The output Filename Enter the file name as sine and save the file to the location C directory Since Properties Writer WriteNow is set as False the file will not be saved yet Now change the WriteNow option to True and the file will be saved in C directory Select OutputFileName Dell3100 BJPrinter Documents and Settings My Recent extra Documents lava Matlab output Program Files JRECYCLER iC3sleep housekeeper _ System Volume Information temp tmp WINDOWS i Yanhui TransferInfo txt File name sine Save as type Text files txt WriteNow True LENA 111 Teel Tr foo aim OutputFile
313. original signal carry out different calculations on it and output the results in different format Then use nput Switch to select one of the channels Steps are shown below 1 Create Source Noise in Network panel set Properties TimeLength to 3 set Properties SamplingFreq to 1000 and set Properties Amplitude to 1 Properties lx Module Noise MoiseTvpe White El Source TimmeUnit sec TimeLength 1 SamplingFreq 1000 DataLength 1001 Amplitude 1 0 TimeStart 2 With default settings connect the Noise SFO to Compute Transform Fourier Transform Compute Transform RCADA EEMD Conversion Convert to Audio Compute TFA Short Term Fourier Transform and Conversion Convert to Matrix respectively All outputs of the calculation are connected to Compute Channel nput Switch and show the result in Channer Viewer Change Active Input setting in Input Switch to view different results T J ToAudio La a ee me me m m m me m Properties ix El Input Switch Active Input 3 RCADAz EEMD w Module 1 Moise 2i FFT ROADS EEMO 4 Toudic 5 6 ToMatrix 4 And connect Input Switch to TFA Viewer and change Active Input setting to observe the result of STFT 500 400 0 006 K I 300 gt 0 004 uw 200 m 0 002 100 0 of 02 03 04 05 06 07 08 09 1 time sec 5 Change Active Input setting to ToMatix and use DataViewer
314. otations for the Sine function Create a Sine function with Source Sine Wave and viewing its results with Viewer Channel Viewer Set the ViewerHeight of the Channel Viewer to 400 Properties El Appearance BackColor White ViewerWidkh default 600 ViewerHeight 400 ListOrder RetainPlot False Add a Rect a Ellipse a Text to the Viewer and set the properties as below ZOrder 1 Start X 0 25 0 End X 0 75 0 75 LinePen Red Solid 1 Module Set the properties of both Ellipse and Rect as above E Annotation ZOrder 1 Text below Position X 0 5 0 65 TextColor S RoyalBlue TextFont Arial 15 75pt Set the properties of the Text as above After pressing we can get the updated figure as below Sine 0 1 0 2 0 3 0 4 0 5 0 7 0 5 1 time sec Link a Line a HRegion a VRegion to the Viewer as shown below and set the properties Properties x E Annotation Order 1 Skart 3 0 2 Y 0 5 End 1x 0 4 Y 0 7 LinePen DarkGoldenrod Dot 5 Set the properties of the Line as above Properties x Annotation 2Order 2 Position 0 5 Positionz 0 5 PixelIndent Colori B Red Colorz 3 DarkTurquoise Set the properties of the HRegion as above E Annotation 2Order 3 Position 0 25 Positions 0 75 PixelIndent 0 Colori IN SeaGreen Colorz BurlyWood Set the properties of the VRegion as above
315. ource to True This makes the DoMatlab changed from a calculation component to a signal source component And its color is changed from red to turquoise The blue input triangle also disappears X Matlab updated Auta gt El DoMatlab MatlabEditor Yo Matlab script X1 Column Veckors Troe Server Visible True E Dumpaoutput False MinInputPorts he MinInputPorts Specifies the minimum number of input ports Matlab updated Auto gt In the Matlab Command Window type in whos to search for variables The result is shown below Since there is no input data and only a variable of Y DESC exists the variable Y needs to be created first and then the setting of data format needs to be filled in Y DESC MATLAB Command Window To get started type one of these helpwin helpdesk or demo For product information visit wwu mathworks size Bytes Class 1x1 664 struct array Grand total 15 22 elements using 684 bytes i 3 Next use Properties MatlabEditor to create a signal By setting Y DESC DoMatlab can generate signals in all formats This step shows how to create an impulse signal Open a new Project and repeat step 1 to create DoMatlab source and then enter the editor page by Properties MatlabEditor Properties E DoMatlab MatlabEditor 09 Matlab script file o o M Calumn veckors True 5erverVisible True DurnpOurpuk False AsSource True Module MatlabEdi
316. ow where the time axis presents the time of the peak and the vertical axis presents the time difference of the peak and the last peak CustomVVave Peak to Peak interval 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 sec the manual signal with the trend pattern Generating the wave by the Source Custom Wave with default properties the Expression is cos 2 pi 30 t cos 2 pi 30 t exp 2 t The figure is shown as below CustomvVave 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec The correct peak can not be intercepted with the default properties of the Peak Detection Viewer T awww RARAANAANAARANIT skryva VAS 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time seg Turning on the EMD setting the Threshold Ratio to be 0 6 and the TargetFrequency to be 70 the result is shown as below Viewer time sec the manual singal with the Speckle Noise Mixing the Sine Wave frequency 10 with the positive Speckle Noise whose amplitude is the 3096 of the Sine wave the mixed wave is shown as below Mixer 2 1 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec Intercepting by the Peak Detection with the default properties the result is shown as below Viewer4 time Sec Turning on the EMD reserving the value that is lower than frequency 10 the Target Frequency is set to be 12 The result is shown as below Viewerz time sec The result is better pul
317. pedia Wikipedia has a good article on the Cauchy principal value at http en wikipedia org wiki Cauchy principal value Cohen s paradoxes First instantaneous frequency may not be one of the frequencies in the spectrum Second if we have a line spectrum consisting of only a few sharp frequencies then the instantaneous frequency may be continuous and range over an infinite number of values Third although the spectrum of the analytic signal is zeros for negative frequencies that instantaneous frequency may be negative Fourth for a band limited signal the instantaneous frequency may go outside the band Cohen 40 Curvature calculation to determine how much an object derivate from being flat Used in the curvature sift Degree of stationarity How much a signal s statistics vary over time Empirical Mode Decomposition An algorithm that decomposes data into Hilbert Transform friendly signals known as Intrinsic Mode Functions Extrema A local maximum or minimum in a signal For example in a signal sin x there would be a maximum extrema at pi 2 and a minimum extrema at 3 pi 2 Filter device that creates a new signal based on the old one by permitting only certain properties of the original signal to come through Traditional filters are non adaptive functioning by cutting off specific frequencies for the entire signal Fourier transform The Fourier transform converts a signal into a sum of multiple sinusoidal
318. provides calculation of time frequency analysis 1 Short Term Fourier Transform 2 Morlet Transform The generating function is Morlet function 3 Enhanced Morlet Transform An enhanced Morlet Transform which holds the characteristics of Short Term Fourier Transform and Morlet Transform 4 Hilbert Spectrum Calculate the instantaneous frequency of every time point after the input signal is processed by Hilbert Transform 5 Marginal Time Marginal Frequency Perform integration on the TFA result in time frequency spaces 3 5 1 Short Term Fourier Transform Short Term Fourier Transform STFT is a mathematical transform related to Fourier Transform which is used to calculate the instantaneous frequency amplitude and phase of signals Introduction Use continuous time function as an example a function could multiply a time window function which is not zero perform one dimensional Fourier Transform and then shift this window function along the time axis to get a series of Fourier Transform results which can be arranged to form a two dimensional result Mathematically such an operation could be written as x r o 00 where o t is the window function x t is the signal to be transformed Essentially X r c is a complex function obtained by performing Fourier Transform on x t e t which represents the amplitude and phase of the input signal in time and frequency space Properties
319. put signal while the imaginary part is the result of convolution on the original signal Based on the analytic complex signal instantaneous frequency instantaneous amplitude can be defined Hilbert Transform has shown good performance in communication system and wireless signal processing and analysis dr to convert a real time signal to an analytic complex signal whose real Introduction Let X t bea time series its Hilbert Transform y t can be defined as Y t P aa and an analytic function Z t is defined as Z t X iY alte a t x e Y E 60 ZO J where a t is the amplitude i e the envelop of the original signal while 0 r is the phase angle In the Polar Coordinate representation of the analytic function Z t the instantaneous frequency of the Hilbert Transform could be defined as below dO t dt e t For more details please reference to Hilbert Spectrum Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The output format is complex single channel Regular signal Theres are two properties in Hilbert transform The Output Type is used to set the signal output of conversion Available options are Complex Split Complex Unwrapped Phase InstantFrequency and Instant Amplitude The calculation methods of InstantFrequency incl
320. quency of 10Hz 0 5 sampling frequency of 1000Hz and length is 1 second Then change the Properties TimeUnit to minute SamplingFreq to 10000 SignalFreq to 600 for obtaining a signal whose x axis unit is in minute and signal frequency is 10Hz Connect the signal to Compute Transform Fourier Transform for FFT calculation and then connect the Viewer to show the curve where the x axis Is in frequency and the unit is in cycles per minute Viewer updated Auto El Source TimeLlInil min TimeLength 0 1 SamplingFreg 10000 DataLength 1001 SignalFreg 600 Amplitude 1 AmplitudeOfFsek 0 Phase TimeStart E SignalFreq The Frequency of the to be generated signal Sine FFT 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 frequency cycles per min From the result the frequency is 600 cycles per minute It is not in Hz Connect Change X Axis Unit to the output of FFT change the Properties Abscissa unit and use Channel Viewer to show the result Now the x axis has changed to Hz and the values on x axis has also changed to second automatically changexaxisuniE Viewer Updated XAxisUnit Abscissa Unit Hz E Convert to period False v Module Sine FFT 0 5 0 0 10 20 30 40 50 60 70 80 frequency Hz 2 In addition the Properties Convert to period can be set to True This converts the x axis from frequency to period as shown in the figure below The x axis is converted to
321. quency of the to be generated signal Mixer 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 3 On the icon of Mixer select Compute Transform Fourier Transform to perform FFT and then use Channel Viewer to plot the spectrum in the left window FFT example X Viewers updated mous gt Mixer FFT 0 50 100 150 200 250 300 350 400 450 500 frequency Hz Because most frequencies are less than 20Hz and the default xmax is 500 in Properties of Viewer set this field to 30 for better observation Mixer FF T 0 5 10 15 20 25 30 frequency Hz 4 n the spectrum diagram generate by FFI frequency components mainly concentrate at 10Hz and 3 Hz However the magnitude around 3Hz is under estimated due to the low frenquency This could be enhanced by changing the resolution Click on the FFT icon change the Properties Resolution to 5 to obtain new result It is shown that the spectrum around Hz has been improved significantly after changing the resolution Please note that increasing the resolution would result in multiplication of output data length in FFT In this example the input data length is 901 the output length of FFT is 451 when the resolution is 1 After changing Mixer FFT 0 5 0 5 10 15 20 25 30 frequency Hz the resolution to 5 the output length would increase 5 times to 2255 5 Change the FFI resolution back to 1 right click the FFT icon to select Compute Transform nverse
322. r a column in the data contains time axis coordinates it is recommended to use the Specify Time column row in the Text Importer As such the data format is marked as Indexed and the sampling periods are assumed to be different However most modules require the signal format to be Regular This module can be used to convert Indexed signals to Regular signals In Indexed format it is assumed that the data points on time axis are discrete and the intervals are uneven Therefore there exists a corresponding time coordinate for every data point Let the input signal be x Ix xt xt A and the signal time axis is defined as 2 0 0 1 Convert to Regular performs re sampling on the signal above to convert the time axis of Indexed signal into Regular which is discrete and equidistant t t jxAt O gt 1 jaeM 1 where is the time axis after Convert to Regular processing Ar is the output sampling period M is the number of the output data points The output signal X is obtained by the formula below O 4 00 0 O x x4 pu Two types of calculations FillGap and RemoveGap can be used to convert Indexed to Regular The details are given below FillGap Fill ap can preserve the signal time characteristics and add values at the locations where the time intervals are too large In calculation it can detect the minimum sample period Ar in the input signals and then use it to perform re min
323. ram Files DanaDx DataDemon Data Viewer updated After clicking Open Batch Run Dialog button as shown in the above figure The Batch Run window interface is shown below kJ Batch Run demo25 STFT BT fF Output Directory C Program FilespynaDxNDataDemondata E Batch Runs The fuction for each button is Click on to clear all Batch Runs and click on k to save Batch Run to the project Click on to delete the selected Batch Run item from the list Click to open the Parameter List which contains modifiable components to be applied to selected runs If you have a component that you wish to add to all the Batch Run profiles then you can click on gt to add it to all Batch Run profiles Or else use to add one component to the selected Batch Run profile Click on to hide the Parameter List Run demo25 STFT Ao om 15 amp Output Directory C Program Files DynaDx DataDemon data Paramater List From Project demo25 STFT Batch Runs amp ial Viewer amp 5 amp TFViewer w Selection H Viewers V hello 4 Both and i allow the user to create Batch Run profiles allows the user to create and edit Batch Runs from the exisiting SFO parameters The user can pick and choose the parameters to alter for each Batch Run i can only be clicked when a file has been i
324. raph of the firstly created Viewer SFO will be shown as the first graph and the graph of the secondly created Viewer SFO will be shown as the second graph and so on DataDemon provides many useful functions to control display and export the graphs shown in the Visualization Window pls The Visualization Window Toolbar is located under the menu toolbar at the top left corner of DataDemon 1 Visualization Window Toolbar L5 Copy to Clipboard allows you to copy the graph into the clipboard to be pasted into another application Note Copy to Clipboard provides two types of file format Bitmap and Meta file Export File allows you to save the graph into variety of file formats such as PNG BMP JPEG TIFF and WMF etc Besides the first two buttons and the last button the rest of the buttons on the tool bar will directly affect the graph displayed in the Visualization Window 1 rHome Clicking on the it Home button will reset the graph to its default position and size This button is useful when you get lost with zooming and moving around the graph and want to set the graph to its default view 2 Zoom X Firstly click on the Zoom X button and then click on any part of the graph and drag it along the x axis Part of the graph is highlighted As you release the mouse button after dragging the highlighted area will be zoomed in and displayed Sine Sine 0 3 0 35 0 4 045 05 0 55 0 6
325. requency Most of these situations are avoided by using the Empirical Mode Decomposition to eliminate riding waves i e multiple extrema between zero crossings Intrinsic Mode Functions however only satisfy the necessary condition for a nonnegative frequency This situation can be found for example in the signal y cos t 2 5 cos t This example can also be found in Hahn 1996 Although this particular signal is not IMF since the middle extrema does not cross the zero axis it provides a clean example of the physical properties that can result in negative frequency The signal y cos t 2 75 cos t Negative frequency will occur due to the differences in amplitudes of the different waves Note the differences in amplitudes between the waves Due to the phasor having to change the direction of rotation as the angular frequency is calculated this will result in negative frequency The limitation of the amplitude change is given by Bedrosian theorem 1963 which requires that the Fourier spectrum of the envelope should be disjoint with the Fourier spectrum of the carrier waves Otherwise the phase would not be separated from the amplitude fluctuation of the amplitude Below is a graph of the analytic signal 0 5 0 5 The analytic signal of y cos t 2 75 cos t The red sections indicate where negative frequency occurs due to the phasor s change of rotation oince negative frequency does not have physical meaning in th
326. results Quantile Method allows selection of the estimation methods for quantile Here we describe the breakdown of various parameters below Properties El Quartiles and Quantiles View Quartiles and Quantiles Quartiles and Quantiles fo Guantile Method Nearest Quantile Fractions D 01 0 1 0 25 0 5 0 75 0 9 0 Heneral E E Ouartiles and Quantiles for Noise Quartiles and Quantiles 00238 0489 0 976 0 798 0 498 0 0239 0 499 0 704 0 99 Quantle 0 974 The above is the pop up window when clicking c button to the right of View Quartiles and Quantiles The results of each calculation of the signal are presented in the columns with the first column showing the names of Quartile and Quantile From the Second Column each Column corresponds to the channel of each input signal The first three rows calculate three quartile values followed by rows calculating quantiles Users can set parameters with Quartile Fractions The following describes parameters for Quantile Fractions There are two ways to set quantiles fractions The first method is directly to change the data in the fields eg between 0 1 and 0 25 type 0 2 to add see below J Quartiles and Quantiles View Quartiles and Quantiles Quartiles and Quantiles for Quantile Method Linear 0 01 0 1 0 25 0 5 0 75 0 9 0 _ Quantile Fractions Specify the quantile Fractions E Quartiles and Quantiles View Quartiles and Qu
327. rier Transform Morlet Transform Enhanced Morlet Transform Viewer Reference 1 A Wavelet Tour of Signal Processing 2nd Ed 3 5 2 Morlet Transform Wavelet Analysis or Wavelet Transform uses a finite length or fast decaying oscillating waveform known as Mother Wavelet to represent signals Mother Wavelet would shrink or expand automatically based on the signal characteristics Morlet transform uses Mother Wavelet to perform Wavelet Analysis Introduction Different from Fourier Transform the Wavelet Transform converts a signal to a time frequency signal Subject to the uncertainty principle the multiplication of frequency resolution and time resolution is a fixed value i e when the frequency resolution is good the time resolution must be bad and vise versa The time resolution and frequency resolution of high band and low band frequency are fixed values in Short Term Fourier Transform However it is desired to have good time resolution in high band frequency and good frequency resolution in low band frequency Wavelet Transform can achieve this requirement The formula of Wavelet Transform is given below ene qao where a is the scale parameter and b is the shift parameter of mother wavelet Via the transform the a value is converted to frequency Mother wavelet y t must satisfy 3 conditions listed below 1 T dt 2 fw dt oo 3 Morlet Transform is one type of Wavelet Transform whose mother wa
328. rix A Properties This module accepts real number complex number and Numeric data And the output has the same format as the input Module Transpose Complex Conjugate True Default Property Name Property Definition perty idi Value Complex For complex element matrix take conjugate ins Conjugate calculation Example The matrix A is 2 X 3 and its elements are 2 8 34 9i 9 O 7 Calculate transpose without conjugate the output matrix A is 2 81 5 3 6 4 9 7 A is Calculate both transpose and conjugate the output matrix 2 8i 5 3 6 4 91 7 3 9 4 Extract Region of Interest Extract a matrix S from a matrix A The Start Indexes is sx sy the row length is Ix Row and column length is ly Column matrix and the End Indexes is sx Ix 1 sy ly 1 If the End Index exceeds the dimension of matrix A O is filled Introduction It is very close to the definition of Sub Matrix However this module can handle with higher dimension matrix The elements are filled with O if the dimenstion is larger than the original matrix Properties This module accepts real number complex number and Numeric data And the output has the same format as the input Extract ROI 0 o m ROI Dimensions 1001 256 Module Propert Property Definition Default Value Name otart Starting element for extraction 0 0 Indexes ROI Row and Column length for Row and Column length of the
329. rm Haar Wavelet Transform Hilbert Transform Inverse Hilbert Transform Auto Correlation Calculate the auto correlation between signals Cross Correlation Calculate the cross correlation between signals Multi Scale Entropy MSE Calculate signal multi scale entropy 3 6 1 Fourier Transform and Inverse Fourier Transform Fourier Transform converts a time signal to a frequency signal for checking the frequency and amplitude distribution in the signal The frequency signal could be converted back to time signal by Inverse Fourier Transform This method is widely used in communication voice signal system analysis and other scientific fields Introduction Let X x x x xy be a N length time signal x be the n signal O lt n lt N 1 the discrete Fourier Transform of signal X is defined as a N length series 1 B ET F x Dime N O0 lt k lt N 1 n 0 The Inverse Fourier Transform is defined as follows Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The definition of properties and corresponding setting are given below Properties Resolution 5 Window Hanning The property of RemoveDC is used to remove the average of signal The properties of Min and Max define the frequency range of FFT Ihe Property of Resolution is used to duplicate
330. roperty Name Property Definition Seran Value Set True to play the audio file after the file has been saved or play the audio file right away if Play False the file is already saved with the default audio player of the computer WriteNow Select True to write the data to file False Displays the default location of the files to be saved Note You can edit the default location OutputDictory from the main menu under Tools Preference Select the location to save the file NOTE With the file name and location entered the file will only save when WriteNow is set as True OutputFileName Example In this example create a noise wave and a sine wave and combine them to become a multi channel data then convert the multi channel data to audio 1 Create Source Noise Wave with Properties Noise Noise Type set to White Noise Properties Source SamplingFreqg set to 1000 Hz and set the Properties Source TimeLength to 2 seconds Then create Source Sine with the same settings SamplingFreq set as 1000 and TimeLength set as 2 And connect both signal data to a Compute Conversion Merge to Multi channel SFO ToMulti updated TET gt m 2 Connect the ToMulti SFO to Conversion Convert to Audio to turn the signal data to audio Set the Sample Rate to 1000 Hz Bits per sample to 16 bps so that once it is converted to audio it will be accepted by Writer Wave Writ
331. rown 4 2 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec blue 10 10 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Violet 20 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 Connect the Pink Noise SFO to Compute Transform FFT and connect the FFT SFO to Conversion Map To Real and finally connect the result to a viewer SFO Change the Properties MapMethod of the ToReal SFO to PowerSpectrum You can observe that the power spectrum density increases as the frequency decreases PowerSpectrum Map Method Mapping method FFT ToReal 0 3 0 10 20 30 40 50 60 70 80 90 100 110 120 frequency Hz 3 Repeat the steps to the other source signals The Blue noise graph is shown below after the steps FFT2 ToReal 0 8 50 100 150 200 250 300 350 400 450 500 frequency Hz eo You can observe that the power spectrum density increases as frequency increases 4 Set the Noise Type to Gaussian Noise and set the Time Length to 100 seconds and view it with Viewer Histogram Viewer Histogram CH1 15000 Related Functions Channel Viewer Fourier Transform Map To Real Reference http en wikipedia org wiki Colors of noise http en wikipedia org wiki Gaussian noise 5 3 Sine Wave Explanation is given here for the Source Sine Wave SFO Introduction Let t time N length of the signal t t t t _ is the representation of the time coordinate and sine wave can be
332. rs for DoMatlab PEE Reciprocal Matrix Condition Numbers for DoMatlab Reciprocal Matrix Condition Numbers Condition CH1 infinity norm 0 0373 It shows that the value of the Norm is not close to 0 So the inverse matrix does exist It can be calculated via Inverse matrix module Helated Functions Matrix Inverse Matrix Operation Heferences Gilbert Strang Linear Algebra and Its Applications 3rd edition 3 10 External Professional Only 3 10 1 External DII This module is to help users to call self developed algorithms and data input interface etc Users can generate DLL Dynamic Link Library for their application using Visual C Visual Basic and Visual C environments The DataDemon can use this module to call these DLLs Introduction Create DLL in Visual Studio environment first Under Project select Class Library and add vsmExternalBase dll to the References C Program Files DynaDx DataDemon External vsmExternalBase dll remember using VSignal ExternalBase The written Class must inherit TExternalBase and modify two major methods Init and DoCompute The name parameter and modules etc of Init method need to be set The modification of DoCompute is to accept input signal use user s algorithm for data processing and output setting etc All settings can refer to ExternalBase Class Library section The example of DLL can refer to C Program Files DynaDx DataDemon Ext
333. rst channel is the X axis value ranging between the minimum and maximum of the input values the second channel is the Y axis value being the corresponding probalility density value of the series value Properties 5 Kernel Smoothing Density Type Losine of Points 100 width Auto 0 182097620361169 Tvpe Select a kernel type For density estimation s uns Default Properties Property Definitions value The types of kernel function build in function include Uniform Type Triangle Epanechnikov Quartic Triweight Gaussian and Gaussian Cosine Their definitions are in the next table No of Points Descret points of the output signal 100 The width of the sliding window h is the constant to control Width the smoothness level The default value Auto is the best Auto width calculated under the standard normal distribution The following table lists common definitions of the kernel functions Type of Kernel function Definition lu lt l Uniform 42 0 otherwise 1 lt 1 Triangle 0 otherwise 29 5 feci Epanechnikov K u 4 4 0 otherwise i 22 lt 1 u lt Quartic 16 0 otherwise 35 243 390 4 EMES f C Triweight K u otherwise E 2 4 j Qa lu lt Gaussian 4 0 otherwise cm lt Cosine 4 gE 1 0 otherwise Examples Creat a signal using Source
334. rt Spectrum is to perform spectrogram via Normalized Hilbert Transform Introduction Please see 3 7 5 2 NASA Hilbert Transform Properties This module accepts input of Signal which could be real number single channel or multi channel Regular and Audio which could be real number single channel or multi channel Regular The output format is real number and signal channel spectra data The number of discrete lattice in FreqCount requency axis The number of discrete lattice in time axis 1004 Sets number of median smooth points 5 SmoothPoint value of 0 indicates that smoothing would be not used Example In this example LOD78 is decomposed and then all IMFs are transformed into spectra by NASA Hilbert Spectrum 1 Use Source Import data from file to read tfa file LOD78 tfa in the installation directory default to be C ProgramFiles DynaDx DataDemon demo HHT Next perform Compute NASA HHT NASA EMD LOD78 would be decomposed into many IMFs LOD7Z S NASA EMLD 0 500 1000 1500 2000 2500 3000 time day 2 Lastly use Compute gt NASA HHT NASA Hilbert Spectrum to connect NASA EMD and furthermore time frequency result is displayed in the TFA Viewer LOD 78 NASA EMD NASA Hilbert Spectrum Frequency cycles day 1 5 Time day Related Functions Hilbert Spectrum RCADA Spectrum 3 7 3 5 NASA GZC Spectrum NASA GZCSpectrum is to perform spectrogram
335. rties contained within these signals such as extrema zero crossing and the period This new method can derive frequency directly in the time domain Advantages of this method includes that it comes directly from the definition of frequency itself as well as avoids issues with negative instantaneous frequency found in the Hilbert Transform The disadvantage is that the local frequency is smoothed over at least a quarter of a wave length Algorithm The Generalized Zero Crossing GZC method is a weighted calculation of the signal features local extrema zero crossings and the period This method can only be successfully used on signals with the properties of an IMF since these signals are not hampered with riding waves and other distortions Each of these features alone can be used to obtain a frequency value of their own for example the length of the period the traditional definition of frequency but the GZC uses them all together for a distinct calculation that provides insight to local phenomenon 2 It Traditional definition of frequency the inverse of the length of the period Frequency as defined by the Generalized Zero Crossing p is the length of the period h is the distance between zero crossings half the period and q is the distances between extrema and zero crossings quarter of the period These values are weighted to give advantage to measures that are more local The wave period is defined by the critic
336. rty Definition General properties For every IMF show the number of Zero Crossings the number of Extrema Extreme Counts and the average instantaneous frequency The average instantaneous frequency is estimated by the number of zero crossings and the number of extreme Orthogonality To calculate all IMF orthogonal matrix Percentage Power To calculate the energy percentage of every IMF compared to the total energy of the original signal except for Residue Example Following the example of HHT use the IMF Property component to show the signal characteristics after decomposed by EEMD operation Right mouse button click on EEMD SFO and select Computer HHT IMF Property as shown below For every IMF analyzed after clicking the Report button which locates on the right a result window is poped up as shown below A wh E IMF Property IMF Property Report for EMD Module IMF Property Report for EMD General Properties Channel Zero Crossings Extreme Counts Average Frequencies IMF hi 375 190 125 IMF h2 187 96 62 6 IMF h 93 46 313 IMF h4 61 30 207 IMF h5 29 15 9 09 IMF residual 0 0 0 333 Orthogonality Matrix Channel IMF 1 IMF IMF IMF IMF 5 IMF residual IMF_hl 1 0 294 0 0295 0 133 0 0305 0 00669 IMF_h2 0 294 1 0 331 0 0987
337. s TFA Viewer Haar Transform References Proc R Soc Land A 1998 903 995 The Hilbert huang Transform And Its Applications Huang by Norden E EDT Shen Samuel S EDT World Scientific Pub Co Inc 3 5 5 Marginal Time Marginal Frequency Introduction Marginal Time is to obtain a distribution in time domain by integrating a signal x t with respect to the frequency where the signal has been processed by time frequency analysis Mathematically this operation can be written as 00 where X t c is a two dimensional time frequency array x t is a time domain distribution i e Marginal Time If integration is performed with respect to the time frequency distribution of Marginal Frequency could be obtained This operation can be written as xo 00 Properties This module accepts input of Spectra which could be real number or complex number single channel Regular The output format is real single channel and Regular signal The property is Marginal Method which mainly is used to process two dimensional time frequency complex array Different from time frequency integration 7 options are provided as listed in the tables below E Marginal MaregmalMethod PowerSpectrum E Module Hame H Freg Input Port Side Left Port Side Right AcceptableData Types Complex Single Channel Spectra of Ea MarginalMethod specifies a complex component to sum qj Networ
338. s Type Window Overlap Moise Rallingatats 100 200 300 400 500 00 700 200 ann time Sec When window 2 the results from step 2 is not much different from the original signal Adjust window to 50 the result is graphed below Then click RollingStats icon press Data viewer on Network toolbar to see the length of Data count The length is 952 this can be checked with K value described in the Introduction Properties BackColor White Viewer Width default 750 ViewerHeight default 180 ListOrder 1 El Channel Noise Raollingstats 0 100 200 300 400 500 B00 700 200 900 time Sat Related Functions Basic Statistics Equiphase Statistics Quartiles and Quantiles Merge To Multi Channel Channel Viewer 3 4 9 Hypothesis Test Make an appropriate temporary hypothesis about the population and define a standard to reject the hypothesis based on random sampling distribution If the sample data fall in the range of rejection then reject the original hypothesis Otherwise you must accept the hypothsis Introduction Laboratory data often includes chance of errors true differences or other influences Hypothesis testing can be used to solve such problems In general it consists of three steps setting hypothesis selecting methods of testing and determining whether or not to accept the hypothesis Null Hypothesis the differences among samples are purely from chance Alternative Hypot
339. s and Quantiles let Quartile 556 2nd Quartle 0 115 Srd Quartle 0 291 0 01 Quantle 2 03 0 1 Qvantle 1 1 0 245 Quantile 0 604 0 5 Qvantile 0 115 75 Cmantle 0 391 O 9 Cuantie 0 665 B Cmantle 1 52 17 Qmuantile 0 642 Related Functions Basic Statistics Rolling Statistics Channel Viewer 3 4 8 Rolling Statistics Rolling statistics Setup a window with the width of M elements use statistical function to calculate the statistical value within the window such as average and move this window along the data to calculate statistics within the new window This calculation method is called Rolling statistics Introduction Let A 7 o be a data series with N members and the width of the window j for the rolling statistics is M M N The elements within the window can be W pp pr cee eX expressed as j M V with O lt S SN M Rolling statistics is to calculate the statistical value within the window such as Rolling mean i M 1 X j jr 2 M 0x p M Next define an overlap value p p represents the number of elements in the window overlapping with the previous one Let use rolling means as an example If the size of the window M 10 then the 1 point in the output is 9 2 X j j 0 10 seethe following diagram 10 0 1 Cz A 04 cs eT 09 time sec The ranges are signal position 0 to 9 as indicated above If p 9 then the ranges for t
340. s selected a new property of FillMethod is provided for value filling methods which are explained below Property Name Property Definition Default Value FillGap Use to conduct signal re sampling by value filling RemoveGap Directly change the time axis of FillGap the original signal Use the time starting point and the Sampling period to re arrange data time Convert Method When ConvertMethod FillGap different data tilling methods can be selected FixedValue Use NullValue as the fixed filling data PrevValue Previous value NextValue Next Value Linearlnterpolation Linear interpolation FillMethod oplinelnterpolation Use Spline Curve to Linearlnterpolation calculate the difference Monotonic Cubic This is a 3 degree interpolation with damping It has better performance than Spline in case of processing signal with large slope like square wave NoFill The value in this location is Null No value is added To show or set the sampling period of the output signal When AutoDetect is set to True it shows the Sampling minimum sampling period detected of the 0 _ input signals i e Ar Min At When AutoDetect is set to False besides showing it can also be used to set the min sampling period To show or set the sampling time unit of output si
341. se then connect it to HHT RCADA EEMD SFO and display the result with Channel Viewer 0 Of 02 03 04 05 06 OF 08 Q9 1 tme sec Finally connect RCADA EEMD SFO to Compute Statistics Basic Statistics and set Properties Stats Mode to AcrossChannels Then display the results using Compute Channel Channel Switch and Channel Viewe With Channel Switch different channel can be selected for viewing Properties lx Basic Statistics Stats Mode 4crossChannels Unbiased Moment Estimation True Trim Fraction 0 05 Trim at Ceiling False Related Functions Equiphase Statistics Rolling Statistics Merge to Multi Reference Michel Loeve Probability Theory Graduate Texts in Mathematics Volume 45 4th edition Springer Verlaf 1977 Joanes D N amp Gill C A 1998 Comparing measuresof sample skewness and kurtosis Journal of the Royal Statistical Society Series D The Statistician 47 1 183 189 3 4 2 Covariance Matrix Covariance is a measure of how much two series change together relative to their average value If covariance is positive it means that two series change in the same direction If covariance is negative it means that two series change in the opposite direction If there are multiple series involved covariance matrix is used to show the covariance between each pair series Introduction IY A i Tem Let 100 010 TT Dos Yrs 51 be two series the defin
342. se Mull Value Handle Linear Interp bul Time Coordinate Time Unit sec EE hoo Dovwn sample by Date Axis zon Lee Les es File Contents Value CH1 99564 B88258 85087 93061 29194 94502 79006 1 65702 1 57953 1 49517 1 30733 coo co co Oo co eo 8 amp 1 First the data to be imported has to be understood You can see that there is NaN missing data value in 009 and 013 of the CH1 column The first column is the x value time and the second column is the CH1 data value Text Importer will be configured to import this data properly into DataDemon File Contents 001 X Value CHl 002 0 1 99564 003 0 001 1 98258 004 0 002 1 96087 005 0 003 1 93061 006 0 004 1 89194 007 0 005 1 84502 008 0 006 1 79006 009 0 007 NaN a 010 0 008 1 65702 Null 0 011 009 1 57953 Value 012 0 01 1 49517 013 0 011 NaN 014 0 012 1 30733 2 The first row in the data contains the titles for the two columns So in the Rows option under Data Range the Rows should begin from 2 the second row is where the data values begin Because the data contains time information check the Specify Time Column option under Data Range and select 1 first column of the data is the time information Data Range at Columns to Foz Data direction Column based specify Time Column 3 The Field Format does not need to be edited becau
343. se sound diagnostic device signal The original data is shown as below Selection 25 25 5 26 26 5 27 27 5 2B 28 5 29 29 5 time sec Intercepting by the Peak Detection with default properties the result is not good Viewer 25 25 5 26 26 5 27 27 5 B 28 5 29 29 5 lime seg Turning on the EMD setting the Target Frequency to be 40 Hz the result is better The reason is that there is much noise in the signal the EMD is used to filter the useful data from the signal Viewer 25 25 5 6 26 5 27 27 5 B 28 5 29 28 5 time seg The Peak to Peak Interval is selection Peak to Peak interval 26 26 5 Helated instructions HHinterval EMD 21 27 5 28 28 5 time sec 1 29 29 5 30 3 8 7 R R interval The detection of the R wave is the most issue in the ECG signal diagnosis The R R interval could be used to diagnose many kinds of diseases Introduction The ECG signal includes R S and T wave types R T ik 103 Ch1 CH1 400 2 gt E 412 4122 413 4132 4134 4136 4112 414 414 2 4144 4145 4142 415 time sec The R wave is usually the most obvious peak This module intercepts the time interval of two R waves In the output figure the x axis presents the time of the R wave the y axis presents the time difference of two R waves Properties This module accepts standard ECG signals the D value of voltages of two electrodes with the unit Volt or milliVolt Th
344. se the data is separated by White Space which is the default selection Check Use NULL Value Handle option under NULL Value Handle and select Linear Interp calculation from the drop down menu to fill in the NaN values missing value Mull value Handle Use Mull Value Handle Linear Interp b Monotonic ubic If there are NULL or NaN values in the data but Use NULL Value Handle option isn t checked then the following warning message will appear x Warning Data contains null values While data may still be displayed some computation may produce invalid results You may use V alue to fill these null values 4 Although the time information exists in the data you still need to set the unit of the time information Click on the Time Unit option under Time Coordinate and select sec from the drop down menu Time Coordinate Down sampleby 1 l Click on the Import button once the configurations are done viewer updated Auto gt B If the signal data is to be calculated further it needs to connect to Conversion Convert To Regular because Specify Time Column is in the Indexed format It needs to convert it to regular format gt Module Mame tests Nath QutpukPort side Right E OutputData Type OutputDatal ype Output Data 5 1 4 Import csv file format The data in the csv file format is separated by comma character The first row in t
345. sers to show different images in DataDemon User can create different DLL Dynamic Link Library under Visual C Visual Basic and Visual C environment This module can display the images using these DLL Introduction See the description in section 3 10 1 Properties Property BackColor White Auto Resize viewer True viewer Widkh 640 WiewerHeight 503 ListOrder RetainPlot False External ExternalPath C Program Files AnC AD Visual Signal Exte Module demo Local Topy False SystemCopy False DllProperties Path Stretch False True Module Representation Show Title True El Title Title default Property Property Definition Default Value Name External Path The directory to the external DLL None Module Select module in the external DLL None LocalCopy If True copy DLL file to local project False If True copy DLL file to DataDemon special oystemCopy folder C Program False Info Demno b v1 2 2 0 FilesiDynaDx DataDemon External Auto name oet the name for the external modue automatically Properties of DLL which implemented by the user MAL LL or API Version etc BackColor oet background color of the plot Auto Resize If True set the size of the plot based on the Viewer monitor display Otherwise set by the user ViewerWidth Set the width of the plot unit is in pixel ViewerHeight Set the height of the plot unit is in pixel ListOrder Set the or
346. sic Statistics SFO opened in Data Viewer Data iewer emo25 STET Stats UN 15 Channel Information CH1_Stats Histogram Channel 1 1232337419640 0 462935270241 0 868465224158 0 000465683185 GeometricMean 0 138331665540 E Data HarmonicMean Camplin Trimuned Mean 0 001849740480 Median 0 000396740623 stdDev 0 093177832205 B Di Variance 0 008682108414 por 1 VariationCoef 200 0884618428 s E T c 014 in 104522242 025314014 m 1677361101428 Mas 300 08846184282481 Kurtosis 15 08007036975 10 419637 120351004 SemistdDey 0 059070935092 EOL ATE eee SemiVariance 0 003489375372 1 3 5 Batch Run Professional Only Batch Run allows the user to simulate one or more Batch Run calculations based on the current Signal Flow Diagrams in the Network Windows The usefulness of this feature is that the user can edit the properties variables of any SFOs in the Batch Run and create multiple runs to easily test out the different calculation results The edited properties variables within Batch Run do not alter the original settings of the Network Window s SFO network relationship So the user can safely edit any properties of the SFOs in Batch Run without worrying about influencing the original status of the project From the DataDemon Toolbar click on Open Project button or type Ctrl O and open the file demo 25 located in C Prog
347. signal Slope Threshold the maximal absolute value of the gradient is Hatio 5 MUTA 5 ry 5 rur 2 ratio If properties are not appropriate the module may Number of not remove the Bump or Jump completely This iterations number controls the repeat time of searching the Bump or the Jump 0 3 The start time of processing the Bump or the The start time of Jump the entire signal StartPosition The end time of processing the Bump or the The end time of EndPosition TEM Jump the entire signal Example The seismometer data selection d oer 7 dq 7er 20 22 24 26 28 30 32 34 38 38 40 2 44 time i darj Linking the original signal to the Compute Enhanced RemoveBump and then viewing the result by the Channel Viewer All of properties are set with the default values as below i Remove Bump Bump Remove 4 532 e O07 Z 825et07 20 22 24 28 28 30 32 34 36 38 40 az time day Where the two biggest Bump points are removed After the first RemoveBump we add another RemoveBump The properties are set as below a Setting the Jump Threshold Ratio and the Slop Threshold Ratio of the second RemoveBump to be 0 1 and other properties are set with the default values There are two processing methods The first method Bump Rermave Bump Remave 4 23e 07 aq Sszs0er 7 Zg a25et 7 20 22 24 26 28 30 32 34 38 38 an daz time day From the above figur
348. single channel from a multi channel source Replace Value Replace a particular value in the signal data Resample Set a new sampling frequency value to a signal data Time Shift Shift the graph along the x axis time Data Merge Merge two signal data 10 Input Switch Accept all sorts of input signals and one signal is chosen 3 1 1 Channel Switch Select a single channel from a multi channel source Properties This module accepts input of Signal which could be real number or complex number single channel Regular or indexed numeric which could be real number or complex number single channel Regular or indexed and Audio which could be real number or complex number single channel Regular The output formats are real number single channel and Regular signal The properties and settings of the Channel Switch are introduced below El Channel Switch Select Last Channel False Module Property Name Property Definition Default Value L Shows the number of channel currently Channel Count connected to the SFO Positive integer Channel 1 the Active Channel Select the active channel 1 channel If Select Last Channel is set as True Select Last Channel then the channel to be removed will always be the last channel Example Combine a sine wave data with a triangle wave data into multi channel and use Channel Switch to select
349. sn file through Load Macro the file will be opened as a macro within the project Related Functions Dup 8 2 Container Professional Only Container allows user to pack SFOs up to an element so that user can manage programs of complex signal computation Introduction When complex signal anlysis assignments are processing module elements may fulfill the Network panel window Now a Container module is added to pack SFOs up into an element The user can add a Container in the same way of adding a Project but the compiler of this module belongs to Container so that it can be operated in the compiler area of Container module Different Containers can have their visual plot areas and input sources Dataln but just can own one output DataOut L a e ll Functions of Container are instructed as below NAME ACTION Add Adda Container Dataln In Container gives the data input entry DataOut In Container gives the data output entry When many modules connect to a Container the user should set the origin of the data by the InputFrom function of Dataln E DataIn 0 data1 M dul e 1 data2 One Container just can own one DataOut Example Pack up SFOs into a Container Mix Sine Triangle and Noise For easy viewing frequencies of the Sine wave and Triangle are different from the Noise The original signal is snd
350. source 5 Matlab script file t O 0 01 2 sine sini t z pi l 0 amplitudes sini t z pi l sections amplitudes zine Y sections sections Y DESC intervals 0 01 Y DESC type Siognal DoMatlab 0 0 5 1 1 5 2 2 5 3 3 5 4 time sec 2 Select Compute Iransform Hilbert Transform from DoMatlab to perform the calculation directly The Output Type is the default value of Complex Use Viewer Channel Viewer to plot the result Note that the output signal is complex while the default of Properties YValueType in Channel Viewer is Magnitude and therefore the output shown in the Viewer is Magnitude of the output signal After the calculation connect the result to the same Channel Viewer can be seen that the result of Hilbert Transform is the upper envelop of the DoMatlab signal Projecti X Viewer updated Auto gt E Viewer time sec 3 Next create a sine wave source and perform Hilbert Transform Change the Hilbert Output Type in Properties to Split Complex Hilbert Transform splits the real part and imaginary part into two channels Use Viewer Channel Viewer to plot the values of the real part and imaginary part where the black curve is the real part and the blue curve is the imaginary part It is shown that the imaginary part is 90 phase shift of the real part with respect to the phase angle bal Viewer updated Auto gt Hilbert
351. stimation methods are plenty This module presents 5 most common used methods for the users to choose Interpolation Definition Notes xg 7x t q i x x The values before and after ri i the quartile position are Linear E Which i represents the integer part used for the linear of q interpolation quantile OE 0 The value of the next A E Next point 3 0 position after the quantile floor q HI position The average values of the Average Xg zX tX position before and after the quantile position 2 The point before the x 7x 4 8 x 57X quantile position plus the difference between the Which i represents the integer part points before and after the of N 1 p and g is the fractional quartile points This is part adopted by Microsoft Office Excel Weighted Average X lt 0 5 Xs 20 5 The value of the position Nearest closest to the quantile Which i represents the integer part posten of N 1 p and g is the fractional part Properties This module accepts input signals in real number complex number single channel or multi channel and regular The interface for parameter setting is shown below This module by default calculates quartile values of serie such as quartile median three quarters of the median values Also available under Quantile Fractions is quartile values to calculated next View Quartiles and Quantiles will show pop up window for the
352. t 384 Rung Parameters for module STFT FreqCount Click on to start the Batch Run process If there is a need to stop the Batch Run process click on the Q otop Batch Run button After the Batch Run all results will be shown in the Viewer and the images will be saved in the Output Directory Each Run profile will generate a single image file and the image file format can be configured in the Preference button of DataDemon e Example 2 In this example a single VSN file can be used to calculate multiple data files Firstly a Signal Flow Diagram will be created and then a demonstration of how to calculate multiple data files will be explained Click on the 4 Import data from file in the Netowork Window Toolbar and select Chirp1000 tfa from the location C Program Files DynaDx DataDemoni data Network eS Look in data 8 100 atr d test5 tfa J 100 hea te test tfa Recent E 111 tfa 9 test7 tfa Documents 2 111 01 1 mat gt i tide tfa E chirp10000 tfa A Windows XP mp3 i hello wav A Windows XP wav It multi tfa led smile tfa lE test1 tfa 9 test2 tfa 9 test3 tfa 8 test3 NaN2 tfa 9 j test3 NaN tfa 9 test4 tfa Desktop My Documents Bullfrog gt Fle name chip1000 tfa My Network Files of type All Suppot Files _ Cancel 1 After adding the file add a Viewer Channel Viewer to draw the graph and then use
353. t Port Side allows a change of output lines coming out of the SFO TIPS Sometimes there is a need to change the sides to better display the entire Signal Flow Diagram and Execution Time shows you the time it took to calculate this information Properties Class Sine Wave Mame Sine Pork Side Right ExecuteTime 0 109375 sec GutputDataT ype Real Single Channel Signal a Source TimeUnit TimeLength SamplingFreg DataLength If a SFO contains both input and output function e g Compute and Conversion then there will be a lot more information shown under Module For example there might be new information such as Input Port Side Acceptable Data Type and Output Data Type included Input Port Side is exactly the same as Output Port Side except Input Port Side determines the position of the lines connects to the SFO Acceptable Data Type is a drop down menu which displays all the acceptable data input that the SFO can be connected to Selecting an option from the drop down menu will not perform any action because the drop down menu is just a display Output Data Type displays the output file format Properties Fft FFT Input Pork Side Left OutEpu Pork Side Right ExecuteTime 0 03125 sec 4cceptableDataTypes Real Multi Channel Signal GutputDataT ype Complex Single Channel Sic Signal data Data Definition Real Real Signal Channel Types Complex Complex Signal Single Channel Single Channel Channe
354. t click on St and then drag it to the top graph or the bottom graph NOTE You can only move one position at the time E oo Mixer D 0 0 1 0 2 0 3 0 4 0 5 0 6 07 0 8 0 9 1 time sec Next to the 88 is the Group tick box it is used to synchronize many images so that they can be zoomed and moved together Check the Group tick box to start synchronizing some images A small scrolling bar allows you to enter a number between 1 to 5 and this number indicates the group that the image will be associated with The images belong in the same group will be zoomed and moved with each other Sync option X Y and XY indicates which x axis or y axis or both directions will be synchronized and moved Noise 0 0 1 02 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec S 4 0 0 1 0 2 0 3 0 4 0 5 0 6 07 0 8 0 9 1 time sec After configuring the Group option the configured setting will remain visible on the top left corner of each image Below is an example of how to use Group to synchronize two images so that they can be zoomed and viewed together The Signal Flow Diagram is made up of Source Noise and viewed with Viewer Channel Viewer and the Noise SFO is also connected to Compute gt Morlet Transform and viewed with Viewer Time Frequency Viewer as shown in the image below 4 2 0 t 2 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Noise Morlet 500 400 gt 300 O c o p 2
355. t ec 5 ThirdQuartile Module Type Select a statistics Noise Equiphasestat 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 time sec Helated Functions Basic Statistics Rolling Statistics Quartiles and Quantiles Channel Viewer Reference 1 Michel Loeve Probability Theory Graduate Texts in Mathematics Volume 45 4th edition Springer Verlaf 1977 2 Joanes D N amp Gill C A 1998 Comparing measures on sampleskewness and kurtosis Journal of the Royal Statistical Society Series D The Statistician 47 1 183 189 3 4 5 Kernel Smooth Density Kernel smoothing density estimation is to calculate probability density function using non parametric method Introduction X exo xaxa id m MEME Let 0 v 1 be a series its kernel density estimation is where h controls the smoothness i e the size of the smoothing window K is kernel function This method applys kernel function to every decrete point and superposite the results of each point for smoothing the series The concept is similar to histogram Properties This module accepts input signals of real number single channel or multi channel regular the formats for output signals are real number multi channel and regular The definitions for properties are listed below Please note that for the output signal format for KS Density one group of input signal may generate a group of two channel output signals The fi
356. t is a default variable used to facilitate user s operation It is defined as the value of the 1 channel in the first variable i e X X1_DATA 1 Xn DATA It is defined as the complete input signal value of the input signal Because a signal may have multiple channels the values are saved using cell array Different channel data are stored in different cells following their order Xn It is defined as the signal value of the 1 channel of the n input signal i e Xn Xn_DATA 1 This data is saved in a double array The input signals are divided into 3 types which are Signal time series and spectrum analysis result Spectra time frequency analysis result and numeric data Numeric e g the calculation result of Basic statistics module Methods of saving these 3 type signals in variable of Xn DATA are shown in the table below Note that the property of Column wise could change the definitions of row and column of signals in DoMatlab Data type Format Column wise is True x n double array or complex double array Column wise is False n x m double array or complex signal Signal Spectrum double array Where m is the data length and n is the number channels Column wise is True m x n complex double array the columns represent different time the rows represent Time frequency analysis different frequency and every element represents the Spectra time and frequency of the corresponding
357. t notice this list of conditions and the following disclaimer Redistributions in binary form must reproduce the above copyright notice this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution Neither the author nor the names of any contributors may be used to endorse or promote products derived from this software without specific prior written permission THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT INDIRECT INCIDENTAL SPECIAL EXEMPLARY OR CONSEQUENTIAL DAMAGES INCLUDING BUT NOT LIMITED TO PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES LOSS OF USE DATA OR PROFITS OR BUSINESS INTERRUPTION HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY WHETHER IN CONTRACT STRICT LIABILITY OR TORT INCLUDING NEGLIGENCE OR OTHERWISE ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE Licensing Authorization DynaDx Corporation and NASA have signed an IP license agreement effective on July 22 2009 The agreement includes 11 patents of Hilbert Huang Transformation HHT technology and its related applications DynaDx has exclusive license right o
358. ta Type Displays the output data type testData 10 5 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 time sec 2 Connect JoRegular to TestData for converting the signal into an evenly sampled data and then use Channel Viewer to plot the result In the Properties of ToRegular it shows that the default method is RemoveGap The Sampling Period detects the minimum sample period and this value is used for re sampling Therefore the sampling period is 0 1 second and the total time length is 0 1 x 9 0 9 second Viewerz updated Auta gt ConvertMethod RemovyeGap Sampling Period 0 099999999999999978 Unit SEC Autoetect True Module Convert To Regular testData ToRegular 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 time sec 3 Change the Properties ConvertMethod in ToRegular to FillGap the FillMethod to Monotonic Cubic The output result is shown as below It shows that the FillGap preserves the time axis definition of the original signal and the signal time axis is changed to even interval of an approximate 0 1 second sampling frequency ConvertMethod FillGap FillMethiod MonotonicCubic Sampling Period 0 099999999999999978 Unit True Module Convert To Regular testData ToRegular 10 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 time sec 4 ToReguar allows the users to fine tune the signal sampling frequency First set AutoDetect as False and then change the Sampli
359. tainer Triangle Wave X Delete Supported File Types Using either of above two methods a browser window is opened for displaying all supported files If you click on the file type drop down menu a list of supported file types will be shown The supported file types includes txt csv tfa wave mp3 and special file types like MATLAB MAT SAC for seismology HEA for MIT WFDB and tfa for DataDemon When you open a tfa file the lines which begin with contain information about the detailed aspects of the data and other lines are data signals So a tfa file not only has signals but also has meta data information Look in O data 100 atr 9 test5 tfa 62 ij 100 hea fj test6 tfa My Recent 111 tfa 9 test7 tfa Documents E 111 6 test mat e chirp1000 tfa 89 tide tfa 3 A chirp10000 tfa J Windows hello wav uf Windows XP wav i multi tfa le smile tfa PS 29 test1 tfa 9 test2 tfa 9 test3 tfa El test3_NaN2 tfa 48 ijtest3 NaN tfa i test4 tfa Desktop My Documents Bullrog My Network Files of type All Suppot Files Cancel Wave Files wav Files mp3 WELE Files hea eee ee The Information about the time sampleFreq 1000 _ _ TimeUnit sec coordinate of the Signal TimeFormat Regular StartTime 0 1 8369702e 16 0 0627905195 The time 1256999254 The signal coordinate 187381315 248689887 309016994 3
360. ted IMF of BP and BFV Is shown below BP 01 RCADA EEMD Ch7 IMF h7 2 2 0 50 100 150 200 250 300 Time sec BF 01 RCADA EEMD Ch7 IMF h7 1 0 1 1 0 50 100 150 200 250 300 Time sec Based on the selected IMFs from BP and BFV the comuted phase difference is PhaseDiff 100 0 1 00 i 5 10 15 20 25 30 Time sec Related Functions RCADA EEMD Hilbert Transform 3 11 5 MMPF Auto Macro It s a user defined macro Example Use Compute gt MMPF gt MMPF Auto Macro select input in following dialog ad MMPF Auto Macro x Data Files EF D Hork DataDemon LiGong clMPF Baseline EP_O1 txt BFVI D Work Dat aDlemon LiGong cMMPF Baseline BF_O1 txt 2 WorkhatallemonhLiGonghcMMPF Bazeline BF 01 txt ua Farameters Sampling Frequency Hz Down5ample Step Output Output C Wsers LuiDesktop Directory Cancel Continu BFV1 is the input of left BFV If there is no right BFV you can use BFV1 as the input of the right BFV Set the parameters and the Output Directory and then click Continue The Signal Flow Diagram between the SFOs is shown below By selecting Viewer m SFO the wave of signal is shown If DataWriter m SFO is selected data is written in the Output Directory Related Functions RCADA EEMD Hilbert Transform 3 11 6 MMPF Expert Macro It s a user defined macro Example Use Compute gt MMPF gt MMPF Expert Macro select input in followin
361. ter parameters FH to 2 5 and FL to 0 01 recalculate Now the filtered signal is very close to the original Sine wave viewer Sine CH1 tp uss CH1 time i sec Related Functions Trend Estimator CustomWave Fourier Transform Reference 1 Diffusive and Fast Filter Using lterative Gaussian Smoothing Yih Nen Jeng Department of Aeronautics and Astronautics National Cheng Kung University 2 htto www ancad com blog AnCADSupport wp content uploads 2008 05 it qauss 2008 7 pdf 3 2 5 Trend Estimator Professional Only Trend Estimator is a simplified version of Iterative Gaussian Filter Iterative Gaussian Filter is explained in another section If the characteristic of the signal is not fully understood rend Estimator can be used to estimate its trend without setting parameters as does in nterative Gaussian Filter Introduction The algorithm is the same as the one described in the section of terative Gaussian Filter For the parameters of Trend Estimator TrendPeriod and TrendFrequency determine both FL 2 TrendPeriod 2 TrendFrequency and FH 4 TrendPeriod 4 TrendFrequency in terative Gaussian Filter then calculation follows the algorithm Original signal Noise 0 0 1 02 02 04 05 05 0 7 0 9 time sec Apply FFT on the signal and the period is set as X axis LowPass Zone Noise FFT 1 0 5 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time
362. the differentiation is used to enhance the gradient of the signal so that the maximum is more obvious in this area Here the EMD is the filter If the user would like to intercept the higher frequency peak the EMD could separate the useful data from the signal If the Speckle Noise is mixed with a signal the EMD could separate the noise from the signal To use this module the user should define the threshold firstly CustomvWave ATA D ILL E ELE IU VV 4 os cs eT co 1 time sec The peak above this threshold is intercepted by the Peak Detection Viewer time seg If the signal is in the trend pattern as below CustomVVave T s U VAVA n vi i Im V Af i D 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time The EMD could be used for filtering the trend EMD 0 0 1 0 2 0 3 04 D 5 0 6 D 7 D 8 0 9 1 time sec And then the peak is intercepted Viewerd 30 F LA VIANNA A VVVVAAA VVAAAAAAA A AN g F HA 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time Properties This module accepts real numbers single channels regular signals and audio inputs the format of the input signal is the plural and single channel spectra data Properties are set up as the below table Property 1 El EMD Stop Criteria SbtandardDeviatian 0 1 Max Sifting Iterations 10 Module El Peak Detection Differential False Output Type Peak
363. the input signal For example X1 1 represents the 1 channel of the 1 input signal In addition X1 1 can be abbreviated as X 0 Multi Channel Expression Editor D x ByChannel xz a Output Channels 2 L X1 EMD Channel Expression X1 1 X1 2 MF_h2 X1 3 h3 X1 4 X1 5 h5 X1 5 6 X1 7 h7 X1 8 1 X1 9 MF residual 2 Sine X2 1 Tree Map Display a Double click a signal in the tree map It is added to the Expression field b If there is no calculation applys to the select input output is the same as the input then press button to move the signal to the Output List c When checking the checkboxes in the tree map multi channels can be selected for complicated calculation In addition the signal code such as X X1 2 and math operations such as sin log can be typed directly in Expression field Toolbox x By Channel a abs au The above image shows the Toolbox of MultiChannel Expression Editor Expression field is used for editing math equation 3 clear all the output signals in Output Channel panel add the math equation Expression field to the Output Channel list 5 replace the math equation in one of the output signal of the Output Channel list with the equation in Expression field Other buttons in the
364. there is no input BFV2 1 3 Select output for ALL CH CH NT IMF results H NT 1 CH NT 24 MMPF results Row 1 NBP Row 2 NBV1 Row 3 NBV2 If there is no BFV2 for MMPF Input 1 Row 4 NT 1 Identify the first column of MMPF CH NT 25 Row 5 the number of cycles Row 6 column ID of phase shift for BP LBFV Row 7 column ID of phase shift for BP RBFV If there is no input BFV2 1 Related Functions RCADA EEMD Hilbert Transform 3 11 2 MMPFImf MMPFImf is used to extract IMFs from MMPF output Properties This module accepts input signal of real number multiple channel Regular The properties are introduced below 4 MHMPFImfs SelectedDataGroup BP IndudeResidual True Property Name Property Definition Default Value NN Select a data group BP BFV1 or BFV2 IncludeResidual True to include the residual IMF T rue in the output Example Imf s SelectedDataGroup BP IndudeResidual True You can refer to demo95 in C Program Files DynaDx DataDemon demo MMPF The data used in this example is also in this folder BP 01 TRIAL LICENSE 0 50 100 150 200 250 300 Time sec BF 01 ul 0 50 100 150 200 250 300 Time sec The extracted BP IMFs is as following BP IMFs 600 500 400 300 m 200 0 TRIAL LICENSE 0 50 100 150 200 250 300 Time sec Related Functions RCADA EEMD 3 1
365. tion Default Value Min Freq otart value for Instant Frequency 0 0 5 samplin Max Freq End value for Instant Frequency png frequency Output Freq Number of grid in frequency axis for the 256 Divisions spectra plot Output Time Number of grid in time axis for the spectra 1024 Divisions plot omoothing the curve with Gaussian omoothing 9 True function Normalizing Number of times to obtain envelop 5 Iterations maxtrima Example Continue the analysis for the gsta dat after RCADA EEMD decomposition Connect the results to Compute HHT RCADA Spectrum and display them with Viewer Time Frequency Viewer Please refer to demo68 in C Program Files DynaDx DataDemon demo HHT gesta 1 apt al dil oi e ios a 1 0 5 0 5 1650 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1580 1990 ds gsta RCADA EEMD RCADA HilbertSpectrum e EN 0 01 cycles per year e LJ 0 005 frequency e 1920 1930 1940 1950 1950 1970 1980 1990 Date nn E 1650 1860 1670 1880 1890 1900 1910 Helated Function RCADA EEMD Hilbert Spectrum References http rcada ncu edu tw research1 clip reference htm Norden E Huang Zheng Shen Steven R Long Manli C Wu Hsing H Shih Quanan Zheng Nai Chyuan Yen Chi Chao Tung and Henry H Liu The Empirical Mode Decomposition and the Hilbert Spectrum for Nonl
366. to 0 Noise and set StartPosition to 1 5 then connect Data Merge to Viewer Channel Viewer for displaying result Property Data O DataMerge StartPosition 1 5 ReferenceInput 0 Noise Module Moise Merge 1 5 2 2 5 3 3 5 time Sec 3 Connect Data Merge SFO to Compute TFA ShortTerm Fourier Transform with the default setting then display the result using Viewer Time Frequency Viewer It is shown that the 100Hz Sine Wave is between 1 5s and 3s Noise Merge STFT 500 400 r4 300 Pag 0 00 frequency n3 0 00 100 Jm 05 1 158 2 25 3 time sec Related Functions Noise Sine ShortTerm Fourier Transform Channel Viewer Time Frequency Viewer Active Input The selected channel number 3 1 10 Input Switch select one channel from a multi channel input signal Properties This module accepts input of Signal which could be real number or complex single channel or multi channel regular indexed audio numeric and spectra The definition and default vaule of the parameters are shown below Properties Input Switch Active Input 9 Testindered E Module Mame TSwitch Input Port Side Left Output Pork Side Right Acceptable Data Types Real Multi Channel Signal of Rank 1 Regular Module Property Name Property Definition Default Value Input Count Total number of channels in this SFO Example Use Source Noise as the
367. to be C ProgramFiles DynaDx DataDemon demo HHT Next perform Compute NASA HHT NASA EMD intermit test NASA EMD 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 6 0 9 Time sec 7 In NASA EMD the property set Method to Intermittency Test and Threshold to 10 The result is displayed below EMD Stop Criteria sift rera 3 Marimi ount 10 10 Module NASA EMD Method Intemmittenc y Test Prediction Type PatternPrediction Extremasift Threshold 10 intermit test NASA ENMD 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Time sec Related Functions RCADA EEMD 3 7 3 2 NASA Hilbert Transform This module calculates instantaneous frequencies from the signal by Normalized Hilbert Transform Hilbert Transform is described in the first segment and then Normalzed Hilbert Transform is dicussed in the following segment Introduction Hilbert Transform The Hilbert Transform is used to convert a one dimensional real signal into an analytical signal Unlike the Fourier transform which changes a function of time into a function of frequency the Hilbert transform gives the complex conjugate of the original data also in time domain There are many useful properties of the Hilbert transform which include ninety degree phase shifting envelope function computations and finding the instantaneous frequency Our primary interest is for finding the instantaneous frequency Although it may be te
368. to view the matrix content of Inout Switch SFO Date Viewer Projecti ISwitch Proyecti ToMatrix lt Index 43004 43005 43006 43007 43008 43009 43010 43011 43012 43013 43014 43015 43016 43017 43018 43019 43020 43021 43022 43023 43024 43025 43026 43027 Related Functions Noise Fourier Transform RCADA EEMD Convert to Audio ShortTerm Fourier X 962 42 963 42 1964 42 965 42 966 4 967 42 568 42 969 42 57042 1971 42 972 42 7342 974 42 97542 976 42 97742 97842 979 42 960 42 5681 42 96242 963 42 964 47 985 42 RE 0001955116140 72170201 0 001983786505 0 001973969615 0 062011626563 0 002015053007 0001991418073 0 001970945445 0 001951516274 0 001921981712 0001878197616 0001825567294 0001772872587 0001752455693 0 001720001965 0 00169 0 00164 523 0 001570966468 0 001494150925 0 001458348933 0 001409110270 D 001336088967 0001315375945 0 001277546960 0001214662117 Transform and Convert to Matrix CHI IM 0 000325997214 0000328560010 0 000311223892 0 000322472365 0 000305716427 0 000304697235 0 000290994967 0 000266841108 0000291715448 0 000306249183 0000316465182 0 000314335316 0000296472497 0 000322100837 0 000324161990 0
369. top level selection is input signals instead of each channel under the signal Once the signal is selected all channels under it are selected automatically As shown below select input signal X1 and X2 then select By Input and click basic operator the full calculation equations are added to the Expression field 2 Multi Channel Expression Editor DER T TET 7 eT CDT i Expression X1 1 X2 X1 4 2 4 X1 5 X 2 5 X1 6 Output Channels 2 veg m MF v X1 2 MF_h2 X1 3 1 h3 X1 4 MF X1 5 MF h5 1 6 MF v X17 MF_h7 v X108 9 X10 MFH e Ls oF X2 2 MF_h2 v X2 2 MF_h3 X2 4 v X2 5 IMF h5 2 6 MF_h6 X2 7 MF_h7 X2 8 IMF residual In Output Channels panel there are 8 calculation channels added Since there are 10 channels in X1 and 8 channels in X2 Math uses the less number for the output i e CH1 CH8 HE Hult Channel Expression Editor Input List v 1 EMD e X1 1 MF gt X1 2 h2 f ii EHE X1 3 h3 RAEI OME Mh EL ajena X1 5 h5 X1 5 X2 5 X1 5 h amp X1 v X2 7 v X1 7 IME ho X1 B X2 8 1 8 h8j v X1 9 1 amp 5 gt X1 10 MF residual E X3 EMI gt X2 1 vw X2 2 12 X2 3 X2 4 h4 X2 5 h5
370. tor Matlab script editor In the editor window type the codes to generate an Impulse signal The codes are listed below DoMatab Editor 45 Matlab script file 0 001 length ti zerosil n Yriround n z 1 set variable p 0 001 as the sampling period variable t is the corresponding time of every signal data variable n is the signal length variable Y is the output signal all data point are pre set to O and set the approximate middle point of the data to 1 Thus the numerical part of the output signal Y has been created Next the time axis variable Y DESC needs to be set The codes are shown below FS DoMatlab Editor DIEE ecript Help amp Examples gt Matlab script file 0 001 p 1 lenqthit Eeros l n round n 2 1 Y DESC intervals name DoMatlab type Signal lengths n Starts 0 units sec formats Reqular For user convenience DoMatlab has a pre set type of output signal as Signal the start time Starts is 0 the time unit Units is in sec the discrete format Formats is Regular All these default values are in the comments as shown in the figure above The users only need to set the sampling period Y DESC intervals to obtain Y output Now close the Matlab Editor and go back to Network Connect Channel Viewer to DoMatlab and it can be seen that a group of Impulse signals are generate
371. tores the time information of the signal and CH 1 Real column stores the real data values CH1 Imag column stores the imaginary part and if there are more than one channel the information will be listed in the same way DataDemon will view a spectrum signal like a multi channel signal X Value will store the frequency and the rest will be the same as above 3 Spectra Export to Excel with a Spectra signal will result in something like this Frequency Coordinate D z U UU 1965 U UU IS U UU 9 0 001800 UUULisf 0 001082 U UU U UU 140 0 002214 0 002207 0 002183 0 002138 0 002064 0 001955 0 00181 0 00163 0 002403 0 002404 0 002401 0 00238 0 002324 0 002219 0 002059 0 001846 0 002507 0 002522 0 002555 0 002576 0 002552 0 002459 0 002297 0 002041 0 002501 0 002539 0 002627 0 002712 0 002737 0 002665 0 002485 0 002208 0 002373 0 002444 0 002612 0 002783 0 002872 0 002831 0 002648 0 002342 0 002116 0 002235 0 002511 0 00279 0 002956 0 002952 0 002772 0 002445 0 001738 0 001928 0 002344 0 002746 0 002995 0 003034 0 002863 0 002522 0 001257 0 001559 0 002144 0 002673 0 003002 0 003084 0 002928 0 002579 0 000704 0 001199 0 001964 0 002598 0 002993 0 003114 0 002974 0 002622 0 000986 0 00186 0 002549 0 002984 0 003135 0 00301 0 002656 Time Coordinate The first column represents the time the first row represents the frequency and the data in between the first column and the first row represents the signal strength R
372. ts of Stbtistical Learning Chapter 6 Springer 2001 3 4 6 Orthogonality Matrix Orthogonal matrix is calculation of dot product of the serie If the two signals are orthogonal the value will be zero It can be used to determine whether the IMFs calculated from EMD are orthogonal Introduction Let 250 F7 Wor Viw are two series The orthogonality is defined as the inner product of the two series calculated as follows N 2 X Vj h Y i 0 ini j f If there are M series their corresponding orthogonal matrix as follows Oy orthu Where and k are for the channel number Properties This module accepts the input of real number multi channel regular signals The output is a M x M square matrix M for the number of channels of the input signal The output format is the indexed data values In the Properties View Matrix you can use the Reporter window to see the results Pro Pe rhes Module El Orthogonality Matrix view Matrix Orthogonality Matrix For View Matrix Display the orthogonality matrix H Ortho zonality Matrix for ToMulti Orthogonality Matrix for LoMul Orthogonality Matrix Channel fine CHE Noise CHI 1 0 00201 316838850173 CHz Nose O 00201 21092050173 l Example Different phase angle and frequency of sine wave as the input signal to calculate orthogonal matrix In the Network window right press select Source Si
373. ts statistical values For example equiphase mean is calculated as following Please note that if N M is not an integer the length of the last small series M last N so if the element j 2M last the number of calculated element is if the element J M last the number of calculated element is K 1 Equiphase statistics can calculated many different statistical values including the values in basic statistics Most of them are the same as the ones described in Basic statistics module Some of them such as First quartile Third quartile and Quantile are described in Quartiles and Quantiles module Properties This module accepts input of real number single channel and multi channel signal Paremeters are defined as following Properties Period Period Start Time Unit Type Module Equiphase Statistics Property Name Property Definition Default 10 of the total time length of Period Set Period time Period Start Set Period Start time 0 TimeUnit oet Unit of Time Sec Type oet statistics to be calculated Mean The option of Type is listed below These statistics is calculated within the window Type Options Option Definition Sum Sum of the series Min Minimum Max Maximum Mean Mean value Geometric Mean Geometirc Mean Value Harmonic Mean Harmonic Mean Value Trimmed Mean Trimmed Mean First quartile 1 4 quantile Median Median value Third quartile 3 4 quantile Quantile Quant
374. ty distribution This Biased Estimation IS Moment This is Unbiased Moment Estimatiom A measure of the peakedness of the probability districution Higer Kurtosis means more of the variance is the result of infrequent extreme deviations This is Biased Moment Estimation This is Unbiased Moment Estimatiom Degree of spatial dependences of a spatial stochastic process The default threshold is the average value This is Biased Moment Estimation This is Unbiased Moment Estimatiom gt Y cx w 0 x gt x N gt x x b This is Biased V Moment Estimation 1 x lt x X 7X Standard Deviation N 25 X x bp i 0 This is Unbiased Ned Moment Estimatiom Properties This module accepts input of Signal which could be real number or complex number single channel or multi channel regular Property lx Basic Statistics Stats Mode PerChannel View Sbatistics Basic Statistics for Unbiased Moment Estimation True Trim Fraction 0 05 Trim at Ceiling False Module Property Default Property Definition Name perty Value If the input is a multi channel signal this option is activated PerChannel or AcrossChannel Stats Mode For PerChannel setting the result is a 15 n matrix PerChannel where n is the channel number of the input 15 is the number of calculated statistical value The output is in Indexed for
375. uantiles In Network panel right click to add Source Noise adjust Properties Noise Type to Brown use Viewer Channel Viewer to graph results Properties MaoiseTvpe Source TimeLlIniE TimeLength 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time i sec Connect Compute Statistics Quartile and Quantiles after Noise to calculate quartile values click Properties View Quartiles andQuantiles to examine results Properties Module 5 Quartiles and Quantiles View Quartiles and Quantiles Method Linear Fractions D 01 0 1 0 25 0 5 0 75 0 9 View Quartiles and Quantiles Display qartiles and quantiles 0 Quartiles and Quantiles for Noise Bl x 3 E Ouartiles and Quantiles for Noise Quartiles and Quantiles 3 Select Properties Quantile Fractions to edit the different quantile values Press the Add button in the interface below will add a O under Members Double Collection Editor xl Members properties Then on the righthand of the editor interface you can setup the percentage for the quantile For example set to 0 17 and then press OK Double Collection Editor x Members 7 properties Value 4 Select View Quartiles and Quantiles again you can see that the 17 quantile has been added E P Qmartiles and Quantiles for Noise General EJ Quartiles and Quantiles for Noise Quartile
376. uced below The inverse DCT does not have this type of property Froperties F emoveDpc Window Mone Module RemovreDC Remove DC component Property Name Property Definition Default Value To remove the signal shift in the HemoveDC True amplitude To decide whether window filter are Window needed before FFT processing Please None reference to FFT for details Example In this example use Source to create a combined signal of two wave signals The 1st signal has frequency of 10Hz TimeLength of 0 9 second The 2 signal has frequency of 3Hz and TimeLength of 0 9 second Then use DCT to calculate the signal spectrum and use Inverse DCT on this spectrum to obtain the original signal 1 In the Network window select Source Sine to create a sine wave Change its TimeLength field to 0 9 seccond Prajecti x Viewer TimeLlniE TimeLength 5 SamplingFreq DataLength ignalFreq Amplitude Sine 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 2 Similar to the step1 create another sine wave which has frequency of 3 Hz and TimeLength of 0 9 second Add a Compute Mathematics Mixer component to mix these two signals and use Viewer Channel Viewer to plot the output Projecti Viewer I Auta a Properties TimeLlniE eet TimeLength 0 9 SamplingFreq 1000 DakaLength 901 SignalFreq 3l Amplitude 1 AmplitudeofFset 0 The Frequency of Ehe Ea be generated si
377. ude Simple and Barne The details of these options are given in the tables below To output the analytic signal Z and data are saved in Complex complex number To split the real part X and the imaginary part Y ofthe oplitComplex TEN analytic signal into two channels and save the values obtain the phase angle 0 r corresponding to every time point Unwrapped means that when the phase angle is bigger than 360 it would not be wrapped into the range of 0 360 InstantAmplitude The amplitude values of analytic signal Z a t The differentiation of phase angle O t with respect to UnwrappedPhase InstantFrequency the time of the analytic signal Z i e the instantaneous frequency ox t Example In this example use Math DoMatlab module to create a sine wave signal with amplitude of sine perform Hilbert Transform and show the meanings of property options by changing the Output Type of Hilbert Transform 1 Select Math DoMatlab to create a signal whose amplitude varies with time i e sin 2z t Perform dot product of amplitude and sin 27t to generate a sine wave whose amplitude is time variant The code of DoMatlab is shown below Use Viewer Channel Viewer to plot the result Projecti x viewer updated Calumn veckars True Server visible True DumpOukpuk False 45S50Urce True v oL 4 GI d 45Source Specifies True if DoMatlab is to be used as a
378. ue auto 0 Hold Plot Range Holding plat range when module is updated 4 Use 2 Zoom X and zoom in between 0 2 sec and 0 5 sec on the x axis Square 0 5 0 5 0 25 0 3 0 35 0 4 0 45 0 5 time sec Create Source gt Sine Wave and connect it to the same Channel Viewer SFO Because the Auto box is checked the Channel Viewer automatically updates with the new Sine wave graph Since HoldPlotRange is set to True the new update does not return the graph to the default position Viewer 1 Ann LM M M 0 35 0 5 time sec Viewer UELUT 6 0 8 1 6 Click on the Properties Representation Plot Elem Editor and click on the button to open up the Plot Element Setting window 0 5 4 time sec Display Channel Name Line Color Line Width Line style Marker style Equa CH HN Sine w Display Hide All Done Cancel Apply In the Plot Element Setting window you can edit the display of all the input channel data on the graph Set the Line Color of Square CH1 to red change the Line Style to dotted line and change the Marker to and click on the Apply button to see the change on the graph Display Channel Name Line Color Line Width Line style Marker Style Square CH Sine None Display Hide All Done Cancel Viewer 0 0 2 0 4 0 6 0
379. umber single channel or multi channel Regular The output formats are real complex single channel multiple channel Regular signal and audio signal If the property of Convert to period is changed to True the format of output signal would be changed from Regular to Indexed because the data in x axis are not separated with equal interval anymore Property of Abscissa Unit shows the unit of x axis to be converted to The defaults is in second Changing the Abscissa Unit can trigger the unit conversion on x axis for the input data The explanation of the unit is given in the table below E Module E XAxisUnit Input Time Unit Hz Abscissa Unit Hz Convert to period True Abscissa Unit Covert to Freq Unit Property Name Property Definition Default Value When the unit of x axis is frequency this option can convert the unit of frequency to the unit of period on x axis Convert to period ELS Property Name Property Definition Terahertz THz Cycles per 10 second Gigahertz GHz KHz Hz Cycles per 10 second Megahertz Cycles per 10 second Hertz Cycles per second Kilohertz Cycles per 10 second Cycles per min Cycles per minute Cycles per hour Cycles per hour Cycles per day Cycles per day Cycles per week Cycles per week Cycles per month Cycles per month Cycles per year Cycles per year Example 1 Select Source Sine Wave to create a sine wave with default fre
380. ups of signals X t each group of which has different time axis t and sampling frequency The mixed signal Z t is Z t a X t b X t oc OS X t where a b c are weights k 3 In this module because the time axis of input signals are supposed to be different the minimum sampling frequency freq of the input signals is extracted first then all other signals are re sampled by freg After the time axis of all input signals are unified the signals are added at every time points Notice that the weights from the 3 group of signal are all equal to Properties This module accepts input of Signal which could be real number single channel Regular and Audio which could be real number single channel Regular Multiple signal input is also allowed Gaini Gain2 and GainN are the weights of the first the second and the third group of input signals respectively The difference between this module and Math is that the Mixer can perform faster addition subtraction computation and also perform addition subtraction on signals with different length while Math does not have this type of functionality E InputPortside OutputPortide Gainl The gam for input 1 Property Name Property Definition Beraun dili iiid Value Set the weight a for the first group of signal 1 Set the weight for the second group of signal Set the weight c for the signals from the 3 GainN group Example Th
381. usted Properties lx El Hypothesis Test view Test Results Hypothesis Tests for Square TestType z_Test Mean 0 Sigma D 03 SigniFicanceLevel 0 1 Hypothesis Mull al Hypothesis Tests for Square General 7 3 iy Hypothesis Tests for Square z Test SignificanceLevel 0 0733 0 000139 ClI High 0 00325 Example 2 For example we have a class of 51 students The head teacher is on leave we want to know if the test score goes down because of this The average score for the whole school is 55 We set the null hypothesis to that the test score of the class was not affected by the leave of the teacher then preferm t Test First use Source Noise to generate a group of scores for the students Set SamplingFreq to 50 Amplitude to 30 AmplitudeOffset to 50 then connect to Compute Statistics Basic Statistics Under Basic Statistics press View Statistics observe the Mean i Froperties Module El Noise MaiseTvpe White El Source TimaeLlnil SEC TimeLength 1 SamplingFreg 50 DataLength 51 Amplitude 30 AmplitudeOFFsek 50 Time Start al Basic Statistics for Nois Basic Statistics for Noise Basic Statistics Channel CH1 Sum 2 51E 03 Min 20 1 Wean 49 3 Connect Noise to Hypothesis Test set TestType t Test Mean 55 then use View Test Results to check the results The SignificanceLevel calculated from
382. ut List Output Channels gt 1 Triangle RCADA EEMD Channel Expression h1 CH1 111 2 IMF_h2 CH2 lt 1 2 1 3 IMF h3 CH3 13 h4 CH4 114 15 IMF h5 CH5 1 5 118 IMF h5 gs 2 h7 CHE SATB C x1 8 IMF CH9 1 9 IMF residual 1Xx2 S5quare RCA amp DA EEMD x2 1 IMF h1 C x2 2 IMF h2 C x2 3 IMF h3 I x2 4 IMF h4 X215 IMF h5 X2 5 IMF h5 C xX2 7 IMF h7 x2 8 IMF C X2 3 IMF residual 1 In order to sum channel 2 of X1 and channel 4 of X2 together select both channels and click basic operator The summation equation is added to the Expression field This equation X1 2 X2 4 can be typed in the field directly 21 Multi Channel Expression Editor EHE 2 By Channel 4 abs E Expression X1 2 X2 4 h Input List Dutput Channels 1 gt Triangle RCADA EEMD Channel Expression 1 lt 1 1 IMF_h1 CH1 sat 1 CH2 1 2 TETISTIMF CH3 x1 3 1 4H IMF h4 CH4 AT 4 X1 5 IMF h5 up d 116 IMF h5 Cus 5 h7 CHS CI 21 8 IMF_h8 CH9 1 SH IMF residual CH10 1 2 lt 2 4 1X2 Square RCADA EEMD _ X21 IMF h1 _ X2 2 IMF h2 23 IMF h3 1 x2 5 IMF_h5 2 6 IMF h5 _ 2 7 IMF h7 X2 8 IMF _ X2 9 IMF residual
383. ute TFA Short Term Fourier Transform and present the result with Viewer Time Frequency Viewer Jaehne signal is close to Chirp signal The frequency of the signal varies with time It increases when time increases Jaehne STFT 500 400 0 02 I 300 0015 e T 200 0 01 E 100 0 005 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Helated Functions Channel Viewer Time Frequency Viewer Short Term Fourier Transform Chapter 6 Viewer Signal Flow Object 6 1 Annotation Professional Only When data is presented in Channel Viewer or XY Plot the user can add annotations and curves on the figure Introduction This module includes Ellipses HLines HRegions Lines Rects Texts VLines VRegions and other annotation functions Properties Each annotation module is a little bit different in properties If the coordinate of figures are included in properties annotations are drawn according to the coordinates in Channel Viewer or XY Plot They can also be directly added to the proper places using mouse Common Properties Property Property Definition Default Value Name perty The layer of the figure The higher the figure is superposed the larger the ZOrder is The original figure ZOrd MOS 1 es is at Oth layer ZOrder 1 is above the original figure Zorder 1 is below the original figure Plot settings of annotations The user can set Color Color Red LinePen DashStyle and Width of lines
384. uttons Hl im dB Q magnitude phase real part imagine part gain and power spectrum buttons at the top left corner of the Data Viewer Each button will change the looks of the graphs and the channel data based on the option selected Data Viewer Channel Information Histogram Channel 1 X Value CHI RE aM E MA o 1L 1 325689524567 1803944606215 1 37 md poe 0 833270349935 4 900163277977 3 113940978396 4 Value Type 1 66654069987151 4974969959978 9 224616172375 Lgs 2 49981104980727 4 287223135695 5 952735991436 3 33308139974302 6 024816068787 2 656039396163 6 59 Bottom left screen contains the table which holds the information of the spectrum X Value represents frequency and each channel contains four column vector Real part RE Imaginary part IM Magnitude MAG Phase PHASE Index X Value CH1 RE CH1 IM CHI MAG CH1 PHASE 2455269054735 0 2455269054735 0 10 0003200102403 6 727150509830 0 000551901395 0000555998276 06 25076583867 20 0006400204807 0 000107569773 0 001446670680 0 001450564438 85 74749606478 30 000960030721 5 5790812186581 0 001241813580 0 001243111490 92618439712072 AQ 0012800409513 0 000194001695 0 0003192023671 0 000373534160 50 71012132169 50 00160005120165 0 000260690876 0 000542531736 0 000651489519 1216171155060 Histogra
385. v es es os File Contents 0 l 2009 01 02 16 2009 01 05 17 2009 01 06 16 a 009 01 07 16 a 009 01 08 l16 2009 01 09 16 2009 01 12 15 2009 01 13115 nnn rn 12511 Connect Trend result to Conversion Convert to Indexed and connect the 2 Source GE2 to Convert to Indexed also Then connect Convert to Indexed to Viewer Channel Viewer for displaying the date information is shown on the X axis GE l saussFilter Tolndexed 1 0 2009 04 2009 07 2009 10 Late Using Data Viewer can also view Convert to Indexed signal There is no Saturday Sunday and Holidays And the signal is in Indexed format H Data Fiewer FX Projectl TaIndexed 1 Channel Information Histagram Channel 1 2009 04 2008 07 2009 10 3 i gt From Step i N 237 Channels 2008 04 2008407 2008710 X Value CHI 2009001229 BA 00 00 00 0 30 793686306431817 2009 01 30 ERR 00 00 00 0 1140125801032084 200902702 ERR 00 00 00 0 40498662395537261 Channel Channel 1 2009 0203 BA 00 00 00 0 051094590516786 20090204 E RR 00 00 00 0 086526034061644788 2009002005 E84 00 00 00 0 10759214238096399 20090206 BEAT 00 00 00 0 26882749057 360229 11200910206 BAT 00 00 00 0000000 20090410 CE RR 7 00 00 00 0 8924862451263484 E Data Channel Related Functions Open Data from File Channel
386. velet i definition is y t e e 2 where a is set to 6 in DataDemon Morlet Wavelet time sec Properties This module accepts input of Signal which could be real number single channel Regular and Audio which could be real number single channel Regular The Output format is real signal channel Regular spectra data The starting and end points must be set and the unit is the time unit of the input signal F TOPE rtie is FregqAxis LinearAxis FregMin 0 Freqmax auto 500 Freqcaunt 128 Time aunt 2048 Remavepic True Property Name Property Definition Default Value The frequency axis could be LinearAxis Linear measurement or LogAxis FregAxis IE LinearAxis logarithmic measurement LogAxis are used in audio analysis 0 0 5 Sample Frequency FreqCount The number of discrete lattice in frequency The number of discrete lattice in time 2048 Use to choose whether remove the DC or HemoveDC True not before Morlet Transform FreqMin To define the frequency boundary for FreqMax frequency plotting Example The following example is using a bird sound Chirp to show the change in frequency against time 1 Press the 2 in the Network tools or use Source Open datafrom file to read a signal file chirp1000 tfa in the installation directory the default directory is C Program Files DynaDx DataDemon demo basic Projecti X Viewer updated v Auto Chirp 10000 0
387. verage in the range of the data s time or frequency When the method is the SlidingFFT the users could set the First or the Second Order Solution As for the FirstOrder FFT the choice is just the First Order The distribution of the circular frequency could be FregAxis the linearAxis or the LogAxis The LogAxis is usually LinearAxis used audio analysises 0 0 5 Sample Frequency FreqMin these properties the users could set the up and FreqMax down borders of frequency in the figure This value affects the size of the window function Sample FreqResolution The lower the setting is the longer the window Frequency function is 40 Showing the grid number of the STFT in the Auto direction of the frequency 4 FreqCount Showing the grid number of the STFT in the Auto direction of the time TimeCount This value decides whether the DC signal is T removed before the STFT analysis HemoveDC During the time axis segmentation the STFT filters Cause the signal by the window function eet Window Example The configuration of the mudule is as below The result of the analysis is as below sound003 FastSTFT 0 05 0 04 0 03 B ble bo nt dont NN E 2000 0 02 WIEN AANA 10 time sec By modifying the value of the FreqMax and the FreqMin the users can get the results in the range of 1000Hz to 3500Hz sound003 FastSTFT 3500
388. very easy to remove a connection that is connecting two SFOs together Click on the connection arrow head which is currently connected to the input port of the second SFO and hold on the mouse to drag the arrow head back to the first SFO By releasing the arrow head back into the first SFO the connection between the two SFOs will be deleted 2 To remove a connection between SFOs Direction of mouse drag 3 Connection types Different types of SFO will have different output connection types and they differ by their looks e g line thickness dashed line and different colors Blue Real Signal Purple Complex Signal Hed opectra Light Brown Annotation Connection Thin Single Channel Connection Thick BM Multi Channel or Spectra Connection Dashed gt Unavailable Connection no calculation 4 Signal Flow Object warning When a SFO does not receive any input data or part of the output data is missing an exclamation mark will appear on the Switch of the SFO to notify that there is a calculation mistake Chapter 3 Compute Signal Flow Object 3 1 Channel 8 9 Channel Switch Select a single channel from a multi channel source Data Selection Select a time frame from a source data to be analyzed Dup Duplicate a signal data Fill NULL Value Use mathematical methods to fill any data that is missing NULL value Remove Channel Remove a
389. wo signals and then use Viewer Channel Viewer to show the result in the window median Filter Viewer Updated Properties x El Noise Speckle E Probability 0 25 Probability Occurrance probability of speckle noise Mixer 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 2 Click on the Mixer icon to select Computer Filter Median Filter change the Properties FilterOrder to 5 and then use Channel Viewer to show the result Viewer Updated O Median Filter FilterOrder Module FilterOrder The Filter order Mixer Median 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 time sec 3 n step 2 good result is achieved As shown below FilterOrder could be increased 4 times if the Median Filter is adjusted to 21 i e FilterOrder 21 Not only is the speckle noise removed completely but also the wave preserves good edge sharpness Properties FilterOrder 21 Module Median Filter Mixer Median 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec O 4 Last step to test characteristics of Median filter come back to Noise to change Speckle noise to White noise in Noise As shown below it can be seen that the Median Filter cannot eliminate the effect caused by White noise completely However the wave edges are mostly retained This is the main characteristic of Median filter Mixer Median gt 0 5 0
390. wo sine waves with the sampling frequency of 1000Hz length of 1 second and amplitude of 1 are used as input signals 1 In the Network Window use the Source Sine to create two sine waves and then change their Property SignalFreq to 10Hz and 20Hz respectively Then use Compute Conversion Merge to Complex to merge these two signals to a complex signal and use Viewer Channel Viewer to plot the result Projecti Viewer updated noc gt sine ToComplex 0 5 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec 2 Use Map to Real to convert this complex signal to a real signal Change the Map Method in the Properties and then use Viewer Channel Viewer to show the result in the window The default output of Map to Heal is the signal Magnitude Projecti he El Representation TireLlinE SEC LegendPosition Mone Line AA xisTvpe LinearAxis Plot Elem Editor PlotEditor YW WalueT ype Magnitude Hold Plot Range Magnitude s Min Phase RealPart ImagPart ain Powers pectrum YYalueType The data representation of th Sine ToComplex 0 5 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 time sec Note that although the computation procedure is different the results shown in Channel Viewer are identical For the 1st one it is obtained by calculating the Magnitude of the complex signal by Channel Viewer for the 2nd one Magnitude is obtained by Map To Heal then plotted by Channel Viewer R
391. y ve X Diff time Sec Then input velocity signals to Compute Transform MSE for calculation and display the results with Viewer Channel Viewer It shows that the balance of the elderly is not as good as the young subject The change of elderly s COP is not adaptive the complexity value becomes lower when the scale increases However for young adults their balance can adapt to changes quite well The complexity value stays the same when scale increases A DI MSE 5 10 15 20 25 30 scale Here is another example The ECG recordings of 18 and 55 year old healthy subjects are shown below Viewer 154 155 156 157 158 158 160 161 time sec Calculate heart beat intervals of both recordings i e the RRinterval then apply MSE method the results are shown in the graph It is shown that the complexity of the young is higher than the one of the elderly The heart of the young subject has better ability to handle external stimulus and adjust to the pressure accordingly Viewer Young Elderly SL qu Tas 2 3 B scale Related Functions Noise Viewer References Pincus S M Approximate entropy as a measure of system complexity Proceedings of the NationalAcademy ofSciences USA Vol 88 pp 2297 2301 1991 Costa M Goldberger A L Peng C K Multiscale entropy analysis of physiologic time series Phys Rev Lett 2002 89 062102 Costa M Peng C
392. ysical meanings of the system explain physical phenomenon and solve engineering problems Introduction EMD Empirical Mode Decomposition is a mathematical method which can be used to decompose a signal into several Intrinsic Mode Functions IMF and a residue IMF can be viewed as a generalized Fourier Transform The time varing amplitude and the instantaneous frequency have not only greatly improved computation efficiency but also make it possible to extract non linear and non stationary characteristics from signals With IMF the amplitude and the frequency modulations are also clearly separated Thus the restriction of the constant amplitude and fixed frequency of the Fourier transform has been overcome with a variable amplitude and frequency representation This component decomposes a raw signal into several sub signals based on signal characteristics by EEMD In contrast to other mathematical methods EEMD is empirical and intuitive This method is based on an assumption that any data consist of different simple intrinsic modes of oscillations called Intrinsic Mode Function IMF Every IMF includes characteristics listed below 1 The number of extrema and the number of zero crossings either be equal or differ at most by one 2 At any point the mean value of envelope defined by the local maxima and the envelope defined by the local minima is zero i e symmetric 3 No constant amplitude and fixed frequency

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