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Signal Processing Toolset Reference Manual

1. Figure 11 10 Specifying a Path Image Test You can use the Image Test panel shown in Figure 11 11 to test the designed wavelet and filter bank for a 2D image To access the panel in LabVIEW open Image Test Panel examples in Examples 11b in the Examples Signal Processing Toolset Wavelet and Filter Bank Designer directory in your LabVIEW directory If you are not using LabVIEW the Wavelet Application dialog box appears when you launch the Wavelet and Filter Bank Design toolkit Use the pull down menu in this dialog box to select and open Image Test Panel As introduced in Chapter 10 Digital Filter Banks by applying wavelet transform one image is broken into four subimages low low low high high low and high high National Instruments Corporation 11 13 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Percentage of Data Used from Sub Images high low high high Figure 11 11 Image Test Panel The following sections describe the controls on the Image Test panel Data Usage displays the percentage of the wavelet coefficients from each of the subimages used to restore the image In Figure 11 11 the original image size is 353 x 148 or 52 244 data samples The reconstruction uses 25 percent of the largest wavelet transform coefficients 25 percent of 52 244 or 13 061 sam
2. eere 18 6 Table 20 1 Suggested Specification Filename Extensions sssussseseee 20 5 Table 20 2 Filter Specification Transfers ccccsssseessssssessseeeeseeeceeeeceeeeeeeeeeeess 20 7 Table 21 1 FIR Coefficient Text Files and Descriptions seeeeese 21 5 Table 21 2 IIR Coefficient Text Files and Descriptions eseeeeeee 21 6 Table 24 L Pilter Bands for ANSO l 2 33433 SEA 24 2 Table 26 1 Third Octave Analyzer Sampling Rates ANSI Bands and Center Erequencl188 5o dreotostut osa tiesa luat eda au dolce uu pads adi get t us 26 2 Table 26 2 Different Sampling Frequencies sese 26 3 National Instruments Corporation xvii Signal Processing Toolset About This Manual Organization of This Manual The Signal Processing Toolset Reference Manual is divided into six sections and is organized as follows Chapter 1 Signal Processing Toolset Overview provides an overview of the Signal Processing Toolset components system requirements and installation instructions Part I Joint Time Frequency Analysis Toolkit Chapter 2 The Need for Joint Time Frequency Analysis explains the need for and the approaches to joint time frequency analysis JTFA Chapter 3 Joint Time Frequency Analysis Algorithms describes the algorithms the JTFA VIs use The JTFA algorithms implemented in this package fall into two categorie
3. sssssseeeeeee 16 4 Algorithms for Super Resolution Spectral Analysis and Parameter Estimation 16 5 Covariance WIC LOC uos 5 eol Me oce Aid es modum tu duse fo uum betur a Rute cl cas o dere Dau 16 5 Principle Component Auto Regressive Method esses 16 6 Prony s Method c senten idees evt ts dot s cc bua inue de darent n Du Sc 16 7 Mais Pencil Mehadia oit e sotto Date oet eo tu o ut auto ute NERA qutd iut 16 8 Mirum Desenption LEengtli iui pee tete oreet e E 16 8 Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs Covariance Meot oomen m mrets a aue ii a tine bon ao CIS ER dad umida 17 1 Covariance Power Spec pui ouf RE Eee SEND a Se Pu Ett mmo ode nre acti te eend 17 2 POA RIC UNO Cass eed Grm dpa ditat e bdo Fa b o sP Dado anda meee ea enaaacanens 17 3 PUCAR Poner Spect eo ovo ot we did a ext imus uae Doo Lome UN 17 4 National Instruments Corporation IX Signal Processing Toolset Contents Prony s Metodi Sodotusmib itudin qe debe Sadun bez bue d Lese Rondo 17 5 Matx Pellet MeUIOQ as tonc e pudica eb meten Decet vowed antes Gout oo aan S 17 6 Minimum Descrpiom Lensi oss us oe een ut epe presta de a a Lore b ro leis 17 7 Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation Sampin arce se EO DO 18 2 Select Tet D oic erm 18 2 The Upper Bound AR Onder 536p ELT Eee abe aaa LE aos xe ORO EAE 18 3 FPT Based VICI Od D C 18 3 Se
4. of frequency bins must be a power of two plil k is the adaptive spectrogram residual indicates the mean square error of the signal x i and the adaptive representation The MSE reduces as the number of elementary functions increases error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions National Instruments Corporation 4 9 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS Cohen s Class Computes the general Cohen s class Analytical Signal 7 r t afl pii kernel Function Cohen erar H of rows Analytical Signal determines whether the signal to process is an TF analytical signal I LII DBL x i 1s the time waveform kernel function is the first quarter of a user defined 2D kernel function The number of rows of the kernel function determines the number of distinct frequencies the number of columns of the spectrogram p i k It must be a power of two DBL of rows determines the maximum number of rows of the spectrogram pli k plil k is the Cohen s class ma z Ex t error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions CWD Choi Williams Distribution Computes the Choi Williams distribution Analytical Signal 7 UIEITUISM t fl Plilk parameter H of rows pet EU H of frequency bins Analytical Sig
5. 8000 00 jk 1000 pretrigger trigger condition scans lI na change 2 no change lo analog chan amp level 0 V trigger channel empty level 0 V c gu scan Clock source na change l no change lo Figure 11 9 DAQ Setup Panel Usually you need to configure only the following parameters device indicates which DAQ board you are using to acquire data channel indicates which channel on your DAQ board you are using to acquire data You can specify only one channel sampling rate indicates how fast you sample your data of samples indicates how many samples to acquire The Acquire Data to a File button acquires a block of data and saves it to a text file i Note The remaining parameters on the DAQ Setup panel are for advanced data acquisition users Refer to the LabVIEW Data Acquisition Basics Manual from National Instruments for more information about these parameters Signal Processing Toolset 11 12 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit path specifies a path for the output for that plot You can type in any path While 0 represents passing a lowpass filter Go z 1 represents passing a highpass filter G z An example of this is demonstrated in Figure 11 10 eG gt Y gt gt G gt y2 gt e G amp Y2 gt Ge y gt 00 G gt Yo gt
6. o 00E 0 sec block length E OOE 1 sec Setting Time Parameters Time parameters allow you to process the part of signal in which you are most interested t0 controls the start point of the analyzed signal If t0 is out of range it reverts to zero The block length control determines the length of the signal to process If block length is larger than the signal length it is ignored selecting the JTFA Method Use the method control to specify any of the following quadratic JTFA algorithms the Offline Analyzer contains e SIFT spectrogram e Gabor spectrogram e adaptive spectrogram e Pseudo Wigner Ville distribution e Choi Williams distribution e cone shaped distribution i Note Generally you should start with the STFT spectrogram because it is fast and simple Signal Processing Toolset STFT Spectrogram To run the STFT spectrogram you need to input values for window selector and window length The Offline Analyzer provides four window types rectangular Blackman Hamming and Hanning window length must be less than 256 If you enter a length greater than 256 the length automatically truncates to 256 The longer the window the higher the frequency resolution but the poorer the time resolution and vice versa Consider the long window as narrowband and the short window as wideband Adjust the window length and type such that the resulting STFT spectrogram achieves the best compromise between
7. Controls MERK Display 1 gt Channel Measurement Time Waveform Magnitude Di Sp ay Vims Settings Ea a a 4 dB a Degrees Markers E Dual Markers markers E Display 2 Al Controls ln Run Single Ar Pause l aj E 4 99 t Main Control Bar Figure 31 1 Front Panel of VirtualBench DSA National Instruments Corporation 31 1 Signal Processing Toolset Chapter 31 VirtualBench DSA 5 Channel 4 Magnitude Markers Dual Markers La Le Signal Processing Toolset The Display Settings provide individual control of the measurements VirtualBench DSA performs on Display 1 and 2 You can switch between Display 1 and 2 by clicking on the left and right arrow buttons above the display settings control Use the Channel Select control to select which channel A or B to display Use the Function control to select which function to perform on the selected channel Functions include single channel measurements time waveform amplitude spectrum and power spectrum and dual channel measurements coherence cross power spectrum frequency response and impulse response VirtualBench DSA performs the function on the selected channel for single channel measurements and on channels A and B for dual channel measurements Use the Magnitude Phase Mode control to determine whether the magnitude or phase result of t
8. National Instruments Corporation 15 7 Signal Processing Toolset Chapter 15 Introduction to Model Based Frequency Analysis When to Use This Software This software contains VIs for several effective model based analysis methods Some of them such as the matrix pencil method have previously not been commercially available Using these VIs you can build your own applications to perform super resolution spectral analysis and parameter estimation In addition there is also a comprehensive test panel to assist those who are not familiar with model based frequency analysis Refer to Chapter 16 Model Based Frequency Analysis Algorithms and Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs for more information about the algorithm Signal Processing Toolset 15 8 National Instruments Corporation Model Based Frequency Analysis Algorithms This chapter outlines the theoretical background of model based frequency analysis and describes the relationship among the model coefficients the power spectra and the parameters of damped sinusoids In most cases only the conclusions are presented without justification For more information refer to Kay 1987 and Marple Jr 1987 Models Power Spectra and Damped Sinusoids This section introduces the signal models used for model based frequency analysis and explains the relationship among the model coefficients the power spectra and the parameters of damped s
9. Third Octave Analysis Applications in LabWindows CVI This section describes the instrument driver for LabWindows CVI included with the Third Octave Analysis toolkit and provides information on running third octave analysis applications in LabWindows CVI Third Octave Analysis Instrument Driver The Third Octave Analysis toolkit provides an instrument driver octave fp for LabWindows CVI users You can find this file in the CVI Support instr subdirectory of your installation directory The following is the prototype for the instrument driver long status ThirdOctave_Analyzer double input long nx double fs long winType long FFTSize long avgNum 2 double Power 31 double CenterFreq 31 long outputNum National Instruments Corporation 28 1 Signal Processing Toolset Chapter 28 Building Windows Applications for Third Octave Analysis Parameters Input Return which can be only 256 or 512 CenterFreq Center frequencies of the 31 third octave filters Output Pora daaa array Outputs SospusoNeclImdecaveHMem the 31 third octave filters CenterFreq double array Center frequencies of the 31 third octave filters Value monu 73 Tene r integer Reprbochpue oa een ears to Chapter 30 Third Octave Error Codes for a list of error codes Parameter Discussion input is the input data array The size of input must be 28680 if FFTSize 256 and must be 54280 if FFTSize 512 nx is the array size of
10. 2 ntn snsS2n Hn 1 National Instruments Corporation 12 3 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Figure 12 2 shows how the VI constructs X7 in this case The lengths of Xi and Xf are the same as in the zero padding case Figure 12 2 Symmetric Extension If you want to construct Xi and Xf in a different way you can open the diagram of this VI and modify it making sure the lengths of Xi and Xf are equal to n After constructing X7 this VI computes outputs y0 and y1 the same way as the outputs in the Decimation Filter VI Refer to the Decimation Filter VI in this chapter to learn how to compute y0 and yl Synthesis Filter Bank VI This VI computes the outputs of a synthesis filter bank yl i is the input data array for the synthesis highpass filter often the output DEL from the analysis highpass filter DEL yO i is the input data array for the synthesis lowpass filter often the output from the analysis lowpass filter Synthesis Filter Bank contains the synthesis filter coefficients DBL Lowpass contains the lowpass synthesis filter coefficients DBL Highpass contains the highpass synthesis filter coefficients Signal Processing Toolset 12 4 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference DEL x i is the output from the synthesis filter bank error Refer to Chapter 14 Wavelet Error Codes for a description of the error The VI
11. F OBL x i is the time waveform Gauss window var controls the resolution and crossterm interference It must be greater than zero The greater the variance the better the resolution but the more severe the interference The opposite is also true This process suppresses only those crossterms that correspond to two autoterms with different time centers H of rows determines the maximum number of rows of the spectrogram pli k of frequency bins determines the number of columns of the spectrogram plillk from Equation 4 4 It must be a power of two plil k is the pseudo Wigner Ville distribution z ian t error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions National Instruments Corporation 4 13 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS Gabor Spectrogram Gabor Expansion Based Spectrogram Computes the Gabor expansion based spectrogram with given analysis functions COB 3 E z i ta Signal Processing Toolset basis i gabo plillk order H of rows tolerance spect BITOI basis selects the analysis and synthesis functions used for the Gabor spectrogram Three types of functions are provided wideband mediumband and narrowband The default is mediumband x i is the time waveform either a real valued or complex signal order balances the resolution and crossterm
12. e They can be designed to have linear phase by ensuring coefficient symmetry e They are always stable e You can perform the filtering function using the convolution A delay generally is associated with the output sequence E doloe ES elay 5 where n is the number of FIR filter coefficients You design FIR filters by approximating a specified desired frequency response of a discrete time system The most common techniques approximate the desired magnitude response while maintaining a linear phase response Format of the Filter Coefficient Text Files When you save your filter coefficients to a text file the DFD application generates a readable text file that contains all the information you need to implement the designed FIR or IIR digital filter This section describes the format for both FIR and IIR filter coefficient files FIR Coefficient File Format Table 21 1 provides example FIR coefficient text files and descriptions You can implement the FIR filter using Equation 21 4 directly Signal Processing Toolset 21 4 National Instruments Corporation Chapter 21 IIR and FIR Implementation Table 21 1 FIR Coefficient Text Files and Descriptions o mese m meme 0 ECCE NN Wand Mew S meme aame SSS isomer Bss NN Gemma hw Due Gee 0 Ese ooo mew Gamma o ooo aans o o o mowe National Instruments Corporation 21 5 Signal Processing Toolset Chapter 21 IIR and FIR Implementation Table
13. oversampling rate P plot pop up National Instruments Corporation G 7 Glossary A signal containing significant energy concentrated around more than one distinct and separate frequency Analyzing a signal in several different scales Program execution element Nodes are analogous to statements operators functions and subroutines in conventional programming languages In a block diagram nodes include functions structures and subVIs Signal whose frequency content changes within a captured frame Front panel objects used to manipulate and display or input and output numeric data Half the sampling rate Generic term for any item on the front panel or block diagram including controls nodes wires and imported pictures Interval between two frequencies one of which is twice the other For example frequencies of 250 Hz and 500 Hz are one octave apart as are frequencies of 1 kHz and 2 kHz Refer to third octave A filter bank where both the analysis and synthesis filter banks are orthogonal to themselves It is a special case of biorthogonal filter banks Ratio between the number of Gabor coefficients and the number of test samples Graphical representation of an array of data shown either in a graph or a chart To call a special menu by right clicking Windows or command clicking Macintosh an object Signal Processing Toolset Glossary pop up menu preemphasis PWVD R reentrant exe
14. From the concept of expansion and series Dennis Gabor a Hungarian born British physicist suggested expanding a signal into a set of weighted frequency modulated Gaussian functions Because the Gaussian function is concentrated in both the time and frequency domains the weights describe the signal behavior in local time and frequency The resulting presentation is known as the Gabor expansion In fact you can consider the Gabor expansion the inverse of the STFT However this inverse relationship was not clear during Gabor s lifetime and not well understood until the 1980s At present both the theory and implementation of the Gabor expansion and STFT are mature enough to apply to real application problems As the linear JTFA develops the quadratic JTFA time dependent spectrum attracts great attention The simplest time dependent spectrum is the square of the STFT which was named the STFT based spectrogram or the STFT spectrogram As mentioned earlier the STFT spectrogram suffers from the window effect A more elegant method is the Wigner Ville Distribution WVD which originally was developed in the context of quantum mechanics by Hungarian born American physicist Eugene P Wigner The WVD has high resolution and many other useful properties for signal analysis but it suffers from crossterm interference To reduce crossterm interference you can use two proven algorithms Cohen s class and the Gabor expansion based spectrogram als
15. In short every algorithm has advantages and disadvantages National Instruments Corporation 6 3 Signal Processing Toolset Chapter 6 Frequently Asked Questions As an example Figure 6 1 shows an STFT spectrogram with a test signal that contains 10 sine cycles at 10 Hz Although the signal starts at t 1 s and ends at t 2 s the STFT spectrogram clearly shows something before t 1 s and after t 2 s as indicated by the arrows Moreover the time dependent spectrum indicates that the signal does not contain only 10 Hz but that it possesses a certain bandwidth doen cumentdata testdat datalengih sec 300E 0 i Spectrum 5 0E 1 0 pe sec 0 0E 0 B 0E ile 0E 0 1 5E 2 0E 0 E BE 0 30E 0 CHBA A control Figure 6 1 STFT Spectrogram Hanning Window By applying other methods you can substantially suppress the energy outside 1 s to 2 s and 10 Hz thereby achieving a near point to point measurement Figure 6 2 shows the Gabor spectrogram As shown most of the signal s energy is between 1 s to 2 s and 10 Hz The higher the order the higher the concentration and the closer you come to achieving a point to point measurement On the other hand the higher order Gabor spectrogram produces negative values which might be difficult to accept from the classical energy definition point of view Moreover the Gabor spectrogram generally requires more computation time than the STFT spectrogra
16. The source code for this algorithm was developed by Professor Qinye Yin and Zhifang Ni at Xi an Jiaotong University China Yin 1997 National Instruments Corporation 3 13 Signal Processing Toolset Joint Time Frequency Analysis VIs This chapter describes the JTFA VIs Adaptive Transform Computes the coefficients of the adaptive representation A k parameters residual MSE error i adapt af Termes trans cne xli is the time waveform either a real valued or analytical signal of Terms determines the maximum number of elementary functions used for the adaptive representation The more elementary functions the more accurate the presentation However computation time increases as the number of elementary functions increases A k is a 1D array that indicates the weight of each elementary function Azli Lr z e DBL parameters is a 2D array that indicates four tuple parameters of elementary functions i i i p h i an 7 apl p danti NA il 4 1 20 2 National Instruments Corporation 4 1 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS ss REM wvarame o lance normalized center EE CEN 0 27 frequency frequency changing rate residual MSE indicates the mean square error MSE of the signal x i and the adaptive representation The MSE reduces as the number of elementary functions increases error indicates a JTFA
17. double y0 long ny0 double y1 long ny1 Computes the outputs of a 2 channel analysis filter bank It performs the same operation as the 2 Channel Filter Bank VI Refer to the description about that VI for more information Parameters Input X double precision The input data array array long integer The size of input array x AnalysisFilters FilterBankPtr The structure holding the analysis filter bank coefficients padtype long integer The type of padding used at the beginning and the end of the input data 0 zero padding 1 symmetric extension long integer The array size of y0 It must be ceil nx nh 1 2 nh is the size of the highpass filter in AnalysisFilters long integer The array size of y1 It must be ceil nx nl 1 2 nl is the size of the lowpass filter in AnalysisFilters Output y0 double precision The output from the analysis lowpass array filter yl double precision The output from the analysis highpass array filter Signal Processing Toolset 12 22 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference Return Value status integer Refer to Chapter 14 Wavelet Error Codes for a description of the error Example Example 1 How to call function AnalysisFilterBank include wfbd h FilterBankPtr anaptr synptr double x yU yL long err nx ny0 nyl anaptr AllocCoeffWFBD allocate filter bank structure if anaptr
18. e STFT spectrogram e Wigner Ville distribution WVD e Pseudo Wigner Ville distribution PWVD e Cohen s class e Choi Williams distribution CWD e cone shaped distribution e Gabor spectrogram e adaptive spectrogram STFT Spectrogram The STFT based spectrogram is defined as the square of the STFT j2xni N 2 SP mAM n X sUlYLi mAM e i 0 where N denotes the number of frequency bins and AM denotes the time sampling interval The STFT based spectrogram is simple and fast but suffers from the window effect Figures 3 1 and 3 2 illustrate the window effect of the STFT spectrogram With a narrowband window Figure 3 1 the time dependent spectrum has high frequency resolution but poor time resolution With a wideband window Figure 3 2 the time dependent spectrum has poor frequency resolution but high time resolution National Instruments Corporation 3 3 Signal Processing Toolset Chapter 3 Joint Time Frequency Analysis Algorithms Z O 00E 0 sec 2 15E 2 Hz 1 7E 0 i i sec 0 0E 0 2 UE 2 4 0E 2 6 0E 2 B UE 2 1 0E 1 1 3E 1 Ed control Figure 3 1 STFI Based Spectrogram with a Narrowband Hanning Window for the Three Tone Test Signal spectrum Hz curent data gauss3 tst data length sec 1 28E 1 spectrum Z 0 00E 0 sec 2 15E 2 Hz 1 7E 0 i i l sec D OE 0 2 UE 2 4 0E 2 6 0E 2 B 0E 2 1 0E 1 1 3E 1 pi control Figure 3 2 STFI Based Spectr
19. 1 x N 1 which is named a forward prediction Alternatively there is a backward prediction explained later in this chapter The AR MA and ARMA models cover a wide range of signals in nature In most applications you confidently can apply model based methods for frequency analysis Usually you can choose the appropriate model based on physical modeling In practice you might not know which of the given models is best for the problem at hand An important result from the Wold decomposition and Kolmogorov theorems is that any AR or ARMA process can be represented by an MA process of possibly infinite order Likewise any MA or ARMA process can be represented by an AR process of possibly infinite order Refer to Kolmogorov 1941 and Wold 1954 for more information If you choose the wrong model among the three you might still obtain a reasonable approximation by using a high enough model order The next task is determining the model order As shown in the previous chapter the wrong model order might lead to an incorrect result To select the right order you need some knowledge about the signal Each complex 16 2 National Instruments Corporation Chapter 16 Model Based Frequency Analysis Algorithms sinusoid component counts as one order Each real sinusoid component generates two complex sinusoids that correspond to two orders If you are not sure what order you should use you can estimate it with the minimum description len
20. 20 24 specifications for pole zero filter designs 20 20 to 20 21 Digital Filter Design DFD utilities 22 1 to 22 9 LabVIEW DFD utilities 22 1 to 22 3 DFD Filter 22 3 Read DFD Coefficients 22 2 Signal Processing Toolset Index LabWindows CVI utilities 22 4 to 22 8 AllocCoeffDFD 22 5 DFD instrument driver 22 4 FilterDFD 22 8 FreeCoeffDFD 22 7 ReadCoeffDFD 22 6 Windows DLL DED utilities 22 9 Digital Filter Design toolkit overview 1 2 to 1 3 reference materials 23 1 discontinuity detection application wavelet analysis 9 9 to 9 10 documentation conventions used in manual xxii xxiii organization of manual xix xxii related documentation xxiii E electronic support services A 1 to A 2 e mail support A 2 error codes joint time frequency analysis JTFA 8 1 Third Octave Analysis toolkit 30 1 Wavelet and Filter Bank Design toolkit 14 1 to 14 2 F Fast Dual VI 4 7 to 4 8 fast Fourier transform compared with model based frequency analysis 15 1 to 15 6 comparison of FFT JTFA wavelets and model based methods table 15 7 windows for FFT based spectrum in Super Resolution Spectral Analyzer 18 3 fax and telephone support numbers A 2 Fax on Demand support A 2 Signal Processing Toolset l 4 filter banks See digital filter banks Wavelet and Filter Bank Design toolkit FilterDFD function 22 8 finite impulse response filters See FIR filters FIR filters See also Digital Filter Design D
21. Although you do not follow the ordinary wavelet decomposition scheme discussed in the earlier chapters in this case you can still fully recover the original signal X if the coefficients are not altered This generalized wavelet decomposition is called a wavelet packet which offers a wider range of possibilities for signal processing The path is completely determined by your application One common method is to check each node of the decomposition tree and quantify the information Then continue to decompose those nodes that contain more information Such technique is traditionally called an entropy based criterion Online Testing Panel To assist you with testing your own applications the main design panel saves the filter coefficients as the following global variables in the Wavelet Global VI e Analysis Filter Coefficients Contains coefficients Go z and G z e Synthesis Filter Coefficients Contains coefficients H z and H z These variables simultaneously change as you change the design If you incorporate those parameters into your own application you can see the effect of the different design Figure 11 15 illustrates how LabVIEW uses these two parameters to implement a wavelet packet similar to the one displayed in Figure 11 14 Signal Processing Toolset 11 18 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Analysis Filter Coefficients e e Synthesis Filter Coef
22. Chapter 4 Joint Time Frequency Analysis VIs describes the JTFA VIs Chapter 5 Joint Time Frequency Analysis Applications introduces some JTFA applications Because JTFA is relatively new it is less known among practicing engineers and scientists unlike the well known Fourier analysis The examples in this chapter reveal only the potential of JTFA The power of JTFA has not been fully explored These examples can help you learn and apply JTFA to your applications Chapter 6 Frequently Asked Questions addresses some questions JTFA users frequently ask Chapter 7 JTFA References lists reference material that contains more information on the theory and algorithms implemented in the JTFA toolkit Chapter 8 JTFA Error Codes lists the error codes the JTFA VIs return l 1 Signal Processing Toolset The Need for Joint Time Frequency Analysis This chapter explains the need for and the approaches to joint time frequency analysis JTFA Review of the Classical Fourier Transform From a mathematical point of view you can describe a given signal in many different ways For instance you can write the signal as a function of time which shows how the signal amplitude changes over time Alternatively you can write the signal as a function of frequency which tells us how frequently the amplitude changes The bridge between time and frequency representations is the Fourier transform first introduced by Jean Baptiste Joseph Fo
23. Classical FIR Filter Design Get Info Pole Zera Placement Arbitrary FIR Filter Design Load Spec Preferences Cuit Figure 20 2 DFD Main Menu Panel Signal Processing Toolset 20 2 National Instruments Corporation Chapter 20 Digital Filter Design Application Opening the Filter Design Panels From the Main Menu panel you can open any of the four digital filter design panels Classical IIR Filter Design Classical FIR Filter Design Pole Zero Placement and Arbitrary FIR Filter Design For more information about each design panel refer to the Digital Filter Design Panels section later in this chapter Directly Loading a Filter Specification File You also can load a previously designed filter specification file directly from the Main Menu panel When you click the Load Spec button the DFD application prompts you to select the filter specification file that you saved during previous design work After you select the file you can open the appropriate design panel for that specification file You then can resume work on an ongoing design project Editing the DFD Preferences To customize your DFD application preferences click the Preferences button on the Main Menu panel You can edit your DFD application preferences for future design sessions Quitting the DFD Application Click the Quit button on the Main Menu panel to quit the DFD application Digital Filter Design Panels When you double click on
24. DBL Lowpass contains the lowpass analysis filter coefficients DBL Highpass contains the highpass analysis filter coefficients EFA extension decides the initial condition and final condition extension has two options 0 zero padding changes all the initial conditions and final conditions to zeros 1 symmetric extension extends signal X symmetrically as the initial condition and final condition Refer to the Analysis Filter Bank VI for more information about how to add data in these two cases Low_Low contains the output of the first subimage from the analysis filter bank Low_High contains the output of the second subimage from the analysis filter bank High_Low contains the output of the third subimage from the analysis filter bank High_High contains the output of the fourth subimage from the analysis filter bank error Refer to Chapter 14 Wavelet Error Codes for a description of the error Signal Processing Toolset 12 6 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference 2D Analysis Filter Bank for 116 VI This VI computes the outputs of a 2D image passing through an analysis filter bank perfect reconstruction Poss Low Low Analysis Filter Coefficients Low High extension High Low High High eror When a 2D image passes an analysis filter bank it is broken into four sub images Refer to Chapter 10 Digital Filter Banks for more information about computing the four
25. Factor to mimic Hz 1 3 Octave human hearing NO NO NO National Instruments Corporation 24 3 Signal Processing Toolset Chapter 24 Overview of the Third Octave Analysis Toolkit Signal Processing Toolset Table 24 1 Filter Bands for ANSI 1 11 Continued A weighting dB Center Frequency Factor to mimic Hz 1 3 Octave human hearing The Third Octave Analyzer uses 1000 Hz as its reference frequency The following paragraphs describe how the analyzer calculates its center frequencies Define an array as CF CF 20 25 31 5 40 50 63 80 100 125 160 200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000 6300 8000 10000 12500 16000 20000 If the sampling rate is 51200 Hz the center frequencies are the same as in Table 24 1 from ANSI Band number 13 to 43 Thus from 20 Hz to 20000 Hz is the same as the array CF If the sampling rate 1s fs define Af fs 51200 then the i center frequency is CF i Af where CFTi is the i element in the array CF 24 4 National Instruments Corporation Operating the Third Octave Analyzer This chapter describes the Third Octave Analyzer application and explains the program features For information on the analyzer algorithm refer to Chapter 26 Third Octave Analysis Design Setting Up the Third Octave Analyzer In Windows 95 NT first configure your data acquisition DAQ device using the NI DAQ Configuration Utility Ru
26. National Instruments Corporation Third Octave Analysis Design This chapter describes the design specifications and algorithms of the Third Octave Analysis toolkit ANSI Standard 51 11 defines clear specifications for octave band filters Octave band filters can be either passive or active analog filters that operate on continuous time signals or analog and digital filters that operate on discrete time signals Traditional octave analyzers typically use analog filters but newer analyzers most often use digital filters Digital octave filters are designed in several ways A set of bandpass filters usually infinite impulse response filters can be designed directly from the time domain at different center frequencies and bandwidths In particular ANSI S1 11 uses Butterworth filters to define the order and attenuation of the octave filters Digital octave filters also can be designed in the frequency domain using the fast Fourier transform FFT Many instrument manufacturers use a spectrum analyzer to synthesize the octave analyzer The Third Octave Analysis toolkit also follows this approach Algorithm Description In the frequency domain approach to octave analysis you first collect a block of data Then you apply the FFT to the data to obtain the spectral information Because the spectral information appears in a discrete format several discrete spectral values or bins are weighted and then summed to obtain the power for each of t
27. PE CNN C x 0 x 2 x 3 a x p 1 2 XE 16 10 x IN p xIN p 1 xIN I a x N p 1 The forward and backward predictions in Equation 16 8 are interchangeable For instance let P P A z 1 az or A z 1 4 y a 2 16 11 k 0 k 0 The resulting P z in Equation 16 7 are the same AR Model and Damped Sinusoids Damped sinusoids are common in applications such as noise and vibration Many natural phenomena can be formulated as a linear combination of damped sinusoids p p x n Y C expt o j2nfj n Y C Q z forO lt n lt N 16 12 k 1 k 1 where the parameter Ot indicates the damping factor and Cj denotes the complex amplitudes Equation 16 12 also can be written in matrix form as z z5 en z C x 0 CD Xm xm Dex xU 16 13 N 1 C x N 1 Signal Processing Toolset 16 4 National Instruments Corporation Chapter 16 Model Based Frequency Analysis Algorithms where the matrix of the time indexed z elements has a Vandermonde Structure At first glance Equation 16 12 does not seem to belong to any of the models described by Equations 16 1 16 2 and 16 3 However it is closely related to the AR model in Equation 16 3 In 1795 Baron de Prony discovered that z in Equation 16 12 actually are roots of the polynomial P P A z 1 Paz Q 722 16 14 k 1 k 1 where a are nothing more than the coefficients of the regular AR model in Equation 16 3 Consequently the procedure
28. Refer to the description for that VI for more information Parameters Input mu eocepeacan precision The input data array array double precision M array of filter coefficients array double precision The initial condition of the input data array double precision The final condition of the input data array ny long integer The size of output array y it must be ceil nx ni nf ncoef 1 decfact Output we double precision Mietin oae o output from the decimation filter array National Instruments Corporation 12 29 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Return Value status integer Refer to Chapter 14 Wavelet Error Codes for a description of the error Example Example 3 How to build 2 channel analysis filter bank using DecimationFPilter include wfbd h FilterBankPtr anaptr synptr double x yO 7 yb init ilal scp long err ix ny 0 ny i m phy npada anaptr AllocCoeffWFBD allocate filter bank structure if lanaptr return synptr AllocCoeffWFBD If lsSynptE 4 free anaptr return err ReadCoeffWFBD coef dat anaptr synptr Read filter bank coefficients if err goto errend nl anaptr gt nl nh anaptr gt nh x double malloc nx sizeof double if x goto errend npad nl nh 2 1 Compute the size of initial and final condition arrays init
29. The JTFA algorithms implemented in this package fall into two categories linear and quadratic For more information on a particular algorithm consult Qian s 1996 and Cohen s 1995 works Linear JIFA Algorithms Linear JTFA includes the following methods e Gabor expansion considered the inverse short time Fourier transform STFT e STFT used for computing the Gabor coefficients e adaptive representation considered the inverse adaptive transform e adaptive transform Gabor Expansion and STFT The Gabor expansion represents a signal s i as the weighted sum of the frequency modulated and time shifted function A i N 1 sil yy C hli mAM e 7 3 1 mn 0 where the Gabor coefficients C are computed by the STFT Cnn STFTUnAM n Y slilY Li mAM e i 0 where N denotes the number of frequency bins and AM denotes the time sampling interval You can use any function as y i as long as its dual function A i exists For the perfect reconstruction the oversampling rate N AM must be greater than or equal to one For a given A i or i use the FastDual VI to compute the corresponding dual function National Instruments Corporation 3 1 Signal Processing Toolset Chapter 3 Joint Time Frequency Analysis Algorithms If the STFT is not used for computing the Gabor coefficient C there are no restrictions for y i or the ratio V AM Adaptive Representation and Adaptive Transform In the Gabor expan
30. This section of the manual describes the Third Octave Analysis toolkit National Instruments Corporation Chapter 24 Overview of the Third Octave Analysis Toolkit explains how you can use this program The Third Octave Analysis toolkit can act as a stand alone application or as an add on toolkit for LabVIEW The toolkit also provides the instrument driver for LabWindows CVI users and dynamic link libraries for Windows users Chapter 25 Operating the Third Octave Analyzer describes the Third Octave Analyzer application and explains the program features Chapter 26 Third Octave Analysis Design describes the design specifications and algorithms of the Third Octave Analysis toolkit Chapter 27 Third Octave Filters VI describes the Third Octave Filters VI and its parameters Chapter 28 Building Windows Applications for Third Octave Analysis describes how to build a third octave analysis application under Windows 95 NT Chapter 29 Third Octave References lists reference material that contains more information on the theory and algorithms implemented in the Third Octave Analysis toolkit Chapter 30 Third Octave Error Codes lists the error codes returned by the Third Octave Filters VI and the C function ThirdOctave Analyzer V 1 Signal Processing Toolset Overview of the Third Octave Analysis Toolkit This chapter explains how you can use this program The Third Octave Analysis toolkit can act as a stand alone appl
31. Wiksell 1938 republished 1954 National Instruments Corporation 19 1 Signal Processing Toolset Digital Filter Design Toolkit This section of the manual describes the Digital Filter Design DFD toolkit e Chapter 20 Digital Filter Design Application describes the DFD application you use to design infinite impulse response IIR and finite impulse response FIR digital filters e Chapter 21 ZIR and FIR Implementation describes the filter implementation equations for IIR and FIR filtering and the format of the IIR and FIR filter coefficient files e Chapter 22 Using Your Coefficient Designs with DFD Utilities describes the DFD utilities you use for filtering applications e Chapter 23 DFD References lists reference material that contains more information on the theory and algorithms implemented in the DFD toolkit National Instruments Corporation IV 1 Signal Processing Toolset Digital Filter Design Application This chapter describes the Digital Filter Design DFD application you use to design infinite impulse response IIR and finite impulse response FIR digital filters The DFD application provides complete filter design and analysis tools you can use to design digital filters to meet your precise filter specifications You can design your IIR and FIR filters graphically review filter responses interactively save your filter design work and load your design work from previous sessions You c
32. chart checkbox CIN cluster code interface node constant Q analysis continuous run Signal Processing Toolset A core or fundamental function A filter bank in which analysis and synthesis filter banks are orthogonal to each other Pictorial description or representation of a program or algorithm In G the block diagram is the source code for the VI It consists of executable icons called nodes as well as wires that carry data between the nodes Front panel objects used to manipulate and display Boolean TRUE or FALSE data Several styles are available such as switches buttons and LEDs A special kind of filter in which the low frequency asymptope is a constant See scope chart strip chart and sweep chart Small square box in a dialog box that can be selected or cleared Check boxes generally are associated with multiple options that can be set More than one check box can be selected See code interface node Set of ordered unindexed data elements of any data type including numeric Boolean string array or cluster The elements must be all controls or all indicators CIN Special block diagram node through which you can link conventional text based code to a VI Analysis where the ratio between the center frequency and frequency bandwidth is constant Execution mode in which a VI is run repeatedly until the operator stops it You enable it by clicking the Continuous Run button G 2 Nationa
33. n is the size of lowpass filter in SynthesisFilters nh is the size of highpass filter in SynthesisFilters Output JEN LH double precision iie dup kon heye s bier Bank output from the synthesis filter bank array Signal Processing Toolset 12 40 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference Return Value status integer Refer to Chapter 14 Wavelet Error Codes for a description of the error Example Example 5 How to call function SynthesisFilterBank include wfbd h FilterBankPtr anaptr synptr double x v0 vl x05 long err nx nyO nyl anaptr AllocCoeffWFBD allocate filter bank Structure 1if lanaptr return synptr AllocCoeffWFBD 1fi lsynptr free anaptr return err ReadCoeffWFBD coef dat anaptr synptr Read filter bank coefficients if err goto errend nx 128 x double malloc nx sizeof double it bx goto errend Chirp ix 10 UU D 303 ny0 ceil 0 5 nxtanaptr gt nh 1 Compute the size of output array yO double malloc nyO sizeof double if y0 goto errend nyl ocerl 0 5 nxtanaptr nl 1 4 yl double malloc ny1 sizeof double if y1 free y0 goto errend err AnalysisFilterBank x nx anaptr 0 y0 ny0 yl nyl National Instruments Corporation 12 41 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Allocate memor
34. n 0 n N which implies that P z is non negative Similar to biorthogonal cases the selection of Po z in orthogonal cases is dominated by maximum flat and equiripple halfband filters However because of constraints imposed by Equation 10 13 Po z must be the time shifted non negative function P z Although the maximum flat filter in Equation 10 9 ensures this requirement special care must be taken when P z is an equiripple halfband filter Figure 10 8 plots the third order Daubechies filter banks and wavelets It is derived from the same maximum flat filter as that depicted in Figure 10 5 In this case however Go z contains three zeros at 7t and all zeros inside the unit circle therefore possessing minimum phase Because of the orthogonality its dual filter bank has the same convergence property Compared to the B spline cases in Figures 10 6 and 10 7 the third order Daubechies wavelet and scaling function is not as smooth as that of Go z and G z refer to Figure 10 6 but is much smoother than that of Ho z and H z refer to Figure 10 7 Signal Processing Toolset 10 10 National Instruments Corporation Chapter 10 Digital Filter Banks Scaling Function Mother Wavelets 2 Figure 10 8 Third Order Daubechies Filter Banks and Wavelets 2D Signal Processing The preceding sections introduced two channel PR filter banks for ID sign
35. 21 1 FIR Coefficient Text Files and Descriptions Continued 6 35087 1E 3 last coefficient h N 1 IIR Coefficient File Format Signal Processing Toolset IIR coefficient files are slightly more complex than FIR coefficient files IIR filters usually are described by two sets of coefficients a and b coefficients A total of M x S a coefficients and M 1 x S b coefficients exist where M is the stage order usually 2 and S is the number of stages An IIR filter with three second order stages has two a coefficients per stage for a total of six a coefficients and three b coefficients per stage for a total of nine b coefficients You can implement the IIR filter in cascade stages by using Equation 21 1 maintaining two past inputs and two past outputs for each stage or by using the direct form II equations maintaining two past internal states Table 21 2 provides example IIR coefficient text files and descriptions Table 21 2 R Coefficient Text Files and Descriptions o mese 21 6 National Instruments Corporation Chapter 21 IIR and FIR Implementation Table 21 2 R Coefficient Text Files and Descriptions Continued ooo mmewhseiens National Instruments Corporation 21 7 Signal Processing Toolset Using Your Coefficient Designs with DFD Utilities This chapter describes the DFD utilities you use for filtering applications LabVIEW DFD Utilities This section contains descriptions of the DFD
36. 25 3 Four Channel Third Octave Analyzer Panel The following sections define the several control buttons on the Third Octave Analyzer front panel that you can select to perform functions Setup opens the Setup dialog box Acquire acquires and analyzes a block of data The analyzer does not start acquiring data until you click this button Signal Processing Toolset 25 6 National Instruments Corporation Chapter 25 Operating the Third Octave Analyzer Use the control to the left of the Acquire button to acquire your data in Single or Continuous mode When you select Single every time you click the Acquire button the analyzer acquires and analyzes a new data block When you choose Continuous the analyzer starts to acquire and analyze data when you click the Acquire button When one block of data finishes the analyzer acquires the next block of data and analyzes it This process continues until you click the Stop Acquire button The Acquire button which is shown in Figure 25 3 becomes the Stop Acquire button during an acquisition Amplitude Table shows a table with all 31 bands of output power values for each channel Save saves the 31 bands of power values to a file in a spreadsheet format where each column represents 31 bands of power value for each channel This button saves the power amplitude as well as some status information such as channel numbers window type average type and weighting values Recall recalls a file th
37. 6120092 02 413091 03 5472 2970 02 596 7456 5 520 2635 0348 433466 32 84 84 00 2265886 91 640 0085 08 730 49 70 056 200 51 51 02 377 1200 01635 523545 512 795 8248 A 2 Fax 03 9879 6277 0662 45 79 90 19 02 757 03 11 011 288 8528 905 785 0086 514 694 4399 45 76 26 02 09 725 725 55 01 48 14 24 14 089 714 60 35 2686 8505 03 6120095 02 41309215 03 5472 2977 02 596 7455 5 520 3282 0348 430673 32 84 86 00 2265887 91 640 0533 08 730 43 70 056 200 51 55 02 737 4644 01635 523154 512 794 5678 National Instruments Corporation Technical Support Form Photocopy this form and update it each time you make changes to your software or hardware and use the completed copy of this form as a reference for your current configuration Completing this form accurately before contacting National Instruments for technical support helps our applications engineers answer your questions more efficiently If you are using any National Instruments hardware or software products related to this problem include the configuration forms from their user manuals Include additional pages if necessary Name Company Address Fax Phone Computer brand Model Processor Operating system include version number Clock speed MHz RAM MB Display adapter Mouse yes no Other adapters installed Hard disk capacity MB Brand Instruments used National Instruments hardware product model Revision Configuration National Instrumen
38. AllocCoeffW FBD function 12 19 Joint Time Frequency Analysis toolkit overview 1 1 to 1 2 Analysis2DArraySize function 12 20 to 12 21 Joint Time Frequency Analyzer Offline a adaptive spectrogram 5 13 to 5 14 applying pre emphasis filter 5 11 changing spectrogram display 5 9 Choi Williams distribution 5 14 cone shaped distribution 5 15 frequency zooming 5 11 Gabor spectrogram 5 13 illustration 5 9 inputting data 5 10 Pseudo Wigner Ville distribution 5 14 saving results 5 10 selecting JTFA method 5 12 setting time parameters 5 12 STFT spectrogram 5 12 switching between conventional power and instantaneous spectrum 5 10 to 5 11 Signal Processing Toolset l 6 AnalysisFilterBank function 12 22 to 12 23 AnalysisFilterBank2D function 12 24 to 12 28 calling WFBD functions 12 17 DecimationFilter function 12 29 to 12 32 FreeCoeffWFBD function 12 33 InterpolationFilter function 12 34 to 12 36 ReadCoeffWFBD function 12 37 Synthesis2DArraySize function 12 38 to 12 39 SynthesisFilterBank function 12 40 to 12 42 SynthesisFilterBank2D function 12 43 to 12 46 WEBD instrument driver function prototypes 12 17 to 12 18 LabWindows CVI DED utilities 22 4 to 22 8 AllocCoeffDFD 22 5 National Instruments Corporation DFD instrument driver 22 4 FilterDFD 22 8 FreeCoeffDFD 22 7 ReadCoeffDFD 22 6 linear JTFA algorithms 3 1 to 3 2 adaptive representation and adaptive transform 3 2 examp
39. Analysis Signal Processing Toolset wavelet to measure s t The wavelet w t used to measure s t is one cycle of sinusoidal waveform as shown in Figure 9 2 frequency spectrum Figure 9 2 Wavelet Because w t spans 1 second consider the frequency of y t to be 1 Hz As in the case of Fourier analysis you can achieve the comparison process with the following correlation or inner product operation Wan ws tdt 9 2 T where W n denotes the wavelet transform coefficients and Y t are the elementary functions of the wavelet transform However the structure of the elementary functions WY 1 differs from the Fourier transformations which are the dilated and shifted versions of y t m 2 Win nt 2 v 2 1 n2 9 3 where m and n are integers 9 4 National Instruments Corporation Chapter 9 Wavelet Analysis By increasing n you shift y t forward in time By increasing m you compress the time duration and thereby increase the center frequency and frequency bandwidth of w t Qian and Chen 1996 You can consider the parameter m as the scale factor and 27 as the sampling step Therefore the shorter the time duration the smaller the time sampling step and vice versa Assuming the center frequency of y t is po the center frequency of Yn 1 would be 2 Consequently you systematically can adjust the scale factor m to achieve different frequency tick marks to measure the signal
40. Applications 2D Short Time Fourier Transtorm analysis 1 ri i ER EFIE dti C ret m J en2 ne 3 L5 91EH0 3 88E H x i k nm zh zi DEH r2 k p TIE 0 N22h O Figure 5 4 2D STFT for the Image Analysis in Figure 5 2 Time Dependent Spectrum Analysis Examples A primary motivation of JTFA is to discover how the power spectrum of a signal changes over time While classical algorithms such as the square of the Fourier transform indicate only the average of a signal s power spectrum JTFA algorithms allow you to examine the instantaneous spectrum Consequently you have a better understanding of the nature of the signal in which you are interested For your convenience this toolkit provides a comprehensive combination of online and offline joint time frequency analyzers Using these analyzers you can perform rather sophisticated time dependent spectrum analysis Because each algorithm has advantages and disadvantages you should select an algorithm based on the application The simplest and fastest algorithm is the STFT spectrogram which is suitable for online analysis If the frequency contents of a signal change rapidly consider one of the other algorithms included in this toolkit Signal Processing Toolset 5 6 National Instruments Corporation Chapter 5 Joint Time Frequency Analysis Applications Online STFT Spectrogram Analyzer The Online Analyzer allows you to collect real data and perfor
41. Array SIZE isst Iud OE AUTRAISSU RUIN AT a 12 20 JATIN SIS PINGED aN 3250 ore edid a ND Hm Ens eduut C dS 12 22 AmalysisEilterBatk2L ipte ce ret o a 12 24 DECIMATION Tel saith a tas e pinea aptos ome pU UD GN Uds 12 29 bicceCoe WEB D esnaera MI 12 33 Herpa h on PNE 25 oci ee pios Ica pu Md ELTE 12 34 Reide Gert W FD e 12 37 Synthesis2 D ATETYS1Z6 50 1 30 20 9 525 diu id eene dam Oeste eae oes 12 38 Signal Processing Toolset Vill National Instruments Corporation Contents Synthesis Fiter Bank oj ssu2s ie irecd tes eed nowaadeadseereacgay th madee MN 12 40 5ynthesisEilterDank 2D unit reiten doe a Tee areas 12 43 MWandows Appl CaliOns c usi eot od aen Qoa adea mivem c euet lods uda dead Uti o EE cue E 12 47 Chapter 13 Wavelet References Chapter 14 Wavelet Error Codes Part Ill super Resolution Spectral Analysis Toolkit Chapter 15 Introduction to Model Based Frequency Analysis The Need for Model Based Frequency Analysis eese 15 1 Applying Model Based Method Properly sss 15 6 When to Use Ihis SOIUCU AEG eioaccece a ace Mens n EE E EA de da co hada doe deu 15 8 Chapter 16 Model Based Frequency Analysis Algorithms Models Power Spectra and Damped Sinusoids sse 16 1 ARMA MA a d AR MI OG EES ace e y ee reete eei ee Eee EN DE 16 1 Model Coefficients and Power Spectra eeeeeeeeeeeeeeeeeeeeeeeeennes 16 3 AR Model and Damped Sinusoids
42. Corporation Chapter 5 Joint Time Frequency Analysis Applications current datal seismic tat seismic tat seismic Ixt data lenath sec 3 DE 1 instant spectrum x ies s 2 5E 1 2 0E 1 1 5E 1 1 0E 1 5 0E 0 0 0E 0 mui z 1 0E 0 1 T 1_ sec 0 0E 0 1 0E 0 aie de ASIN 0 0E 0 5 DE 2 1 0E ile BE 1 z E 2 BE 1 3 DE control eS Figure 5 7 Instantaneous Spectrum Display Frequency Zooming The control fs determines the frequency range to display The highest frequency is equal to fs 2 By using the freq zoom control you can examine the signal in the frequency domain The frequency range displayed is equal to fs 2 x zoom factor The maximum zoom factor is limited to 16 so the smallest frequency range is fs 32 The f0 parameter determines the start frequency to display and must be greater than or equal to zero Moreover f0 fs 2 x zoom factor lt fs 2 If fO is out of the valid range the selection is ignored Applying the Pre Emphasis Filter fs Hel Click the pre emph button to apply the pre emphasis filter to the import 0DE 3 signal The pre emphasis filter suppresses DC and enhances high frequency components As the factor control increases the DC cet remaining decreases The factor control ranges from 0 to 1 030 pre emph National Instruments Corporation 5 11 Signal Processing Toolset Chapter 5 Joint Time Frequency Analysis Applications pu
43. Digital Filter Banks Two Channel Perfect Reconstruction Filter Banks eeeeeeeesssseeee 10 1 Bbiotthosonal Piller Banks ueri RR EE Ebr Eo etie eue Sn odd E ITUR 10 4 Ornhosonal Filter Bank S edere rea eodeni citari an evisos biuda todo dbi dua cud 10 9 2D SVS TAL PTOGESSIDe eod citatio dene E bea tos eetusesu ute tenute ca eue nf 10 11 Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Waveletand Milter Bank DSIeris ocio diae eicicoe obire animi Ee tai sedi is Quat nocte ac sucede E 11 1 Desis Pane err 11 6 Designing Wavelets and Filter Banks sseeeeeeeenneneeennnn nnns 11 7 IBBXDE INE eere TET 11 10 Wl eS eS astutus Mss E uu atc EA aee ben D ae npR c ioca a 11 13 Wavelets and Willers oido tid avs sda ad A uM an ment caus 11 15 Create Your Own Applications ides i T VAR etie pre RT aides 11 16 Wavelet Packet 2XHabysis2 o oem beg t rta in tedc atas dad NU M Med 11 17 Online Vestine Pane kessa Doa pn dot e iacit pne emectostest o equi eseede abo sioe 11 18 Chapter 12 WFBD Toolkit Function Reference LabVIEW VIZXNpDICALUOBS 95 9 2 RO ED tte ion cA ue 12 1 LabWindows CVI Applications cesses nnne nnn nnn nnn nnn nnn nns 12 17 Calling WFBD Functions in LabWindows CVI eeeeeeeeeeeeeenenn 12 17 WFBD Instrument DEVE sen sarcarpasacecs LER taU Io eSud a tduun Mota A 12 17 Alloc COTE WE BD s i aot n HR IM ee Eom caren ive Du REI Un 12 19 Atialysis2D
44. Display 1 Iv Fel Display 2 M Ll zemane Ine Smith Corners can read this fle with my spreadsheet application I Heb OK Cane Figure 31 10 Generate Report Dialog Box Use the Save checkboxes to save the waveforms in the front panel displays you select Name sets names for the waveforms you are saving Use the Save Computations checkboxes to save the computations for the waveforms you are saving Username saves a user name with the waveforms for future reference Comments saves user provided information with the waveforms for future reference 4 Select the channels and reference waveforms that have computations you want to save Click OK 5 Inthe File dialog box enter the name of the report file and select the location to store the file Click OK Waveform data that you save with the Generate Report option cannot be loaded as a reference waveform To load a waveform as a reference waveform you must use the Save Reference Waveform options to load the waveform National Instruments Corporation 31 13 Signal Processing Toolset Customer Communication For your convenience this appendix contains forms to help you gather the information necessary to help us solve your technical problems and a form you can use to comment on the product documentation When you contact us we need the information on the Technical Support Form and the configuration form if your manual contains one about your syste
45. Instruments Corporation Chapter 12 WFBD Toolkit Function Reference Windows Applications The WFBD toolkit provides a 32 bit dynamic link library DLL wfbd32 d11 for all Windows platforms users The DLL is located in the Libraries subdirectory of your installation directory Four import libraries for different compilers also are provided e Microsoft Visual C C Borland C C e Watcom C C e Symantec C C You can find these four import libraries under the Libraries subdirectory of your installation directory The functions in the DLL are the same as for LabWindows CVI Refer to the previous WF BD Instrument Driver section for the function descriptions Call these functions the same way in your code as you call any functions in DLLs National Instruments Corporation 12 47 Signal Processing Toolset Wavelet References This chapter lists reference material that contains more information on the theory and algorithms implemented in the WFBD toolkit Crochiere R E and L R Rabiner Multirate Digital Signal Processing Englewood Cliffs N J Prentice Hall 1983 Donoho D L De noise by soft thresholding IEEE Transactions Information Theory vol 3 41 1995 613 627 Qian S and D Chen Joint Time Frequency Analysis Upper Saddle River N J Prentice Hall 1996 Strang G and T Nguyen Wavelets and Filter Banks Wellesley MA Wellesley Cambridge Press 1995 Vaidyanathan P P Multirate
46. Third Octave Analysis toolkit algorithm description 26 1 to 26 2 calculation of center frequencies 24 4 error codes 30 1 filter band center frequencies for ANSI S1 11 table 24 2 to 24 4 internal data averaging 26 5 to 26 6 multistage decimation techniques 26 2 to 26 4 formula for frequency resolution 26 2 sampling frequencies table 26 3 using FFT figure 26 4 octave analyzer description 24 1 overview 1 3 24 2 reference materials 29 1 sampling rates ANSI bands and center frequencies table 26 2 specifications 26 6 to 26 7 Signal Processing Toolset Index Third Octave Analyzer front panel Acquire button 25 6 to 25 7 Amplitude Table button 25 7 Clear Reference button 25 7 illustration 25 6 one channel panel with reference signal figure 25 8 Quit button 25 7 Recall button 25 7 Reference button 25 7 Save button 25 7 Setup button 25 6 running 25 5 to 25 8 Setup dialog box 25 1 to 25 5 Average Type control 25 3 Channel control 25 3 data blocks to average control 25 2 device control 25 2 FFT size control 25 4 illustration 25 2 Internal Data Averaging control 25 4 Internal Data Averaging dialog box 25 5 sampling rate control 25 2 View Weighting button 25 4 Weighting control 25 3 to 25 4 Window Type control 25 3 Third Octave Filters VI 27 1 to 27 2 time dependent spectrum analysis examples 5 6 to 5 15 Offline Joint Time Frequency Analyzer 5 8 to 5 15 Online STFT Spectrogra
47. This toolkit can be used to perform high resolution spectral analysis and parameter estimation These parameters include the amplitude phase damping factor and frequency of damped sinusoids You can use the toolkit for other applications such as linear prediction signal synthesis data compression and system identification You can use these tools in diverse applications such as biomedicine economics geophysics noise and vibration and speech analysis Digital Filter Design Toolkit Signal Processing Toolset The Digital Filter Design toolkit provides a general purpose design tool for signal conditioning control systems digital signal processing and virtual instrument applications Using the Digital Filter Design toolkit you can design bandpass bandstop lowpass and highpass filters and filters with 1 2 National Instruments Corporation Chapter 1 Signal Processing Toolset Overview an arbitrary magnitude response Use the powerful graphical user interface to design finite impulse response and infinite impulse response filters You design filters by interactively editing the magnitude response graph or the pole zero plot in the z plane You test your design online with a built in function generator and you analyze the filter using the step and impulse responses magnitude and phase responses and pole zero plot When you complete your design you can save the filter coefficients to a file for use in other applications Thi
48. VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions Inverse Adaptive Transform Reconstructs the time waveform based on the adaptive representation COB DBL Signal Processing Toolset Analytical Signal AR parameters signal length s Analytical Signal determines if the reconstructed signal is an analytical signal A k is a 1D array that indicates the weight of each elementary function Azli parameters is a 2D array that indicates the four tuple parameters of the elementary function h i from Equation 4 1 Column Parameter k Elementary Function 2T normalized center range 0 27 gm 4 2 National Instruments Corporation Chapter 4 Joint Time Frequency Analysis VIS signal length controls the length of the reconstructed signal yli is the reconstructed time waveform error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions ma Lr z e Short Time Fourier Transform Computes the Gabor coefficients of the 1D Gabor expansion or the Gabor transform C mln emor H of frequency bins cne xli is the time waveform either a real valued or general complex signal DEL r i is the analysis window function dM is the Gabor time sampling interval The length of the analysis function r i must be evenly divisible by dM of frequency bins determines the nu
49. Ville Distribution for the Three Tone Test Signal Notice that Equation 3 4 is equivalent to PWVDLi k Y Y hln RU n m e 7n 3 5 m L 2 n where A n is the inverse Fourier transform of H m in Equation 3 4 Because the crossterm highly oscillates in the joint time frequency domain another intuitive way of reducing the crossterm interference is to perform 2D filtering to the Wigner Ville distribution The result can be described as L 2 f clid Y Yon m Rli n ne 3 6 m L 2 where i m denotes the kernel function Notice that the window functions w m in Equation 3 3 and h m in Equation 3 5 are special cases of i m in Equation 3 6 In 1966 Leon Cohen developed the representation C i k in Equation 3 6 so itis traditionally known as Cohen s class Compared with the PWVD in Equation 3 3 or 3 5 the Cohen s class method is more general and flexible 3 8 National Instruments Corporation Chapter 3 Joint Time Frequency Analysis Algorithms Most quadratic equations known so far such as the STFT spectrogram WVD PWVD Choi Williams distribution and the cone shaped distribution belong to Cohen s class Choi Williams Distribution When the kernel function in Equation 3 6 is defined by Q ai Am 2 i m 3 7 4mm the yield is the Choi Williams distribution CWD By adjusting the parameter ot in Equation 3 7 you balance crossterm interference and time frequency resolution
50. X You can choose from the following four options rectangular Hamming Hanning or Blackman The window type parameter defaults to Hanning Average Number indicates the number of blocks of data to average in the higher frequency bands This is a two element array The first number should be in the range of 1 150 and the second number should be in the range of 1 15 The lower bound corresponds to no averaging The upper bound corresponds to complete averaging Any number in between corresponds to partial averaging The more the averaging the slower the execution time Refer to the nternal Data Averaging section in Chapter 26 Third Octave Analysis Design for more information i Note This control also is referred to as Internal Average Times in Figure 25 2 Internal Data Averaging Dialog Box Signal Processing Toolset Band Power contains the power outputs of the 31 third octave filters Center Frequency contains the center frequencies of the 31 third octave filters Refer to the ntroduction to the Third Octave Analysis Toolkit section in Chapter 24 Overview of the Third Octave Analysis Toolkit for information on how to compute the center frequencies error Refer to Chapter 30 Third Octave Error Codes for a list of error codes 2 2 National Instruments Corporation Building Windows Applications for Third Octave Analysis This chapter describes how to build a third octave analysis application under Windows 95 NT
51. You access this panel by selecting Wavelet and Filters from the Menu control of the Design Panel Filter banks do not always converge to a wavelet function The Wavelets and Filters panel helps you examine whether the filter bank you selected converges National Instruments Corporation 11 15 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Ig I gt Wavelets and Filters File Edit Operate Project Windows Help Refinement 5 Save Scaling and Wavelets Close Analysis Scaling 1s Analysis Mother Wavelet Figure 11 12 Wavelets and Filters Panel Refinement defines how many levels to go through to compute the wavelet and scaling function A proper wavelet usually converges after four or five levels Save Scaling and Wavelets saves the scaling functions and wavelets for the analysis and synthesis filters in a text file Create Your Own Applications Signal Processing Toolset You can save all design results as text files for use in other applications The WFBD toolkit includes three LabVIEW VI libraries WaveMain 11b Wavesubs 11b and Wavemisc 11b for LabVIEW users These three libraries contain the basic wavelet analysis VIs such as 1D and 2D analysis and synthesis filters and many other useful functions For more information about these VIs refer to Chapter 12 WFBD Toolkit Function Reference You can test the design not only with the two built in testing panels described in the
52. a powerful JTFA application In general random noise evenly distributes over the entire joint time frequency domain because it is not limited to a short time period or narrow frequency band A signal s joint time frequency representation always concentrates in a relatively small region As a result the regional Signal to Noise Ratio SNR in the joint time frequency domain can be much higher than that in either the time or the frequency domain In other words the noise corrupted signal is easier to recognize in the joint time frequency domain After identifying the National Instruments Corporation 5 1 Signal Processing Toolset Chapter 5 Joint Time Frequency Analysis Applications signal component you can apply a mask to filter the signal components and take the inverse transform to obtain the noise free time waveform Figure 5 1 illustrates the Gabor expansion based denoise example By adjusting the noise control knob you vary the noise level In Figure 5 1 the original SNR is 0 37 db From examining the time waveform power spectrum and Gabor coefficients you might notice that the signal is much easier to recognize from the Gabor coefficients than from either the time waveform or from the spectrum The following procedure describes the Gabor expansion based denoise process 1 Take the STFT with respect to the noise signal x n 2 Mask the signal STFT or Gabor coefficients from the joint time frequency domain 3 To get
53. anaptr synptr Read filter bank coefficients if err goto errend rows 128 cols 256 x double malloc rows cols sizeof double if x goto errend compute the size of output arrays err Analysis2DArraySize rows cols anaptr nl anaptr nh nsize if err goto errend Allocate memory for the output arrays ll double malloc nsize 0 nsize 1 sizeof double if ll goto erreng lh double malloc nsize 2 nsize 3 sizeof double mere 3 Cree li goto errend hl double malloc nsize 4 nsize 5 sizeof double Sq H freetllijs treetlh s goto erreng National Instruments Corporation 12 27 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference hh double malloc nsize 6 nsize 7 sizeof double qopup EF E freet lis Lree tln s tree hl goto errend err Ane lysisrilierBank2zD x rows cols aenaour 0 Ll ing hl bh ns 1 4e treetliyrs free 1h free hl free hh errend free x FreeCoeffWFBD anaptr FreeCoeffWFBD synptr Signal Processing Toolset 12 28 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference DecimationFilter long status DecimationFilter double x long nx double coef long ncoef double init long ni double final long nf long decfact double y long ny Performs a decimation filtering It performs the same operation as the Decimation Filter VI
54. and data types of control attributes Hertz Cycles per second Signal Processing Toolset Glossary I O icon IEEE IIR filters image compression indicator inner product JTFA L LabVIEW local variable matrix maximum flat filter MB mother wavelet Signal Processing Toolset Input output Transfer of data to or from a computer system involving communications channels operator input devices and or data acquisition and control interfaces Graphical representation of a node on a block diagram Institute for Electrical and Electronic Engineers Infinite impulse response filters Using only part of the data to recover the original image Front panel object that displays output A mathematical operation used to test the difference between two functions Joint time frequency analysis Laboratory Virtual Instrument Engineering Workbench Program development application based on the programming language G used commonly for test and measurement purposes Variable that enables you to read or write to one of the controls or indicators on the front panel of your VI Two dimensional array A type I filter that has a maximum number of zeros at T Megabytes of memory An elementary wavelet G 6 National Instruments Corporation multicomponent signal multiscale analysis node nonstationary signal numeric controls and indicators Nyquist rate 0 object octave orthogonal filter bank
55. array is set to j then AN M j is the distance between the two adjacent N point blocks Total number of j N point blocks are averaged at that stage When AN N the averaging is overlapping data averaging as illustrated in Stage 1 of Figure 26 2 When AN 2 N the averaging is non overlapping data averaging as illustrated in Stage 2 of Figure 26 2 National Instruments Corporation 26 5 Signal Processing Toolset Chapter 26 Third Octave Analysis Design For example if M 54280 and N 512 the first element in Internal Data Averaging is set to 150 and AN 54280 150 362 Therefore 512 362 150 so about 30 percent of the data is overlapping For the second stage if the second element in Internal Data Averaging is set to 15 then AN 5400 15 360 Now there is also 512 360 152 Again about 30 percent of the data is overlapping In most applications 30 percent of overlapping data is sufficient for spectral analysis Therefore 150 and 15 are used as the default settings for the Internal Data Averaging array as the complete averaging case in the analyzer They are also the upper bound values for the array elements In the case of no averaging in the analyzer the values of both elements in the array are set to 1 The more data blocks that are averaged the longer it takes to compute the data If the signal is almost stationary no averaging is needed If the signal is not almost stationary some averaging is nee
56. choosing an algorithm 6 2 to 6 3 difference between linear and quadratic methods 6 1 point to point measurements 6 3 to 6 5 saving time dependent spectrum for analysis with other software 6 6 suppressing DC component 6 5 need for 2 4 to 2 5 reference materials 7 1 to 7 2 uses for 2 4 to 2 5 joint time frequency analysis JTFA VIs 4 to 4 16 2D Gabor Expansion 4 6 to 4 7 Signal Processing Toolset Index 2D STFT 4 4 to 4 5 Adaptive Spectrogram 4 9 Adaptive Transform 4 1 to 4 2 Cohen s Class 4 10 Cone Shaped Distribution 4 11 to 4 12 CWD Choi Williams distribution 4 10 to 4 11 Fast Dual 4 7 to 4 8 Gabor Expansion 4 4 Gabor Spectrogram 4 14 Inverse Adaptive Transform 4 2 to 4 3 Normalized Gaussian Window Function 4 8 PWVD Pseudo Wigner Ville distribution 4 13 Short Time Transform 4 3 STFT Spectrogram 4 12 Time Frequency Distribution Series 4 15 to 4 16 L LabVIEW DFD utilities 22 1 to 22 3 DFD Filter 22 3 Read DFD Coefficients 22 2 LabVIEW VI applications 12 1 to 12 16 2D Analysis Filter Bank VI 12 5 to 12 6 2D Synthesis Filter Bank for I16 VI 12 9 2D Synthesis Filter Bank VI 12 8 Analysis Filter Bank VI 12 1 to 12 4 Decimation Filter VI 12 10 to 12 13 Interpolation Filter VI 12 14 to 12 15 Mother Wavelet and Scaling Function VI 12 16 Synthesis Filter Bank VI 12 4 to 12 5 Truncated Decimation Filter VI 12 13 to 12 14 LabWindows CVI applications 12 17 to 12 46
57. dM1 is the Gabor time sampling interval The length of the analysis function r1 i must be evenly divisible by dM1 N1 determines the number of elements for the second index n of the Gabor coefficients It must be a power of two eus analysis 2 is the cluster for the analysis window function of the column analysis 2 NIM oas J dM2 4 N2 5p r2 k is the analysis window function for the column of x il k FA dM2 is the Gabor time sampling interval The length of the analysis function r2 i must be evenly divisible by dM2 FA N2 determines the number of elements for the fourth index n2 of the Gabor coefficients It must be a power of two tpe C m1 n1 m2 n2 is the Gabor coefficient error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions National Instruments Corporation 4 5 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS 2D Gabor Expansion Computes the Gabor expansion for a 2D signal Cim fnt fEmz En 2 wil k synthesis 1 synthesis z C m1 n1 m2 n2 is the Gabor coefficient eus synthesis 1 is the cluster for the synthesis window function of the row gyunthesis 1 H1 i 27 E502 dM1 se O Onus 556 hl i is the synthesis function for the row of x i k EA dM1 is the Gabor time sampling interval The length of the analysis function h1 i must be evenly
58. defines the types of filter banks used with wavelet analysis Two Channel Perfect Reconstruction Filter Banks Two channel perfect reconstruction PR filter banks were recognized as useful in signal processing for a long time particularly after their close relationship with wavelet transform was discovered Since then it has become a common technique for computing wavelet transform Figure 10 1 illustrates a typical two channel filter bank system The signal X z 1s first filtered by a filter bank constituted by Go z and G z ure Processing ure Figure 10 1 Two Channel Filter Bank i Note For a finite impulse response FIR digital filter g n the z transform is defined as N m Gz Y gine Ge G F gln e we n 0 where N denotes the filter order Consequently the filter length is equal to N 1 Clearly w 0 is equivalent to z 1 w p is equivalent to z 2 1 That is G 0 and G p in the frequency domain correspond to G 1 and G 1 in the z domain The outputs of Go z and G z are downsampled by 2 to obtain Y z and Y z After some processing the modified signals are upsampled and filtered by another filter bank constituted by Ho z and H4 z If no National Instruments Corporation 10 1 Signal Processing Toolset Chapter 10 Digital Filter Banks processing takes place between the two filter banks Yo z and Y z are not altered the sum of outputs of Ho z and H z
59. double malloc npad sizeof double if linit goto erreng final double malloc npad sizeof double if final 4 free init goto errend Initialize the initial and final condition arrays to zeros You can initialize these two arrays to different values based on your requirements Signal Processing Toolset 12 30 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference xtmp init LOL renpadsr es xcmpged 110 05 xtmp final Lbor renpsdjd e tmpsr 0 0 Compute the size of output arrays and allocate memory for them nyo Gea 005 54nxtnh 1 35 yO double malloc nyO sizeof double if y0 free init free final goto errend ty cea 02 5 nxor yl double malloc nyl sizeof double De Cyd 3 free y0 free init free final goto errend Compute the output from the analysis lowpass filter if n1 gt 0 err DecimationFilter x nx anaptr gt Lowpass nl init npad final npad 2 y0 ny0 Compute the output from the analysis highpass filter if lerr if nh gt 0 err DecimationFilter x nx anaptr gt Highpass nh init npad final npad 2 y1l nyl1 errend free xX FreeCoeffWFBD anaptr FreeCoetftWFBD synptr National Instruments Corporation 12 31 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Parameter Discussion To obtain the perfect reconstruction you must me
60. double coef long nf long interfact double y long ny long status AnalysisFilterBank2D void x long rows long cols FilterBankPtr AnalysisFilters long padtype void low low vord low high vord high low volid high high Long outsize long status Analysis2DArraySize long xrows long xcols long nl long nh long nsize 8 long status SynthesisFilterBank2D void low low void low high void high low xorid high high long insize FilterBankPtr SynthesisFilters void x long xrows long xcols long status Synthesis2DArraySize long nsize 8 long nl long nh long rows long Co ls 4 FilterBankPtr fptr AllocCoeffWFBD void long status ReadCoeffWFBD char coeffPath FilterBankPtr AnalysisFilter FilterBankPtr SynthesisFilter long err FreeCoeffWFBD FilterBankPtr fptr Signal Processing Toolset 12 18 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference AllocCoeffWFBD FilterBankPtr fptr AllocCoeffWFBD void Use this function to allocate the WFBD filter bank coefficients structure You must call this function once to properly allocate the WFBD filter coefficients structure Return Value fpe FilterBankPtr Pointer to allocated filter bank structure National Instruments Corporation 12 19 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Analysis2DArraySize long status Analysis2DArraySize long xrows long xcols long
61. e adaptive spectrogram If you consider the linear JTFA as the evolution of the conventional Fourier transform the quadratic JTFA is the counterpart of the standard power spectrum The difference between linear and quadratic methods is that you can invert the linear transform As with the fast Fourier transform you can reconstruct the original signal based on the Gabor coefficients The linear transform is suitable for signal processing such as time varying filtering In general the quadratic form is not reversible You cannot restore the original time waveform from the time dependent spectrum However the quadratic JTFA describes the energy distribution of the signal in the joint time frequency domain which is useful for signal analysis National Instruments Corporation 6 1 Signal Processing Toolset Chapter 6 Frequently Asked Questions Signal Processing Toolset Which Quadratic JTFA Algorithms Should I Use Each quadratic JTFA algorithm has advantages and disadvantages You should select a particular algorithm based on the application Generally speaking no algorithm is superior to all others in all applications Table 6 1 summarizes the advantages and disadvantages of all quadratic algorithms provided in this package Table 6 1 Quadratic JTFA Algorithms Resolution and Method Crossterm Description Speed adaptive spectrogram extremely high resolution slow when a signal is made up of linear chirps no crossterms non negat
62. features of the original signal Figures 9 9 and 9 8 illustrate the same S amp P 500 stock index information but Figure 9 9 shows it as a joint time frequency analysis The top plot illustrates the S amp P 500 stock index and its corresponding long term trend smooth curve The center plot displays the residue between the original data and the trend reflecting the short term fluctuation The bottom plot displays the joint time and frequency behavior of the residue It shows that over the past 50 years a four year cycle dominates the S amp P 500 index which agrees with most economists assertions SPS500 dat Long Term Trend Detrended n a me eh 1 j sae cq y v N wi ll Residue time 1947 1993 Frequency Four year Cycle Figure 9 9 Detrend 9 12 National Instruments Corporation Chapter 9 Wavelet Analysis Denoise Unlike conventional Fourier transform which uses only one basis function wavelet transform provides an infinite number of mother wavelets to select Consequently you can select the wavelets that best match the signal Once the wavelets match the signal you can use a few wavelet basis to approximate the signal and achieve denoise Figure 9 10 illustrates one of the most successful applications of wavelet analysis denoise This application works by first taking the wavelet transform of the signal setting the coefficients below a certain threshold to zero and finally inverting the tra
63. filter Increasing this gain increases the overall gain of the designed filter Setting the normalize button to Normalize On adjusts the filter gain so that the maximum response is 1 0 0 dB If you set this button to Normalize On you cannot adjust the gain control manually Setting the normalize button to Normalize Off allows you to manually adjust the gain control but does not guarantee a maximum response of 1 0 20 24 National Instruments Corporation Chapter 20 Digital Filter Design Application Arbitrary FIR Design Figure 20 19 shows the Arbitrary FIR Design panel The panel includes a graphical interface with the Magnitude vs Frequency cursors and plot on the left side and a text based interface with digital controls on the right side gt Arbitrary FIR Design File Edit Operate Froject Windows Help DFO Menu v venas Arbitrary Magnitude Response actual frequency magnitude m 4 0000 0 0000 O lees 1 00 571 428 1 0000 0 80 142 85 2 0000 O 0 60 0 40 i 1653 13 2D 2656 O 0 20 0 00 Ha ok 2051 66 05016 ooo 1000000 2000000 3000 000 4000 000 tiple select OFF VEASE PEN points MH Ig z Vieh no ewm A Doo S enim d message fiterorder 165 ripple 1 3709E 2 T 2857 14 20 0255 Mo Error lockedfrequencies LI sort by frequency uniform spacing impor trom file aj sampling rate 8000 00 Figure 20 19 Arbitrary FIR Design Pan
64. frequency contents In other words as the scale factor m increases the center frequency and bandwidth of the wavelet increases 2 Figure 9 3 depicts the wavelet transform procedure First let m 2 n 0 by aligning y t and s t at t 0 As in Equation 9 3 compare y t with s t for 0 f 1 You obtain Wo 1 Shift w t to the next second let n 1 and compare it with s t for 1 t lt 2 You obtain W 0 Compress y t into 0 second to 0 5 seconds let m 1 and repeat the previous operations with the time shift step 0 5 You obtain the following results also displayed in the shaded table of Figure 9 3 Wig 20 W 9 Wi5 21 Wi4 20 National Instruments Corporation 9 5 Signal Processing Toolset Chapter 9 Wavelet Analysis 0 1 2 sec H H 1 0 I CN W t n 2 gt 1 1 0 0 Y T W s t m n st y By 2 r 2 Two Basis Functions Figure 9 3 Wavelet Analysis You can continue to compress W t by increasing the scale factor m and reducing the time shift step 2 to test s t This procedure is called wavelet transform W t is called the mother wavelet because the different wavelets used to measure s t are the dilated and shifted versions of this wavelet The results of each comparison W n are named wavelet coefficients The index m and n are the scale and time indicators respectively which describe the signal behavior in the joint time scale domain As shown in Figure
65. in Figure 20 20 plots the desired and actual magnitude response of the designed FIR filter Arbitrary Magnitude Response actual desired 1 20 1 00 0 80 0 60 0 40 0 20 0 00 I I I I Hz 0 000 1000 000 2000 000 gm O00 4000 000 ill ets e points multiple select FEET fi c mne 3 Figure 20 20 Desired and Actual Magnitude Response The magnitude y axis is in linear or decibel units depending on how you set the button in the upper left corner of the graph The frequency x axis is in hertz The full scale ranges from 0 0 to Nyquist half the sampling rate Use the linear dB button to control the display units linear or dB of all magnitude and gain controls and displays These controls and displays include Magnitude vs Frequency plot y axis passband response stopband attenuation and tracking cursor magnitude 20 26 National Instruments Corporation Chapter 20 Digital Filter Design Application The points control specifies the number of frequency magnitude points the DFD application uses to create the desired filter magnitude response Reducing this number deletes points from the end of the frequency magnitude array Increasing this number inserts the additional number of points to the right of the selected point dt pnints Lu Lie 5 co roan ae Set the multiple select button to ON to select more than one frequency magnitude point on the response graph Clicking a selected point rem
66. input The size of nx must be 28680 if FF TSize 256 and must be 54280 if FFTSize 512 Signal Processing Toolset 28 2 National Instruments Corporation Chapter 28 Building Windows Applications for Third Octave Analysis fs is the sampling rate of input This parameter determines the frequency range that is being analyzed Assuming i fs 12800 fl is the lower bound of the frequency range and fh is the high bound of the frequency range then f ix 5 Hz fh ix 5000 Hz For example if fs 25600 Hz then i 2 the frequency range is 10 Hz to 10000 Hz The recommended fs should be chosen from 12800 Hz 25600 Hz or 51200 Hz The corresponding frequencies ranges are 5 Hz 5000 Hz 10 Hz 10000 Hz and 20 Hz 20000 Hz winType is the type of window that applies to the input array You can choose from the following four options rectangular Hamming Hanning or Blackman FFTSize is the FFT size that is used to compute the third octave outputs It can be only 256 or 512 Using 512 point FFT gives more accurate results but takes more memory and runs slower than using 256 point FFT avgNum indicates the number of blocks of data to average in the higher frequency bands This is a two element array The first number should be in the range of 1 150 and the second number should be in the range of 1 15 The lower bound corresponds to no averaging The upper bound corresponds to complete averaging Any number in between corresponds to partial
67. interference order must be greater than or equal to zero The greater the order the better the resolution but the more severe the interference The opposite is also true When order is set to zero the Gabor spectrogram is non negative As order increases the Gabor spectrogram converges to the Wigner Ville distribution Computation time is related to the order The higher the order the longer the computation time For most applications choose an order between three and five of rows determines the maximum number of rows of the spectrogram pLil k tolerance controls the precision of the resulting Gabor spectrogram The smaller the tolerance the more computation time required The default value is 102 plillk is the Gabor spectrogram error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions 4 14 National Instruments Corporation Chapter 4 Joint Time Frequency Analysis VIS Time Frequency Distribution Series Computes the Gabor expansion based spectrogram which is the engine of the GaborSpectrogram VI COB COB pii emor H of frequency bins tolerance H of rows order balances the resolution and crossterm interference order must be greater than or equal to zero The greater the order the better the resolution but the more severe the interference The opposite is also true When order is set to zero the Gabor spectrogram is non negativ
68. method and matrix pencil to estimate the parameters associated with damped sinusoids As shown in Figure 18 5 the complex sinusoids indicator shows the estimated number of complex sinusoids the test samples contain The sum of two complex sinusoids produces one real valued sinusoid The 2D array indicates corresponding parameters for each positive frequency sinusoid such as amplitude phase damping factor and frequency Although Prony s method has been known for many years the matrix pencil method is more accurate and computationally economical Estimated Parameters amplitude phase damping frequency 0 50 o oo o oo 0 11 4 complex sinusoids si Matris Pencil Prony s Method Figure 18 5 Estimation of Damped Sinusoids 18 4 National Instruments Corporation Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation synthetic Data Figure 18 6 illustrates the Synthetic Data panel that generates samples that contain two damped sinusoids corrupted with Gaussian white noise i gt Synthetic Data number of samples 25 signal 1 damping damping 0 00 0 00 frequency frequency 20 11 210 13 Gaussian white noise i l D DE D 2 BE 3 5 DE 3 Figure 18 6 Synthetic Data Panel The damped sinusoid has the following form a s n Ae cos 2xfn 0 where A is the real valued amplitude a is the real valued damping factor fis the frequency 0 is th
69. more information about how to add data in these two cases DBL x i contains the input signal DBL h k contains the filter coefficients decimate factor indicates the data reduction rate in the y i array Only every Mth point of the output from filter G is kept in the y i array y i contains the output array error Refer to Chapter 14 Wavelet Error Codes for a description of the error m z Em tar LL L1 Interpolation Filter VI This VI performs an interpolation filter Input Filter Coethicients Interpolation factor Input contains the input signal rma DEL Filter Coefficients contains the filter coefficients DEL interpolation factor indicates the number of zeros to add among the Input data points L 1 zeros are inserted among each data point of the Input array before the filtering operation Output contains the output array EA error Refer to Chapter 14 Wavelet Error Codes for a description of the error Signal Processing Toolset 12 14 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference This VI performs the following operation pora Xl That is n 1 y eam i 0 1 Ln n 1 k 0 where H is the array of Filter Coefficients Nn is the size of H Y is the Output array L is the interpolation factor XI is the interpolated Input that is you insert L 1 zeros among each point of Input data Figure 12 5 shows the case
70. of finding the damped sinusoids parameters is to first compute the AR coefficients aj Then solve the polynomial in Equation 16 14 to determine z Finally the solution of the linear system in Equation 16 13 gives the complex amplitudes C Algorithms for Super Resolution Spectral Analysis and Parameter Estimation This section briefly introduces the algorithms included in the Super Resolution Spectral Analysis toolkit The covariance and PCAR methods are used to compute super resolution power spectra The matrix pencil and Prony s methods are applied mainly for parameter estimation The minimum description length algorithm is used to estimate the number of complex sinusoids Covariance Method Assume that the future data is estimated by the forward prediction Equations 16 4 and 16 5 The covariance method computes the coefficients a such that the error between x n and x n is minimized N 1 min 2 IxEn xEn I n p l Prony developed this method 13 years before the Fourier transform was introduced National Instruments Corporation 16 5 Signal Processing Toolset Chapter 16 Model Based Frequency Analysis Algorithms In Equation 16 5 the optimal coefficients a are simply the solution of the linear system of x p 1 x p 2 x 0 E x p x p x p 1 x 1 _ _ x p 1 x N 2 x IN 1 x N p 1 2 x N 1 The covariance method is simple but it is sensitive to noise Principle Component Auto Regressive Me
71. other types of instruments Indicator that plots data points at a certain rate A transform using wavelet as the elementary functions A method of detrend which is achieved by wavelet transform Signal Processing Toolset Glossary window Technique used to reduce spectral leakage by multiplying the time domain waveform by a window function The process of windowing reduces the amplitudes of discontinuities at the edges of a waveform thereby reducing spectral leakage If the waveform contains an integral number of cycles there is no spectral leakage Refer to spectral leakage WVD Wigner Ville Distribution Signal Processing Toolset G 10 National Instruments Corporation Index Numbers 1D data test Wavelet and Filter Bank Design toolkit 11 10 to 11 13 2D Analysis Filter Bank for 116 VI 12 7 to 12 8 2D Analysis Filter Bank VI 12 5 to 12 6 2D Gabor Expansion VI 4 6 to 4 7 2D signal processing 10 11 to 10 13 2D STFT VI 4 4 to 4 5 2D Synthesis Filter Bank for I16 VI 12 9 2D Synthesis Filter Bank VI 12 8 A adaptive representation algorithm 3 2 adaptive spectrogram description 3 13 historical background 2 7 Offline Joint Time Frequency Analyzer application 5 13 to 5 14 Adaptive Spectrogram VI 4 9 adaptive transform algorithm 3 2 Adaptive Transform VI 4 1 to 4 2 AllocCoeffDFD function 22 5 AllocCoeffW FBD function 12 19 Analysis Filter Bank VI 12 1 to 12 4 Analysis of Filter Design pa
72. performs the following operation Yl A2 H1 X ME The output x i can be described by ide node x Y y0 A0 ji L E 5 l i where n 0 1 L 1 L is the size of output x i L 2 9 npo 1 or L Any Np 1 i Note The lengths of yO i and y1 i must satisfy 2ny0 nh0 2nyl nh0 If your inputs yO i and yl i are the outputs from the same analysis filter bank this condition is satisfied automatically HO is the synthesis lowpass filter coefficients where n o is the size of HO Hl is the synthesis highpass filter coefficients where n o is the size of H1 Refer to the Interpolation Filter VI in this chapter for more information about this operation 2D Analysis Filter Bank VI This VI computes the outputs of a 2D image passing through an analysis filter bank perfect reconstruction m in Low Low Analysis Filter Bank Low High extension High Law High_High eror National Instruments Corporation 12 5 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference When a 2D image passes an analysis filter bank it is broken into four sub images Refer to Chapter 10 Digital Filter Banks for more information about computing the four sub images perfect reconstruction determines if the results can be reconstructed x m n contains 2D input image data Analysis Filter Bank contains the analysis filter bank coefficients
73. points in memory Setting the Analysis Window You can choose one of four types of windows rectangular Blackman Hamming or Hanning The maximum window length is 512 Acquiring Data To start collecting data with NI DAQ set the left switch to Acquire scan backlog refer to Figure 5 5 indicates whether the system can keep up with the incoming samples You must move the right switch to Capture Data to preserve the acquired data Saving Data To save data you must move the right switch to Capture Data as explained in the previous section The indicator of points in memory displays the number of data points in memory When you toggle Capture Data to Stop of points in memory is replaced by the indicator total of points saved which displays the total number data points saved in memory The captured data remains in temporary memory until you stop acquiring data When you finish collecting data a dialog box prompts you to save the data to a text file If you select Discard the memory is cleared and the data is lost If you select Yes the data in memory is saved to a text file you designate Offline Joint Time Frequency Analyzer Signal Processing Toolset If the signal s frequency contents change rapidly the STFT spectrogram is not adequate and you need an Offline Analyzer such as the one shown in Figure 5 6 The bottom plot illustrates the time waveform of the analyzed signal The plot on the right displays the cl
74. previous sections but also from your own applications 11 16 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit This section introduces a few applications that you can develop with the help of this toolkit You can create all the examples described in this section with or without LabVIEW because you always can incorporate the filter bank coefficients into your applications from previously saved text files Wavelet Packet Analysis The preceding sections introduce wavelet analysis in which the signal is continuously decomposed in the lowpass path similar to the path shown in Figure 10 2 Relationship of Two Channel PR Filter Banks and Wavelet Transform in Chapter 10 Digital Filter Banks You also can apply other decomposition schemes to the signal and still maintain the perfect reconstruction Figure 11 13 illustrates the full path for a three level decomposition 111 11 I 110 101 10 100 011 01 010 0 001 00 000 Figure 11 13 Full Path of a Three Level Perfect Reconstruction Tree National Instruments Corporation 11 17 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit For example you can decompose the signal X as 0 100 101 and 11 then use those coefficients to reconstruct the original signal by the synthesis filter banks as shown in Figure 11 14 r M il 101 X z 10 ina X z Figure 11 14 Wavelet Packet
75. procedures and describes some applications you can create with the WFBD toolkit Chapter 12 WFBD Toolkit Function Reference describes the VIs in the WFBD toolkit the instrument driver for LabWindows CVI and the functions in the DLLs Chapter 13 Wavelet References lists reference material that contains more information on the theory and algorithms implemented in the WFBD toolkit Chapter 14 Wavelet Error Codes lists the error codes LabVIEW VIs and LabWindows CVI functions return including the error number and a description Part Ill Super Resolution Spectral Analysis Toolkit Signal Processing Toolset Chapter 15 Introduction to Model Based Frequency Analysis introduces the basic concepts of model based frequency analysis Chapter 16 Model Based Frequency Analysis Algorithms outlines the theoretical background of model based frequency analysis and describes the relationship among the model coefficients the power spectra and the parameters of damped sinusoids Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs describes VIs used to perform super resolution and parameter estimation Each algorithm included has two forms one for real and the other for complex valued samples The real VIs work only for real valued data sets and the complex VIs work for both real and complex samples Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation describes a comprehensive testi
76. retain the time and frequency axis information The time and frequency axis can be determined as follows While t0 and f0 are shown on the front panel of Offline Analyzer the time increment Af is computed by time span At P number of rows and the frequency increment Af is determined by Af sampling frequency 2 X zoom factor x 128 Signal Processing Toolset 6 6 National Instruments Corporation JIFA References This chapter lists reference material that contains more information on the theory and algorithms implemented in the JTFA toolkit Choi H and W J Williams Improved time frequency representation of multicomponent signals using exponential kernels EEE Trans Acoustics Speech Signal Processing vol 37 6 1989 862 871 Cohen L Generalized phase space distribution functions J Math Phys vol 7 1966 78 1 806 Cohen L Time frequency distribution A review Proc IEEE vol 77 7 1989 941 981 Cohen L Time frequency analysis Englewood Cliffs N J Prentice Hall 1995 Mallat S and Z Zhang Matching Pursuits with Time Frequency Dictionaries IEEE Trans Signal Process vol 41 12 1993 3397 3415 Qian S and J M Morris Wigner distribution decomposition and crossterm deleted representation Signal Processing vol 25 2 1992 125 144 Qian S and D Chen Discrete Gabor transform JEEE Trans Signal Processing vol 41 7 1993 2420 2439 Qi
77. return synptr AllocCoeffWFBD Le synptr 1 free anaptr return err ReadCoeffWFBD coef dat anaptr synptr Read filter bank coefficients if err goto erreng nx 129 x double malloc nx sizeof double if x goto errend Chiro ao La Du Qu 203 ny e ceil 0 5 nxtanaptr nh 1 Compute the size of output array yO double malloc nyO sizeof double if y0 goto erreng nyl ocerll 0 5 nxtonspur onl 1 535 yl double malloc nyl sizeof double XQ free y0 goto errend err e AnalyvslsPilLerBanki x nx anaptr 0 y0 nyU yl nyl s errend free x FreeCoeffWFBD anaptr FreeCoeffWFBD synptr National Instruments Corporation 12 23 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference AnalysisFilterBank2D long status AnalysisFilterBank2D void x long rows long cols FilterBankPtr AnalysisFilters long padtype VOld low ow vord ow high ovd high Low VOLO Hron high long oursize Computes the output from an analysis filter bank of a 2D signal It performs the same operation as in the 2D Analysis Filter Bank VI Refer to the description for that VI for more information Parameters Input o UNES precision onemout2Ddatagaw input 2D data array 2D array long integer The number of rows of input array x number of rows of The number of rows of input array x array X long integer The number of co
78. select the Ip checkbox the zero has linear phase If the zero is not real or on the unit circle the DFD application matches it with another zero at a radius of 1 r where r is the radius of the original zero The radius is the distance from the origin Linear phase zeros are important in linear phase FIR filters If your z plane plot contains only zeros and all the zeros have linear phase the FIR filter you designed has an overall linear phase response If you select the uc checkbox the zero is forced to be located on the unit circle radius of 1 0 and is limited to movement along the unit circle The order text entry is the order of the zero or the number of actual zeros at this location in the z plane An Mth order zero at z b has a z transform of H z z b Figure 20 16 shows the array of poles in rectangular coordinates The complex value of each pole represents its rectangular position on the z plane The integer 0 in the upper left box is the index of the displayed pole By changing this index value you can display a particular pole of the 20 22 National Instruments Corporation Chapter 20 Digital Filter Design Application array of poles When you select a particular pole in the z plane plot the DFD application sets the index value of the array to the selected pole value f0 1901 0 9161 real order Figure 20 16 Array of Poles in Rectangular Coordinates Only one special characteristic applies
79. stage using the direct form filter equations yli box i 6 x i 1 box i 2 aqy i 1 a5y Ei 2 Signal Processing Toolset 21 2 National Instruments Corporation Chapter 21 IIR and FIR Implementation The illustration in Figure 21 2 shows the graphical representation of these direct form equations Figure 21 2 Direct Form Structure For each stage you must maintain two past inputs x i 1 x i 2 and two past outputs yli 1 y 7 2 A more efficient implementation of each second order stage is known as the direct form II You can implement each second order stage using the direct form II filter equations sli x i a sli 1 a5s i 2 yli bgs i by spi 1 b spi 2 The illustration in Figure 21 3 shows the graphical representation of these direct form II equations National Instruments Corporation 21 3 Signal Processing Toolset Chapter 21 IIR and FIR Implementation Finite Impulse Response Filters FIR filters are digital filters with finite impulse responses FIR filters are also known as nonrecursive filters convolution filters or moving average MA filters because you can express the output of an FIR filter as a finite convolution n 1 y hx 21 4 k 0 where x represents the input sequence to be filtered y represents the output filtered sequence and h represents the FIR filter coefficients FIR filters have the following characteristics
80. such as noise and trend that corrupt the original signals Figure 9 8 illustrates a multiscale analysis of an S amp P 500 stock index during the years 1947 through 1993 The top plot displays a monthly S amp P 500 index while the last plot describes the long term trend of the stock movement The remaining two plots display the short term fluctuation of the stock at different levels during this time To better characterize the fluctuation that reflects the short term behavior of the stock you must remove the trend To do this first adjust the wavelet decomposition level until you obtain a desired trend Then set the corresponding wavelet coefficients to zero and reconstruct the original samples minus the trend S amp P 500 Index 300 Long Term Trend Figure 9 8 Multiscale Analysis National Instruments Corporation 9 11 Signal Processing Toolset Chapter 9 Wavelet Analysis Detrend Signal Processing Toolset One of the most important issues in the application of joint time frequency analysis is how to remove the trend In most applications the trend is often less interesting It attaches to a strong DC component in the frequency spectrum and thereby blocks many other important signal features Traditional detrend techniques usually remove the trend by lowpass filtering which blurs sharp features in the underlying signal Wavelet based detrend is somewhat superior to this process because it better preserves the important
81. the filter specifications The passband and stopband requirements define a filter specification You can define these requirements by using either text entry or the cursors in the Magnitude vs Frequency graph As you use the mouse to click and drag the cursors the text entries update Likewise as you enter new specifications in the text entries the cursors update The lower passband frequency fp upper passband frequency fp gt and the passband response Gp define the passband specification For the bandpass filter the passband ranges from fp to fp The passband is the region in the frequency domain with a response near 1 0 Gp is the minimum allowable passband gain or filter magnitude response In Figure 20 7 the passband is specified as having a minimum gain of 5 dB between the frequencies of fp 1900 Hz and fp 2600 Hz The following ranges define the passband lowpass O lt sfsfp highpass fpi Sf Sfeamp 2 bandpass fp SfEfp bandstop SfSfpi JP2 SS SS samp 2 where Jp is passband frequency 1 fp is passband frequency 2 samp 18 the sampling rate The lower stopband frequencies fs and fs and the stopband attenuation Gs define the stopband specification For the bandpass filter the stopband ranges from 0 0 DC to the lower stopband frequency fs and from the upper stopband frequency fs to half of the sampling rate Nyquist rate The stopband is the region in the frequency domain with a respons
82. the number of rows of array low high outsize 3 the number of columns of array low high outsize 4 the number of rows of array high low outsize 5 the number of columns of array high low outsize 6 the number of rows of array high high outsize 7 the number of columns of array high high The structure that holds the synthesis filter bank coefficients The row size of output array x Call the function Synthesis2DArraySize to compute Xrows The column size of output array x Call the function Synthesis2DArraySize to compute xcols s a a precision T EE E E fier banks output from the synthesis filter bank 2D array Signal Processing Toolset 12 44 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference Return Value status integer Refer to Chapter 14 Wavelet Error Codes for a description of the error Example Example 6 How to call function SynthesisFilterBank2D include wfbd h FilterBankPtr anaptr synptr double x 5011 5l1h mb me s vp long eSrr rows cols nsniaze o x0fows x0Ucols anaptr AllocCoeffWFBD Je allocate filter bank structure if lanaptr return synptr AllocCoeffWFBD Lr lsynptE free anaptr return err ReadCoeffWFBD coef dat anaptr synptr Read filter bank coefficients if err goto erreng rows 128 cols 256 x double malloc rows cols sizeof double if x goto errend compute
83. to poles whether they are real If you select the real checkbox the pole becomes purely real and is limited to real axis movement The order text entry specifies the pole order or the number of actual poles at this location in the z plane An Mth order pole at z a has a z transform of H z z a If you change the coordinates to polar coordinates the DFD application displays the poles and zeros in polar coordinates as shown in Figure 20 17 polar coordinates r 1 0000 theta 1 2335 reallp uc order E 1E3 Sh r 20 3356 theta 41 7754 SM order O Figure 20 17 Array of Zeros and Poles in Polar Coordinates National Instruments Corporation 20 23 Signal Processing Toolset Chapter 20 Digital Filter Design Application sampling rate 8 0000E 3 al 7 gain sl 5150E Signal Processing Toolset The graph in Figure 20 18 plots the frequency response H f magnitude of the designed digital filter Magnitude vs Frequency J LN i 1000 0 e D 3000 0 4000 0 Figure 20 18 Magnitude vs Frequency The magnitude y axis is in linear or decibel units depending on how you set the button in the upper left corner of the graph The frequency x axis 1s in hertz The full scale ranges from 0 0 to Nyquist half the sampling rate The sampling rate control specifies the sampling rate in samples per second hertz The gain control specifies the gain constant for the designed
84. utilities you can use within your LabVIEW applications to read DFD filter coefficient files and filter your data using the coefficients The two DFD utility virtual instruments VIs are Read DFD Coefficients and DFD Filter To use these VIs connect the file path of your coefficient file to Read DFD Coefficients Connect the output Coefficient Cluster to DFD Filter along with your input signal Once this sequence is followed and the VIs have executed your filtered data is available at the DFD Filter output Filtered X National Instruments Corporation 22 1 Signal Processing Toolset Chapter 22 Using Your Coefficient Designs with DFD Utilities Read DFD Coefficients Reads the DFD filter coefficient files and returns the coefficient data in a DFD coefficient cluster You can use the DFD Filter VI to filter your signals using the DFD coefficient Signal Processing Toolset Coefficient Cluster new file path i file error coefficient file path is the LabVIEW path to the DFD coefficient file This file can be in log or text file format If coefficient file path is empty you can select a coefficient file from an open file dialog Coefficient Cluster is the cluster of coefficient information read from the coefficient file The Coefficient Cluster contains the following parameters coefficient type is either O IIR or 1 FIR sampling rate is the sampling rate in hertz IIR Filter Cluster is the cascade IIR filter cluster
85. when L 2 Figure 12 5 Signal Interpolated by 2 From X to Y is a regular finite impulse response filtering or convolution The operation is the same as shown in Figure 12 3 If you set the proper length of the initial condition and final condition in the Decimation Filter VI when building a two channel filter bank using the Decimation Filter VI and the Interpolation Filter VI you can get a perfect reconstructed signal with no delay as shown in Figure 12 4 This VI is a subVI of the 2 Channel Synthesis Filter Bank VI National Instruments Corporation 12 15 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Mother Wavelet and Scaling Function VI This VI computes the mother wavelet and scaling function of a filter bank For a detailed description of the mother wavelet and scaling function refer to Figure 10 2 Relationship of Two Channel PR Filter Banks and Wavelet Transform in Chapter 10 Digital Filter Banks Filter Bank Coefficients Scaling Functor Mother wavelet refinement di Eror Filter Bank Coefficients contains the filter bank coefficients DEL Lowpass contains the lowpass filter coefficients DEL Highpass contains the highpass filter coefficients refinement indicates how many levels of lowpass filters to go through to calculate the Mother Wavelet and Scaling Function Scaling Function Refer to Figure 10 2 Relationship of Two Channel PR Filter Banks and Wavelet Transform in
86. where V is the measured voltage and Vr is the reference voltage The output of the filter does not preserve all points Remove the noise from the original signal See system developer Digital Filter Design Discrete Fourier transform Discrete Gabor transform Signal Processing Toolset Glossary dialog box distortion term DLL DSA DSP E equiripple filter error message FFT filter bank finite impulse response filter FIR formula node frame Signal Processing Toolset Window that appears when an application needs further information to carry out a command A term that causes distortion in a filter output Dynamic link library Dynamic signal acquisition Digital signal processing A filter with equiripples in the passband and stopband Indication of a software or hardware malfunction or an unacceptable data entry attempt Fast Fourier transform an efficient and fast method for calculating the discrete Fourier transform The number of samples is usually constrained to be a power of 2 The fast Fourier transform or the discrete Fourier transform determines the amplitude and phase of frequency components present in a time domain digital signal A group of filters A filter without feedback and containing only zeros in the z domain Finite impulse response Node that executes formulas you enter as text Formula nodes are especially useful for lengthy formulas that would be cumbersom
87. z The combinations of zeros are not unique Different combinations lead to different filter banks Sometimes Go z and G z work well but Ho z and H z might not refer to Figure 10 6 and Figure 10 7 One way to make this process easier is to limit the selections into a subset The most effective approach is to require Go z and G z and thereby Ho z and H z to be orthogonal as described by Equation 10 11 These constraints reduce the filter banks design to one filter design Once you select Go z you easily can find all other filters The constraints imposed by Equation 10 11 not only guarantee that both filter banks have the same performance but these constraints also provide other advantages For example many applications demonstrate that the lack of orthogonality complicates quantization and bit allocation between bands eliminating the conservation of energy To achieve Equation 10 11 let G z z Go z 10 12 which implies that g n is the alternating flip of go n e 0 gi 1 81 2 g amp o N gglN 1 g9lN 2 see National Instruments Corporation 10 9 Signal Processing Toolset Chapter 10 Digital Filter Banks Equation 10 12 implies that for orthogonal wavelets and filter banks Holz z GG where you use the relation in Equation 10 3 Consequently Equation 10 7 can be written as P z 2 Gy z Gy z If Gy z Gg z P z then 2 10 13 N Pel Y pine gode
88. 0 8 National Instruments Corporation Chapter 20 Digital Filter Design Application Graph Cursors Figure 20 6 shows two cursors on a graph You can move a cursor on a graph or chart by dragging it with the Operating Tool Cursors NI Figure 20 6 Example of Two Cursors on a Graph You also can click the direction diamonds on the cursor movement control to move all cursors selected in the specified direction You select cursors by moving them on the graph with the Operating Tool Classical IIR Filter Design Figure 20 7 shows the Classical IIR Design panel This panel includes a graphical interface with the Magnitude vs Frequency cursors and plot on the left side and a text based interface with digital controls on the right side E Classical IIR Design File Edit Operate Froject Windows Help DFO Menu porum passband resp passband freq stapband atten stopband freq sampling rate type lbsndpass Hl a p Ee design 2 Elliptic Jj 921 gh message filter order ENS Figure 20 7 Classical IIR Design Panel National Instruments Corporation 20 9 Signal Processing Toolset Chapter 20 Digital Filter Design Application Signal Processing Toolset Use this panel to design classical IIR digital filters These filters include the classic types lowpass highpass bandpass and bandstop and the classic designs Butterworth Chebyshev Inverse Chebyshev and Elliptic To design classical IIR filters adjust
89. 0 Digital Filter Design Application Table 20 2 Filter Specification Transfers Design Transfer DFD Menu Option Filter specs from the Classical IR Xfer Classical FIR to Classical FIR Filter specs from the Classical FIR Xfer Classical IIR to Classical IIR Poles and zeros from Classical IIR Xfer Pole Zero to Pole Zero Placement Returning to the Main Menu To return to the Main Menu panel choose DFD Menu Main Menu Panning and Zooming Options Any graph you drop onto the front panel includes the graph palette This palette has controls for panning scrolling the display area of a graph and for zooming in and out of sections of the graph Many DFD graphs include the graph palette Figure 20 4 illustrates a graph with its accompanying graph palette Hz l l l l 1000 00 2000 00 3000 00 4000 00 1 53 Al frequency magnitude 9 31 EU 3375 00 184 6628 Figure 20 4 Example of Graph Palette F When you click the Autoscale X button the DFD application autoscales the x data of the graph When you click the Autoscale Y button the DFD application autoscales the y data of the graph If you want the graph to autoscale either of the scales continuously click the lock switch to lock autoscaling National Instruments Corporation 20 7 Signal Processing Toolset Chapter 20 Digital Filter Design Application dak Unda 4 rx 5 Jj Signal Processing Toolset The Scale Format buttons giv
90. 1 6 Signal Processing Toolset Index cone shaped distribution description 3 10 Offline Joint Time Frequency Analyzer application 5 15 three tone test signal figure 3 10 Cone Shaped Distribution VI 4 11 to 4 12 covariance method 16 5 to 16 6 Covariance Method VI 17 1 to 17 2 Covariance Power Spectrum VI 17 2 to 17 3 customer communication xxiii A 1 to A 2 CWD Choi Williams distribution VI 4 10 to 4 11 D damped sinusoids AR model and 16 4 to 16 5 estimating with model based frequency analysis 15 4 to 15 5 estimating with Super Resolution Spectral Analyzer 18 4 DAQ and Filter panel See Digital Filter Design DFD application Decimation Filter VI 12 10 to 12 13 DecimationFilter function 12 29 to 12 32 denoise application linear JTFA algorithm 5 1 to 5 3 wavelet analysis 9 13 designing wavelets and filter banks See Wavelet and Filter Bank Design toolkit detrend application wavelet analysis 9 12 DFD Filter VI 22 3 DFD instrument driver 22 4 DFD Menu See Digital Filter Design DFD application digital filter banks 10 1 to 10 13 See also Wavelet and Filter Bank Design toolkit 2D signal processing 10 11 to 10 13 two channel perfect reconstruction filter banks 10 1 to 10 11 Signal Processing Toolset l 2 biorthogonal filter banks 10 4 to 10 9 orthogonal filter banks 10 9 to 10 11 relationship with wavelet transform 10 2 to 10 3 two channel filter bank figure 10 1 Digital Filter De
91. 20 8 plots the frequency response H f as magnitude of the designed digital filter National Instruments Corporation Magnitude vs Frequency 0 00 25 00 50 00 75 00 100 00 Hz l l l l 0 00 1000 00 e Dn 3000 00 4000 00 Ill e e frequency magnitude f y 9 3750 00 149 4296 Figure 20 8 Magnitude vs Frequency 20 11 Signal Processing Toolset Chapter 20 Digital Filter Design Application frequency magnitude 3750 00 149 4296 Signal Processing Toolset The magnitude y axis is in linear or decibel units depending on how you set the button in the upper left corner of the graph The frequency x axis is in hertz The full scale ranges from 0 0 to Nyquist half the sampling rate By moving the blue cursor lines or crosshairs you control the passband response horizontal lines and the passband frequencies vertical lines By moving the red cursor lines you control the stopband attenuation horizontal lines and the stopband frequencies vertical lines These cursors represent the filter design specifications for the selected classical IIR filter In the passband the filter has a gain greater than or equal to the specified passband response In the stopband the filter has a gain less than or equal to the specified stopband attenuation Use the linear dB button to control the display units linear or dB of all magnitude and gain controls and displays These controls and displays i
92. 3 Choi Williams distribution 3 9 Cohen s class 3 8 to 3 9 cone shaped distribution 3 10 Gabor spectrogram 3 11 to 3 12 Signal Processing Toolset Offline Joint Time Frequency Analyzer application 5 12 to 5 15 STFT spectrogram 3 3 to 3 4 Wigner Ville distribution and Pseudo Wigner Ville distribution 3 5 to 3 8 R Read DFD Coefficients VI 22 2 ReadCoeffDFD function 22 6 ReadCoeffWFBD function 12 37 reference waveforms loading 31 10 to 31 11 saving 31 11 to 31 12 S short time Fourier transform See STFT short time Fourier transform Short Time Transform VI 4 3 Signal Processing Toolset components 1 1 to 1 3 installation 1 4 overview 1 1 system requirements 1 4 spectrum analysis See model based frequency analysis Super Resolution Spectral Analysis toolkit spectrum analysis applications See time dependent spectrum analysis examples spectrum display switching between conventional power and instantaneous spectrum 5 10 to 5 11 STFT short time Fourier transform computation of Gabor expansion 3 1 to 3 2 historical background 2 6 Short Time Fourier Transform VI 4 3 wavelet analysis vs 9 7 to 9 9 comparison of transform processes figure 9 9 National Instruments Corporation short time Fourier transform sampling grid figure 9 7 wavelet transform sampling grid figure 9 8 STFT spectrogram 3 3 to 3 4 description 3 3 historical background 2 6 Offline Joint Time Frequency
93. 7 fundamentals of 9 1 to 9 3 history of 9 1 to 9 7 innovative analysis 9 3 to 9 7 overcoming Fourier analysis drawbacks 9 1 to 9 3 performance issues 9 13 to 9 14 Wavelet and Filter Bank Design toolkit See also digital filter banks wavelet analysis creating applications 11 16 to 11 19 online testing panel 11 18 to 11 19 wavelet packet analysis 11 17 to 11 18 design considerations 11 1 to 11 5 design steps 11 1 to 11 2 filter combinations table 11 4 linear phase filter figure 11 5 minimum phase filter figure 11 5 Signal Processing Toolset Index orthogonal and biorthogonal filters 11 3 orthogonal filter figure 11 5 Design Panel 11 6 designing wavelets and filter banks 11 7 to 11 10 equiripple filter figure 11 8 factorizing Po z into Go z and H z 11 8 to 11 9 finding product Po z 11 7 to 11 8 selecting filter type 11 7 utilities available on Menu control 11 9 to 11 10 error codes 14 1 to 14 2 Image Test panel 11 13 to 11 15 LabVIEW VI applications 12 1 to 12 16 2D Analysis Filter Bank for I16 VI 12 7 2D Analysis Filter Bank VI 12 5 to 12 6 2D Synthesis Filter Bank for I16 VI 12 9 2D Synthesis Filter Bank VI 12 8 Analysis Filter Bank VI 12 1 to 12 4 Decimation Filter VI 12 10 to 12 13 Interpolation Filter VI 12 14 to 12 15 Mother Wavelet and Scaling Function VI 12 16 Synthesis Filter Bank VI 12 4 to 12 5 Truncated Decimation Filter VI 12 13 to 12 14 LabWindows CVI
94. 9 5 Wavelet Transform Sampling Grid Wavelet transform is closely related to both conventional Fourier transform and short time Fourier transform As shown in Figure 9 6 all these transform processes employ the same mathematical tool the correlation operation or inner product to compare the signal s t to the elementary function ba t The difference lies in the structure of the elementary functions e t In some cases wavelet analysis is more natural because the signals always have a long time cycle at low frequency and a short time cycle at high frequency Signal Processing Toolset 9 8 National Instruments Corporation Chapter 9 Wavelet Analysis inner product Oke Fourier Transform Windowed FT 29 ealt h Dexp j2nkt T y Wavelet Transform Ea Figure 9 6 Comparison of Transform Processes Applications of Wavelet Analysis You can use wavelet analysis for a variety of functions including detecting the discontinuity of a signal looking at a signal from different scales removing the trend of a signal suppressing noise and compressing data Discontinuity Detection Wavelet analysis detects signal discontinuity such as jumps spikes and other non smooth features Ridding signals of noise is often much easier to identify in the wavelet domain than in the original domain For example the top plot of Figure 9 7 illustrates a signal s k made up of two exponential functions The turning poi
95. 9 5 you easily can convert the scale into frequency Hence W also can be considered the signal representation in joint time and frequency domain In the example in Figure 9 3 by checking the wavelet coefficients you know that for 0 lt t lt 1 the frequency of s t is 1 Hz and for 1 1 5 the frequency of s t is 2 Hz Unlike Fourier analysis wavelet transform not only indicates what frequencies the signal s t contains but also indicates when these frequencies occur Moreover the wavelet coefficients W n of a real valued Signal Processing Toolset signal s t are always real as long as you choose real valued y t Compared to Fourier expansion you usually can use fewer wavelet functions to 9 6 National Instruments Corporation Chapter 9 Wavelet Analysis represent the signal s t In the example in Figure 9 3 s t can be completely represented by two terms whereas an infinite number of complex sinusoidal functions would be needed in the case of Fourier expansion Wavelet Analysis vs Fourier Analysis You can apply short time Fourier transform to characterize a signal in both the time and frequency domains simultaneously However you also can use wavelet analysis to perform the same function because of its similarity to STFT You compute both by the correlation or inner product operation but the main difference lies in how you build the elementary functions For STFT the elementary functions used t
96. Analyzer application 5 12 window effect figures 3 4 STFT Spectrogram VI 4 12 2D STFT VI 4 4 to 4 5 super resolution spectral analysis and parameter estimation testing example application 18 1 to 18 6 algorithm selection 18 4 estimation of damped sinusoids 18 4 FFT based methods 18 3 main panel figure 18 1 sampling frequency control 18 2 Select Test Data ring control 18 2 synthetic data 18 5 to 18 6 upper bound AR order 18 3 VIs Covariance Method VI 17 1 to 17 2 Covariance Power Spectrum VI 17 2 to 17 3 Matrix Pencil Method VI 17 6 to 17 7 Minimum Description Length VI 17 7 PCAR Method VI 17 3 PCAR Power Spectrum VI 17 4 to 17 5 Prony s Method VI 17 5 to 17 6 Super Resolution Spectral Analysis toolkit See also model based frequency analysis overview 1 2 reference materials 19 1 when to use 15 8 Synthesis Filter Bank VI 12 4 to 12 5 National Instruments Corporation l 9 Index Synthesis2DArraySize function 12 38 to 12 39 SynthesisFilterBank function 12 40 to 12 42 SynthesisFilterBank2D function 12 43 to 12 46 system requirements for Signal Processing Toolset 1 4 T technical support A 1 to A 2 telephone and fax support numbers A 2 Third Octave Analysis applications 28 1 to 28 4 LabWindows CVI 28 1 to 28 3 running applications 28 3 Third Octave Analysis instrument driver 28 1 to 28 3 Visual Basic 28 4 Windows 95 NT 28 4 Third Octave Analysis instrument driver 28 1 to 28 3
97. Chapter 10 Digital Filter Banks z i oi Mother Wavelet Refer to Figure 9 3 Wavelet Analysis in Chapter 9 Wavelet Analysis ma z En t dt indicates the time duration between two points in the Mother Wavelet and Scaling Function outputs error Refer to Chapter 14 Wavelet Error Codes for a description of the error Bj E Signal Processing Toolset 12 16 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference LabWindows CVI Applications This section describes the LabWindows CVI utilities you can use with the WFBD toolkit Calling WFBD Functions in LabWindows CVI Add the wfbd32 fp to your project to call any functions in the instrument driver in your C code You can find w db32 fp under the CVI Support instr subdirectory of your installation directory wfbd32 fp needs import library w bd32 1ib in the same directory to run correctly wfbd32 1ib calls w bd32 d11 which is installed in the Libraries subdirectory of your installation directory LabWindows CVI complier is compatible with four commonly used C extensions e Visual C C e Symantec C C Borland C C e Watcom C C The installer automatically detects which extension LabWindows CVI supports and installs the correct import library w bd32 1ib If you later change LabWindows CVI to a different extension you need to copy the right import library w bd32 1ib to the same directory as wfbd32 fp You can find four diffe
98. Design Panel Signal Processing Toolset Figure 20 24 shows the Analysis of Filter Design panel Use this panel to complete the following tasks e View the filter magnitude response phase response impulse response step response and pole zero plot e View and print full screen plots of each response e In the full screen views save the analysis results to text files 20 30 National Instruments Corporation Chapter 20 Digital Filter Design Application i gt Analysis of Filter Design File Edit Operate Froject Windows Help Uri DFO Menu v IMS TRUMEHTS Diss EA elena Impulse Response E Classical IR Magnitude Response E BIM 1000 0 2000 3000 4000 A Fhase Response 1000 0 2000 0 3000 0 4000 0 l 1 0 Figure 20 24 Analysis of Filter Design Panel If you select DFD Menu Analysis from a filter design panel the Analysis of Filter Design panel uses that particular filter design to compute the various filter responses You also can analyze any of the four filter designs from the Design Analyzed ring control The Analysis of Filter Design panel uses the filter parameters from the selected filter design Use the DFD Menu to load filter designs from previous work open the DAQ and Filter panel go to the selected filter design panel or return to the Main Menu panel Use the Design Analyzed control to select the filter control to analyze Design Analyzed l l F oan E If you continue
99. FD application characteristics 21 4 FIR coefficient file format 21 4 to 21 6 Fourier transform 2 1 to 2 3 See also STFT short time Fourier transform basis functions figure 2 2 definition 2 1 spectral analysis example figure 2 3 uses 2 1 to 2 2 wavelet analysis vs 9 7 to 9 9 comparison of transform processes figure 9 9 history of 9 1 to 9 3 short time Fourier transform sampling grid figure 9 7 wavelet transform sampling grid figure 9 8 FreeCoeffDFD function 22 7 FreeCoeffWFBD function 12 33 frequency analysis See model based frequency analysis FTP support A 1 G Gabor expansion historical background 2 6 linear JTFA algorithm 3 1 STFT in computation of 3 1 to 3 2 Gabor Expansion VI 4 4 2D Gabor Expansion VI 4 6 to 4 7 Gabor spectrogram description 3 11 to 3 12 fourth order for three tone test signal figure 3 12 National Instruments Corporation IIR filters 21 1 to 21 3 See also Digital Filter guidelines for choosing analysis window table 5 13 historical background 2 6 to 2 7 Offline Joint Time Frequency Analyzer application 5 12 Gabor Spectrogram VI 4 14 Gaussian Window Function VI Normalized 4 8 Design DFD application advantages and disadvantages 21 1 cascade form IIR filtering 21 2 to 21 3 UR coefficient file format 21 6 to 21 7 image analysis JTFA application 5 3 to 5 6 Image Test panel Wavelet and Filter Bank Design toolkit 11 13 to 11 15
100. I semana C arg nafecenice suavefoms loe Smith bo disk Figure 31 9 Save Reference Waveforms Dialog Box Use the Save checkboxes to save the waveform in the display of the front panel you select Waveform Name indicates the names for the reference waveforms being saved Comments saves the information you provide with the reference waveforms for future reference Username saves a user name with the reference waveforms for future reference Name the reference waveforms and click OK 4 In the File dialog box enter the name of the reference waveform file and select the location to store the file Click OK Generating Reports for Use with Other Applications VirtualBench DSA can generate reports in a tab delimited ASCII report format that other applications can use To generate this type of report for your acquired data reference waveforms and computations complete the following steps If VirtualBench DSA is running click Run or Single to stop data acquisition 2 Select File Generate Report Signal Processing Toolset 31 12 National Instruments Corporation Chapter 31 VirtualBench DSA 3 Select the measurement display with the waveforms to save in the Generate Report dialog box as shown in Figure 31 10 Name the waveforms EX Generate Report Saver Hame Display 1 v Sine Specha Display 2 Ref Display 1 f Eme Spectra Rel Ref Display 2 M Save Computations Channel A F Channel B T Rel
101. Narrowband Hanning Window torte Threes one Test Sisal a2 e pU ee tt Maas 3 4 STFT Based Spectrogram with a Wideband Hanning Window ror the Jhtrees Lone Test SIE Hase deno idit p dodo dem esce 3 4 Wigner Ville Distribution for the Three Tone Test Signal 3 6 National Instruments Corporation xiii Signal Processing Toolset Contents Figure 3 4 Pseudo Wigner Ville Distribution with Gaussian Window w m forthe Three Tone Test Sional ac o oe otn eb e edid tun 3 7 Figure 3 5 Pseudo Wigner Ville Distribution for the Three Tone Test Signal 3 8 Figure 3 6 Choi Williams Distribution a 1 for the Three Tone Test Signal 3 9 Figure 3 7 Cone Shaped Distribution a 1 for the Three Tone Test Signal 3 10 Figure 3 8 Gabor Spectrogram Order Four for the Three Tone Test Signal 3 12 Figure 3 9 Adaptive Spectrogram for the Three Tone Test Signal 3 13 Figure 5 1 Gabor Expansion Based Denoise sse 5 3 15 18 5 2 2D STET Tor imase Analysis aieo eR o DE bn D in eris 5 4 Figure 5 3 Subimage Frequency Contents cccccceeeseeeeeeeeeeeseeeeeeeesseeeeeeseeeees 5 4 Figure 5 4 2D STFT for the Image Analysis in Figure 5 2 sss 5 6 Figure 5 5 Online STFT Spectrogram Analyzer Panel sess 5 7 Figure 5 6 Offline Joint Time Frequency Analyzer sese 5 0 Figure 5 7 Instantan
102. Systems and Filter Banks Englewood Cliffs N J Prentice Hall 1993 Vaidyanathan P P and T Nguyen A Trick for the Design of FIR Half Band Filters IEEE Transactions on Circuits and Systems vol 3 March 1987 297 300 National Instruments Corporation 13 1 Signal Processing Toolset Wavelet Error Codes This chapter lists the error codes LabVIEW VIs and LabWindows CVI functions return including the error number and a description Each VI returns an error code that indicates whether the function was performed successfully Table 14 1 LabVIEW VI and LabWindows CVI Function Error Codes 0 j NEm No error the call was successful 20001 OutOfMemErr There is not enough memory left to perform the specified routine 20002 EqSamplesErr The input sequences must be the same size 20003 SamplesGTZeroErr The number of samples must be greater than zero 20004 SamplesGEZeroErr The number of samples must be greater than or equal to zero 20005 SamplesGEOneErr The number of samples must be greater than or equal to one 20008 ArraySizeErr The input arrays do not contain the correct number of data values for this VI 20009 PowerOfTwoErr The size of the input array must be a power of two size 2 0 lt m lt 23 20012 CyclesErr The number of cycles must be greater than zero and less than or equal to the number of samples 20020 NyquistErr The cutoff frequency fc must meet th
103. T OR NEGLIGENCE ON THE PART OF NATIONAL INSTRUMENTS SHALL BE LIMITED TO THE AMOUNT THERETOFORE PAID BY THE CUSTOMER NATIONAL INSTRUMENTS WILL NOT BE LIABLE FOR DAMAGES RESULTING FROM LOSS OF DATA PROFITS USE OF PRODUCTS OR INCIDENTAL OR CONSEQUENTIAL DAMAGES EVEN IF ADVISED OF THE POSSIBILITY THEREOF This limitation of the liability of National Instruments will apply regardless of the form of action whether in contract or tort including negligence Any action against National Instruments must be brought within one year after the cause of action accrues National Instruments shall not be liable for any delay in performance due to causes beyond its reasonable control The warranty provided herein does not cover damages defects malfunctions or service failures caused by owner s failure to follow the National Instruments installation operation or maintenance instructions owner s modification of the product owner s abuse misuse or negligent acts and power failure or surges fire flood accident actions of third parties or other events outside reasonable control Under the copyright laws this publication may not be reproduced or transmitted in any form electronic or mechanical including photocopying recording storing in an information retrieval system or translating in whole or in part without the prior written consent of National Instruments Corporation CVI LabVIEW natinst com National Instruments and NI DAQ are
104. The greater a the less smoothing Figure 3 6 illustrates the CWD for 1 The CWD effectively can suppress the crossterm caused by two autoterms with different time and frequency centers such as crossterm 2 in Figure 3 3 However the CWD method cannot reduce those crossterms that correspond to autoterms with the same time center crossterm 3 or the same frequency center crossterm 1 Furthermore the computation speed of the CWD is very slow a Hz current data qauss3 tat data length sec 1 28E 1 spectrum 0 0E 0 2 0E 0 O 00E 0 sec S O1E 2 Hz sec I l I I I I I OE 0 2 0E 2 4 JE 2 6 0E 2 5 0E 2 1 0E 1 1 3E 1 CHISOT e contral Figure 3 6 Choi Williams Distribution 1 for the Three Tone Test Signal National Instruments Corporation 3 9 Signal Processing Toolset Chapter 3 Joint Time Frequency Analysis Algorithms Cone Shaped Distribution When the kernel function in Equation 3 6 is defined by i m 3 8 for i lt m 0 otherwise the yield is the cone shaped distribution In this toolkit the constant c is set to 500 By adjusting the parameter o in Equation 3 8 you can balance crossterm interference and time frequency resolution The greater o the less smoothing Figure 3 7 illustrates the cone shaped distribution for 1 The cone shaped distribution effectively suppresses crossterms 2 and 3 from Figure 3 3 but it cannot reduce the crossterms that correspond to autoterms wit
105. Toolset 31 6 National Instruments Corporation Chapter 31 VirtualBench DSA Acquiring and Measuring Signals You can start acquiring and measuring signals with VirtualBench DSA by following these steps 1 Connect a signal to the Channel 0 or 1 input of your DAQ device Refer to the user manual of your DAQ device for more information 2 Configure the DSA a Select Edit Settings on the front panel b Select the Hardware tab from the DSA Settings dialog box shown in Figure 31 5 bl DSA Settings Hardware Acquisition Triggering Markers Device 1 AT MID TBE 1 Channel 4 Channel B Channel Coupling Channel Coupling ae quB f Pu MM Los 0 1 gt x Bo p GEN Voltage Range Voltage Range 10 000 High 10 000 High 10 000 Low 10 000 Low Figure 31 5 Hardware Tab of DSA Settings Dialog Box c Select the device that you want to use for the data acquisition The device must be successfully configured in the NI DAQ Configuration Utility to appear in the Device list d Set Channel A or B to Channel 0 or 1 depending on where you connected the signal in step 1 e Change the input Voltage Range to reflect the upper and lower bounds of your signal in volts National Instruments Corporation 31 7 Signal Processing Toolset Chapter 31 VirtualBench DSA f Click on the Acquisition tab in the DSA Settings dialog box shown in Figure 31 6 OSA Settings Hardware Acquisi
106. VI VirtualBench DSA VirtualBench DSA Launching Virtiialbench DSA iod ied prota pe od Ne Ron ur atop Ic UMEN dem osos 31 1 Eront Pane l Eeatufes 2c5 teiat ees deiagaasta ccc osiecasccntace A iu tau cea et 31 1 Computations Pare Eedl tes e cay oan tte edita etur hub iate vi Ra qu enue 31 5 Acquiring and Measuring Signalls ccccccccccccssccsseceseseeeeeeeseeeeeceeeeseeesssssessesesseeeeeeees 31 7 Workin Wit Waly CLOTS ous Dumas tars S bao dena eli mid ole Ia ou d sud oU UU SU a 31 10 Making Precise Measurements Using Marker cc sccssssseesseeesseeeeeeeeees 31 10 Loading Reterence Wa Ve lOr ins a0 osos dq iae eue MART d qu Rd AU DEus 31 10 Saving Reference Waveforms accesso qe ten pa MA PARI DHAR Eb a a 31 11 Generating Reports for Use with Other Applications eesessee 31 12 Appendix A Customer Communication Glossary Index Figures Figure 2 1 Figure 2 2 Figure 2 3 Figure 2 4 Figure 2 5 Figure 2 6 Figure 3 1 Figure 3 2 Figure 3 3 Basis Functions Used for Fourier Transform eeeeuseee 2 2 Se MIC 1 OM al o eesbosmsettotobs seti a mE MR eo sed bantutUS ciues quU 2 2 BCG SIPIdliideuuse desiit tid om ee 2 3 SPec choan an a accu ettam tutu cec sa eS e ie 2 3 Iontzednp lseSIPDalsussds eiie Deseos sua esto et cPe IUE 2 5 I econstructed S194 sooietisco et etate int esum eu comes iai esos cs cesa bes aa ess 2 5 STFT Based Spectrogram with a
107. Wes vases RET m m TT 11 6 BPquirippleBHIe E s ee Codi ada Debs diese alites ui eva nC RE RE 11 8 DEEST Lm 11 10 DAO SCP PINE ll eticeni ente a a a uen 11 12 Speci yin Ga Pai eas A RED eda 11 13 hiace Tes Panel a bsodeuseneavonugaedemeastoedseens 11 14 Wavelets and Filters Panels eese de rite ei d LE Le E ot epd i ugs cosi 11 16 Full Path of a Three Level Perfect Reconstruction Tree 11 17 Wavelet PACK CU usto nite e bts bibe E dildo P PL RO raids 11 18 Implementation of a Wavelet Packet sene 11 19 Zero FACING ocv dote Sic Opt doni a TUE cdc cc aue MM eae 12 3 SyrmmetErc BotenstOTL is 5st oa oos vea Ec EE Pu PEE e La ei p Da ab E Cohen 12 4 Filtering erat Om ae ott Run eret ions Pope UM UU Ud ED EULEE 12 12 Two Channel Perfect Reconstruction System eeeeeesssse 12 13 Sisnal Interpolated DVZ 5 d oe e OM IAE DEDI edt oci uetus 12 15 50 Samples for a Sum of Two Sinusoids eeeeesssssss 15 2 FFT Based Power Spectra Based on 50 Samples ss 15 2 Two Sinusoids with 15 Samples sse 15 3 FFT Based Power Spectra Based on 15 Samples 15 3 Super Resolution Power Spectra Based on 15 Samples 15 3 D atnped SImusolds ossa e quide bastedrdiues lucide iiit ode 15 4 FFT Based Power Spectra for Damped Sinusoids 15 5 Parameter Est
108. York Acoustical Society of America 1986 Randall R B Frequency Analysis Nerum Denmark Briiel amp Kj r 1987 National Instruments Corporation 29 1 Signal Processing Toolset 30 This chapter lists the error codes returned by the Third Octave Filters VI and the C function ThirdOctave Analyzer 20001 There is not enough memory left Third Octave Error Codes 20070 SamplingRateErr The sampling rate is not correct 20071 ArraySizeErr The size of one of the arrays is not correct National Instruments Corporation 30 1 Signal Processing Toolset VirtualBench DSA This section of the manual describes the VirtualBench dynamic signal analyzer DSA e Chapter 31 VirtualBench DSA explains the VirtualBench DSA features and how to acquire and measure signals with the DSA National Instruments Corporation VI 1 Signal Processing Toolset VirtualBench DSA This chapter explains the VirtualBench dynamic signal analyzer DSA features and how to acquire and measure signals with the DSA Launching VirtualBench DSA You can launch VirtualBench DSA by selecting Start Programs National Instruments Signal Processing Toolset VirtualBench DSA Front Panel Features This section explains the features of the VirtualBench DSA front panel shown in Figure 31 1 Measurement Displays RR VirtualBench DSA File Edit Window Help INSTRUMENTS markers Mimi Display 1 Display 1 4 31 2
109. ad The cone shaped distribution is another type of time dependent spectrum cone shaped designed to reduce crossterm interference Like the pseudo Wigner Ville anaes distribution and the Choi Williams distribution you also can take the cone shaped distribution with respect to the analytical function by setting sme analytic to ON The resulting spectrogram has reduced crossterm au interference You also can lessen crossterm interference by setting the control paramet In general the smaller the paramet value the less crossterm interference but the poorer the time frequency resolution paramet defaults to a value of 1 National Instruments Corporation 5 15 Signal Processing Toolset Frequently Asked Questions This chapter addresses some questions JTFA users frequently ask What Is the Difference between Linear and Quadratic JT FA Methods This package includes both linear and quadratic methods Linear transforms include the following methods e Gabor expansion considered the inverse short time Fourier transform STFT e STFT used for computing the Gabor coefficients e adaptive representation considered the inverse adaptive transform e adaptive transform The quadratic JTFA algorithms include the following e SIFT spectrogram e Wigner Ville distribution WVD e Pseudo Wigner Ville distribution PWVD e Cohen s class e Choi Williams distribution CWD e cone shaped distribution e Gabor spectrogram
110. al Instruments Corporation 22 5 Signal Processing Toolset Chapter 22 Using Your Coefficient Designs with DFD Utilities ReadCoeffDFD long err ReadCoeffDFD char coeffPath FilterPtr filterCoefficients double samplingRate Purpose Reads your DFD filter coefficient file You must call AllocCoeffDFD once before calling this function Parameters Input coeffPath Pathname of DFD coefficient file Output filterCoefficients Pointer to filter coefficient structure samplingRate Pointer to sampling rate Return Value Signal Processing Toolset 22 6 National Instruments Corporation Chapter 22 Using Your Coefficient Designs with DFD Utilities FreeCoeffDFD long err FreeCoeffDFD FilterPtr filterCoefficients Purpose Frees the DFD filter coefficient structure and all its coefficient arrays Parameters Input filterCoefficients FilterPtr Pointer to filter coefficient structure Return Value National Instruments Corporation 22 Signal Processing Toolset Chapter 22 Using Your Coefficient Designs with DFD Utilities FilterDFD long err FilterDFD double inputArray long n FilterPtr filterCoefficients double outputArray Purpose Filters the input samples using the DFD filter coefficients You must call AllocCoeffDFD and ReadCoeffDFD once before calling this function You can use this function to filter blocks of one continuous sequence of input samples The input state of the fil
111. al processing In fact two channel PR filter banks also can be used for 2D signals as shown in Figure 10 9 In this case you process rows first and then columns Consequently one 2D array splits to the following four 2D sub arrays e low low e low high e high low e high high National Instruments Corporation 10 11 Signal Processing Toolset Chapter 10 Digital Filter Banks Each sub array is a quarter the size of the original 2D signal columns rows m G z amp 2 high high gt Gzy dae Goz amp Y2 amp high low w Gz amp Y2 low high gt Gz y gt de Gz Y2 iow ow Figure 10 9 2D Signal Processing Figure 10 10 illustrates 2D image decomposition by two channel PR filter banks In this case the original 128 by 128 2D array is decomposed into four 64 by 64 sub arrays The total size of the four sub arrays is the same as the original 2D array For example the total number of elements in the four sub arrays is 16 384 which equals 128 x 128 However if the filters are selected properly you can make sub arrays such that the majority elements are small enough to be neglected Consequently you can use a fraction of the entire wavelet transform coefficients to recover the original image and thereby achieve data compression In this example you use th
112. alled the alias term must be zero To achieve this you want H z Go z H z G4 z 0 10 2 which you accomplish by letting H z G z and H z Gg z 10 3 The relationship in Equation 10 3 implies that you can obtain Ag n by alternating the sign of g n hg n C1 21 n similarly hin CD gin 10 4 Therefore g n and h n are the highpass filters if go n and ho n are the lowpass filters For perfect reconstruction you also want the first term in 10 4 National Instruments Corporation Chapter 10 Digital Filter Banks Equation 10 1 called the distortion term to be a constant or a pure time delay For example H z Go z Hy z G z 2z 10 5 where denotes a time delay If you satisfy both Equations 10 2 and 10 5 the output of the two channel filter bank in Figure 10 1 is a delayed version of the input signal x z z X z However there remains a problem computing Go z and G z or Ho z and H z Once you determine Go z and G z you can find the rest of the filters with Equation 10 3 You also can write Equation 10 3 as G z A z and A z G z Substituting it into Equation 10 5 yields Gy z Hy z Gy z H z Po z Py 2z 10 6 where Po z denotes the product of two lowpass filters Go z and H z Pg z Go z Hg z 10 7 Equation 10 6 indicates that all odd terms of the product of two lowpass filters Go z and Ho z must be zero exce
113. an S and D Chen Decomposition of the Wigner Ville distribution and time frequency distribution series JEEE Trans Signal Processing vol 42 10 1994 2836 2841 Qian S and D Chen Joint time frequency analysis Englewood Cliffs N J Prentice Hall 1996 Wexler J and S Raz Discrete Gabor expansions Signal Processing vol 21 3 1990 207 221 National Instruments Corporation 1 Signal Processing Toolset Chapter 7 JTFA References Yin Q Z Ni S Qian and D Chen Adaptive oriented orthogonal projective decomposition Journal of Electronics Chinese vol 25 4 1997 52 58 Xia X G and S Qian An iterative algorithm for time varying filtering in the discrete Gabor transform domain Submitted to IEEE Trans on Signal Processing Zhao Y L E Atlas and R J Marks The use of cone shaped kernels for generalized time frequency representations of nonstationary signals IEEE Trans Acoustics Speech Signal Processing vol 38 7 1990 1084 1091 Signal Processing Toolset 2 National Instruments Corporation JTFA Error Codes This chapter lists the error codes the JTFA VIs return Table 8 1 JTFA Error Codes ege EmorName Name Description 2080 beer The Gabor time sampling interval is not evenly divided by the window length The oversampling rate N dM is less than one 2081 GaborNErr The number of frequency bins is not a power of two The number of frequ
114. an be infinite in length duration The general difference equation characterizing IIR filters 1s L A N 1 J 1f DA se Yi k 21 1 j 0 k 1 where N is the number of forward coefficients b and N is the number of reverse coefficients a In most IIR filter designs coefficient ag is 1 The output sample at the present sample index i consists of the sum of scaled present and past inputs x and x _ when j 0 and scaled past outputs y x The response of the general IIR filter to an impulse x9 1 and x 0 for all i z 0 is called the impulse response of the filter The impulse response of the filter described by Equation 21 1 has an infinite length for nonzero coefficients In practical filter applications however the impulse response of stable IIR filters decays to near zero in a finite number of samples The advantage of digital IIR filters over finite impulse response FIR filters is that IIR filters usually require fewer coefficients to perform similar filtering operations Therefore IIR filters execute much faster and do not require extra memory because they execute in place The disadvantage of IIR filters 1s that the phase response is nonlinear If the application does not require phase information such as simple signal monitoring IIR filters might be appropriate Use FIR filters for applications that require linear phase responses National Instruments Corporation 21 1 Signal Processing Toolset C
115. an save digital filter coefficients for later implementation from within LabVIEW and LabWindows CVI Also you can call Windows DFD dynamic link libraries DLLs from other applications or other applications can load the filter coefficient files directly This section of this manual includes all required filter coefficient forms and implementation equations If you have a National Instruments data acquisition DAQ device you can perform real world filter testing in the DFD application You can view the time waveforms or the spectra of the input signal and the filtered signal while you simultaneously redesign your digital filters National Instruments Corporation 20 1 Signal Processing Toolset Chapter 20 Digital Filter Design Application Figure 20 1 illustrates the interaction between the DFD toolkit and related applications Digital Filter Design Application Data Acquisition and Filtering Filter Specification Files Filter Coefficient Files LabVIEW LabWindows CVI Windows DLL Figure 20 1 Conceptual Overview of the Digital Filter Design Toolkit Main Menu You can run the application by selecting Start Programs National Instruments Signal Processing Toolset Digital Filter Designer When you launch the DFD application a panel displays the main available options Figure 20 2 shows the Main Menu panel i Main Menu File Edit Operate Windows Help oye es etes Digital Filter Design Classical IIR Filter Design
116. anel objects used to manipulate and display or input and output text Numeric plotting indicator modeled after a paper strip chart recorder which scrolls as it plots data G 8 National Instruments Corporation subVI sweep chart synthesis filter bank system developer T temporal third octave two dimensional type I filter V VI VI library virtual instrument Virtual Instrument Software Architecture W waveform chart wavelet wavelet based detrend National Instruments Corporation G 9 Glossary VI used in the block diagram of another VI It is comparable to a subroutine Numeric indicator modeled on the operation of an oscilloscope It is similar to a scope chart except that a line sweeps across the display to separate old data from new data A filter bank that transfers a signal from the wavelet domain into the time domain Creator of the application software to be executed Of or relating to time domain Ratio between two frequencies equal to 2 5 Refer to octave Having two dimensions such as an array with both rows and columns The filter coefficients are symmetric among the middle point See virtual instrument Special file that contains a collection of related VIs for a specific use VI Program in the graphical programming language G so called because it models the appearance and function of a physical instrument Single interface library for controlling GPIB V XI RS 232 and
117. applications 12 17 to 12 46 AllocCoeffW FBD function 12 19 Analysis2DArraySize function 12 20 to 12 21 AnalysisFilterBank function 12 22 to 12 23 AnalysisFilterBank2D function 12 24 to 12 28 Signal Processing Toolset I 12 calling WFBD functions 12 17 DecimationFilter function 12 29 to 12 32 FreeCoeffWFBD function 12 33 InterpolationFilter function 12 34 to 12 36 ReadCoeffWFBD function 12 37 Synthesis2DArraySize function 12 38 to 12 39 SynthesisFilterBank function 12 40 to 12 42 SynthesisFilterBank2D function 12 43 to 12 46 WFBD instrument driver function prototypes 12 17 to 12 18 ID Test panel 11 10 to 11 13 overview 1 2 reference materials 13 1 Wavelets and Filters panel 11 15 to 11 16 Windows applications 12 47 WFBD toolkit See Wavelet and Filter Bank Design toolkit Wigner Ville distribution WVD See also Pseudo Wigner Ville distribution description 3 5 to 3 6 historical background 2 6 window effect 2 6 Windows applications Third Octave Analysis applications 28 4 Wavelet and Filter Bank Design toolkit 12 47 Windows DLL DFD utilities 22 9 National Instruments Corporation
118. approach the model based method needs fewer data samples and is more accurate if the model fits the analyzed data samples well Employing the model based method you not only can obtain super resolution power spectra with a small data set but you also can estimate the parameters of damped sinusoids The model based method is an important alternative to classical FFT based methods in many frequency analysis applications The Need for Model Based Frequency Analysis Spectrum is a variant of the Latin word specter meaning image or ghostly apparition Sir Isaac Newton first used the term in 1671 to describe the band of light colors Since then the spectrum was generalized for arbitrary signals and it characterizes the frequency behavior of a signal Spectral analysis answers such questions as Does most of the power of the signal reside at low or high frequencies or Are there resonances As one might expect spectral analysis finds wide use in such diverse fields as biomedicine economics geophysics noise and vibration radar sonar speech and other areas in which signals of unknown or of questionable origin are of interest Examining spectra or performing spectral analysis you can often discover some important features of signals that are not obvious in the time waveform of the signal Over the last 30 years a primary tool for spectral analysis has been the FFT However the frequency resolution of the FFT based methods is bounded b
119. assical power spectrum or instantaneous spectrum The upper left plot shows the spectrogram time dependent spectrum 5 8 National Instruments Corporation Chapter 5 Joint Time Frequency Analysis Applications Eb Offline Analyzer File Edit Operate Project Windows Help z fs Hz Hz current data seismic txt data le F spectrum seismic atalength sec 3 00B 1 100E45 5 0E 2 f eae 0 00E 3 0E 2 2 0E42 1 0E 2 mn 0 00E 0 sec 0 0E H block length 0E 1 00E 1 sec 10E method 0 0E H Gabor 1 0EH analysis window 2 E40 i E xw medianband 0 0E 0 0E 2 lc id order Dee a H linear db Figure 5 6 Offline Joint Time Frequency Analyzer Because it demonstrates each quadratic JTFA algorithm included in this toolkit the Offline Analyzer helps you select the algorithm that best fits your application i Note This instrument was designed for demonstration purposes only For most real applications you need to build your own JTFA instrument using the VIs included in this toolkit The following sections explain how to manipulate controls and read indicators in the Offline Analyzer Changing Spectrogram Display cursor Im caer There are three options for the spectrogram display By clicking the cursor H db H eray button you turn the cursor on and off By moving the linear db switch you select linear or db display By moving the color gray switch you control th
120. at contains previously saved status and data If the current status differs from the recalled status the analyzer loads the recalled status and displays the recalled results When you acquire a new data block the analyzer still uses the recalled status until you click the Setup button again Quit stops the analyzer Reference makes the analyzer prompt you to load your reference file which should be the same file format to which you save your data The analyzer plots the reference on the same graph with the power value When you have the reference signal each plot has two more indicators that show the value of reference and the difference of reference with the actual power value at each frequency band Clear Reference clears the reference signal for the analyzer National Instruments Corporation 25 Signal Processing Toolset Chapter 25 Operating the Third Octave Analyzer Figure 25 4 is the front panel for one channel with a reference signal The indicator box in the bottom left corner of the analyzer shows the status of the analyzer In Figure 25 4 the status of this VI is idle Power Reference Difference of Power Value Value Value with Reference Value E Third Octave Analyzer 87 start IU Hz Reference Clear Reference stop 10 0 kHz Setup Single Acquire Amplitude T able Save Recall Quit Idle Figure 25 4 One Channel Third Octave Analyzer Panel with Reference Signal Signal Processing Toolset 25 6
121. ate of shipment as evidenced by receipts or other documentation National Instruments will at its option repair or replace software media that do not execute programming instructions if National Instruments receives notice of such defects during the warranty period National Instruments does not warrant that the operation of the software shall be uninterrupted or error free A Return Material Authorization RMA number must be obtained from the factory and clearly marked on the outside of the package before any equipment will be accepted for warranty work National Instruments will pay the shipping costs of returning to the owner parts which are covered by warranty National Instruments believes that the information in this manual is accurate The document has been carefully reviewed for technical accuracy In the event that technical or typographical errors exist National Instruments reserves the right to make changes to subsequent editions of this document without prior notice to holders of this edition The reader should consult National Instruments if errors are suspected In no event shall National Instruments be liable for any damages arising out of or related to this document or the information contained in it EXCEPT AS SPECIFIED HEREIN NATIONAL INSTRUMENTS MAKES NO WARRANTIES EXPRESS OR IMPLIED AND SPECIFICALLY DISCLAIMS ANY WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE CUSTOMER S RIGHT TO RECOVER DAMAGES CAUSED BY FAUL
122. ave Analysis toolkit provides a 32 bit dynamic link library DLL octave32 d11 for Windows 95 NT users This DLL is located in the Libraries subdirectory of your installation directory The function prototype in this DLLs 1s long ThirdOctave_Analyzer double input long nx double fs long winType long FFTSize long avgNum 2 double Power 31 double CenterFreq 31 long outputNum The meanings of the parameters are the same as for the instrument driver for LabWindows CVI Refer to the previous 7hird Octave Analysis Instrument Driver section for the parameter descriptions Call this function the same way in your code as you call any function in DLLs Third Octave Analysis Applications in Visual Basic The Third Octave Analysis toolkit also provides an example for Visual Basic that shows you how to call the ThirdOctave Analyzer function You can find the source codes in the Libraries V Example NVisualBasic subdirectory of your installation directory For Windows 95 NT copy octave32 d11 from the Libraries folder to your WindowsNSystem folder Signal Processing Toolset 28 4 National Instruments Corporation Third Octave References This chapter lists reference material that contains more information on the theory and algorithms implemented in the Third Octave Analysis toolkit American National Standards Institute ANSI S1 11 1986 Specification for octave band and fractional octave band analog and digital filters New
123. averaging No averaging is used for almost stationary signals and complete averaging is used for signals that are not almost stationary The more the averaging the slower the execution time Refer to the nternal Data Averaging section in Chapter 26 Third Octave Analysis Design for more information outputNum is the size of output arrays of Power and CenterFreq which must be 31 Power is an array that contains the outputs of the 31 third octave filters It is not in the dB format CenterFreq is an array that contains the center frequencies of the 31 third octave filters Refer to the Introduction to the Third Octave Analysis Toolkit section in Chapter 24 Overview of the Third Octave Analysis Toolkit for information on how the center frequencies are computed Running Third Octave Analysis Applications in LabWindows CVI Add the octave fp to your project and call the Thi rdOctave Analyzer function in your C code Depending on the CVI compatibility mode that you selected Borland Msvc Symantec or Watcom during your CVI installation you must copy the appropriate Octave o file from the CVI Support instr win32 folder to the CVI Support instr folder For an example of how to call this function open CVI Support example oct_exam prj National Instruments Corporation 28 3 Signal Processing Toolset Chapter 28 Building Windows Applications for Third Octave Analysis Third Octave Analysis Applications in Windows The Third Oct
124. ay amp Load Reference Waveloms Select which Wavetorms to Load M annis W anceicem Marnie Losd ba 1 Sine 50 Hz Display 1 2 Sine Autospectia Display 2 Comments Username Saving reference wares bo oe Smith disk Figure 31 8 Load Reference Waveforms Dialog Box Wave indicates the order of the reference waveforms 1n the file Waveform Name indicates the name of the reference waveform when it was saved Use the Load to control to select in which front panel display to load the reference waveform Comments shows the comments saved in the file Username shows the user name saved in the file When you finish entering your information click OK 5 Click Single or Run to display newly acquired data with the reference waveform saving Reference Waveforms Acquired data in either measurement display of the front panel that you save to disk is called a reference waveform To save a reference waveform complete the following steps 1 Click Run or Single to stop acquisition 2 Select File Save Reference Waves National Instruments Corporation 31 11 Signal Processing Toolset Chapter 31 VirtualBench DSA 3 Select the measurement display s where the data to save resides in the Save Reference Waveforms dialog box as shown in Figure 31 9 E 5 ave Reference MW avelonms Selmi which W aseedonmir bo Save Save Waneetorm Hame Display 1 7 Sine 500 Hz Display 2 P Sine Autospectra Comments L
125. ays errors that occur during the HR design procedure These errors occur when the filter specifications are inconsistent with the chosen filter type Classical FIR Design Figure 20 10 shows the Classical FIR Design panel This panel functions similarly to the Classical IIR Design panel The panel includes a graphical interface with the Magnitude vs Frequency cursors and plot on the left side and a text based interface with digital controls on the right side gt Classical FIR Design File Edit Operate Froject Windows Help OFO Menu Y Magnitude vs Frequency passband resp 2 04 25 00 50 00 f ai UL 94 24 0 00 TETE TERN message Signal Processing Toolset passband freg stopband atten stopband treq l l l l Hz 1000 00 2000 00 3000 00 4000 00 sampling rate frequency magnitude band 2750 00 13 304 type bandpass filter order 22 minimize filter order ON Figure 20 10 Classical FIR Design Panel 20 14 National Instruments Corporation Chapter 20 Digital Filter Design Application Use the Classical FIR Design panel to design classical FIR digital filters These filters include the classic types lowpass highpass bandpass and bandstop and use the Parks McClellan equiripple FIR filter design algorithm To design classical FIR filters adjust the desired filter specifications The passband and stopband requirements define a filter specification You can define these requirements by
126. below the time waveform as shown in Figure 18 2 The larger the upper bound you select the more precise the result However the larger the upper bound the longer the computing time The upper bound should be two to three times larger than the real order but cannot be larger than the number of samples FFI Based Methods This comprehensive testing software provides the following four types of windows for FFT based spectrum Blackman Hamming Hanning and Rectangular The window type control is above the plot of the FFT based spectrum as shown in Figure 18 3 Blackman Hamming Hanning FFT lt Rectangular a D A o t yt cc P Figure 18 3 FFI Based Methods National Instruments Corporation 18 3 Signal Processing Toolset Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation selection of Super Resolution Spectra Algorithms The testing software contains two types of super resolution spectra algorithms covariance and principle component auto regressive PCAR methods You can select either type by using the ring control located above the super resolution spectra plot as shown in Figure 18 4 Figure 18 4 Super Resolution Spectra The PCAR method is less sensitive to noise than that of the covariance method but it requires more computing time and memory space Estimation of Damped Sinusoids Signal Processing Toolset The built in test software provides two types of methods Prony s
127. cks to average indicates the number of data blocks the analyzer J averages before the final display The analyzer acquires M data points each time for each channel where M 54 280 if FFT size 512 and M 28 680 if FFT size 256 After it analyzes the data block the analyzer acquires another M point data block and analyzes it The Third Octave Analyzer repeats this process the number of times that you have designated in this parameter The final power output is the average of the power output from each block Notice that the analyzer does not continuously acquire the data block which should be satisfactory for stationary signals Signal Processing Toolset 25 2 National Instruments Corporation Chapter 25 Operating the Third Octave Analyzer Channel Channel indicates which channels you want to acquire data from and Dj Cha analyze You can choose up to four channels and the Channel can be the same in every control Each channel has a checkbox If you do not need to use a channel click inside the box until the check disappears to disable all the parameters associated with that channel Window Type selects one of four commonly used windows rectangular Blackman Hamming or Hanning for each channel The window Hanning reduces the truncation effect The Window Type parameter defaults to the Hanning window Window Type Average Type Average Type indicates what type of average the analyzer uses to average em
128. contains three main frequency tones However the power spectrum alone does not clearly indicate how those frequencies evolve over time Obviously the frequency tones of a speech signal are not constant Despite the fact that the frequency contents of most signals change with time the classical Fourier theory allows us to analyze a signal only in the time domain or in the frequency domain E current data Hood tst data length zec spectrum zZ O 00E 0 sec 3 40E 3 Hz 87E 3 zec 1 I 1 r T 1 I 1 E O 0E 0 1 0E 1 2 0E 1 3 0E 1 4 0E 1 50E 1 ELUE 1 0E 1 B 2E 1 control Ball Figure 2 4 Speech Signal National Instruments Corporation 2 3 Signal Processing Toolset Chapter 2 The Need for Joint Time Frequency Analysis The Need for JTFA The large plot of Figure 2 4 is a time dependent spectrum that plots the energy of the signal as a function of both time and frequency As shown the time dependent spectrum clearly reveals the pattern of the formants From the formants you can see how the frequency changes The relative brightness levels of the plot show the intensity of the frequencies In this example the JTFA helps illustrate the mechanism of human speech Another important motivation for applying JTFA is the detection of noise corrupted signals In general random noise tends to spread evenly across the time and frequency domains Ho
129. ction and its parameters in the previous section LabWindows CVI Utilities Call these functions in your code the same way you call other DLL functions The DFD toolkit also provides an example for Visual Basic 4 0 that shows you how to call the DFD utility functions The source code is in the DFDUTILS WINSRC EXAMPLE VB subdirectory of your installation directory National Instruments Corporation 22 9 Signal Processing Toolset DFD References This chapter lists reference material that contains more information on the theory and algorithms implemented in the DFD toolkit Jackson L B Digital Filters and Signal Processing Boston Kluwer 1986 Oppenheim A V and R W Schafer Discrete Time Signal Processing Englewood Cliffs N J Prentice Hall 1989 Parks T W and C S Burrus Digital Filter Design New York John Wiley amp Sons Inc 1987 Parks T W and J H McClellan A Program for the Design of Linear Phase Finite Impulse Response Filters IEEE Trans Audio Electroacoustics vol AU 20 3 Aug 1972a 195 199 Parks T W and J H McClellan Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase IEEE Trans Circuit Theory vol CT 19 March 1972a 189 194 Williams A B and F J Taylor Electronic Filter Design Handbook New York McGraw Hill 1988 National Instruments Corporation 23 1 Signal Processing Toolset Part V Third Octave Analysis Toolkit
130. cution representation S sampling rate scope chart signal discontinuity spectral changes spectral leakage spectrogram STFT string controls and indicators strip chart Signal Processing Toolset Menu accessed by right clicking Windows or command clicking Macintosh an object Menu options pertain to that object Filtering before processing Pseudo Wigner Ville Distribution Mode in which calls to multiple instances of a subVI can execute in parallel with distinct and separate data storage Subtype of the numeric data type Representations include signed and unsigned byte word and long integers as well as single double and extended precision floating point numbers both real and complex Rate at which a continuous waveform is digitized Numeric indicator modeled on the operation of an oscilloscope The point where the first derivative does not exist Changes in the frequency content of a signal Phenomenon whereby the measured spectral energy appears to leak from one frequency into other frequencies It occurs when a sampled waveform does not contain an integral number of cycles over the time period during which it was sampled The technique used to reduce spectral leakage is to multiply the time domain waveform by window function Refer to window A display of the energy distribution of a signal with one axis being time and the other being frequency Short time Fourier transform Front p
131. d zeros and accurately control their important characteristics You can describe the poles and zeros by using either the text entry or the cursors in the z plane plot As you use the mouse to click and drag the cursors the text entries update Likewise as you enter new specifications in the text entries the pole and zero cursors update The following specifications describe pole zero filter designs e pole and zero locations in the z plane e characteristics of each pole and zero e gain e sampling rate 20 20 National Instruments Corporation Chapter 20 Digital Filter Design Application Any change in these parameters corresponds to a change in the filter coefficients The DFD application matches the poles and zeros and creates stable second order stages for IIR filter coefficients The DFD application then uses these coefficients to compute the filter magnitude response For immediate graphical feedback to your pole zero filter designs the Magnitude vs Frequency plot updates automatically when you change the poles or zeros Pole Zero Placement Panel Controls and Displays Use the design panel DFD Menu to complete the following tasks e Save your filter specifications and coefficients e Load filter designs from previous work e Open the Analysis or the DAQ and Filter panels e Return to the Main Menu panel Figure 20 14 shows the z plane plot of the filtered poles and zeros You can move each pole red x anywhere within
132. ded specifications of the Third Octave Analysis Toolkit You set the hardware sampling frequencies at 51 2 kHz 25 6 kHz and 12 8 kHz using the Setup panel Each band filter satisfies Order 3 Type 3 D where D is the sub type designator as defined in the ANSI S1 11 1986 standard These filters are defined as follows e Order 3 Each filter in the filter bank has attenuation characteristics equal to or exceeding the third order Butterworth filters except in the passband ripples The original Third Octave Analyzer is defined using the analog Butterworth filter which has a flat frequency response in the passband range The S1 11 1986 accepts the use of a digital filter in the Third Octave Analyzer Therefore passband ripples are also acceptable Signal Processing Toolset 26 6 National Instruments Corporation Chapter 26 Third Octave Analysis Design e Type 3 The Type 3 D filter meets the following ANSI standards 200 millibels for peak to valley ripple 100 millibels for reference passband attenuation 30 millibels for linearity 41 millibels for white noise bandwidth error e The stopband attenuation is gt 65 dB Note The Sub Type Designator D in Type 3 D means that there are gt 100 millibels for composite bandwidth error National Instruments Corporation 26 7 Signal Processing Toolset Third Octave Filters VI This chapter describes the Third Octave Filters VI and its parameters Third Octa
133. define floatnum double typedef struct lutum vods 7 Lype of filter py hp bp os 7 intnum order order of filter intnum reset 0 don t reset 1 reset intnum a number of a coefficients floatnum a 7 pointer to a coefficients intnum nb number of b coefficients flostnum bs J p inter to b ecoetfticientese Inthum ns number of internal states Lloatnum ts 7 pointer to interme state array FilterStruct FilterPtr FilterPtr AllocCoeffDFD void long ReadCoeffDFD char coeffPath FilterPtr filterCoefficients double samplingrate long FilterDFD double inputArray long n FilterPtr filterCoefficients double outputArray long FreeCoeffDFD FilterPtr filterCoefficients Using the DFD Instrument Driver Add the DFDUTILS FP to your project and DFDUTILS H to your source code Now you can call the DFD utility functions in your C code An example called DFDXMPL PRJ in the CVI Support example subdirectory shows you how to call the DFD utility functions Signal Processing Toolset 22 4 National Instruments Corporation Chapter 22 Using Your Coefficient Designs with DFD Utilities AllocCoeffDFD FIleerPir IDLr APLOCCOSI IDED youd Purpose Allocates and clears the DFD filter coefficient structure You must call this function once to allocate the DFD filter coefficient structure properly Return Value FilterPtr Pointer allocated to filter structure Nation
134. derer petet Ce vta Rupe cdi epe Pudens 5 12 SLED SDOEUOEPADIE uico aote tec d EREN IPLE HISP Reps 5 12 Gabor SPCC OSE AUN uiv ha ed pom diede e Up QUERN TERR OE RUE 5 13 Adap ve SPCC lO CRAIN aae de cias Leve it souesseededewts 5 13 Pseudo Wigner Ville Distribution seessesese 5 14 Choi Williams Distribution ccceecccscccceeeeeeeeeeeeeeeens 5 14 Cone Shaped Distribution essen 5 15 Chapter 6 Frequently Asked Questions Chapter 7 JIFA References Chapter 8 JTFA Error Codes Part l Wavelet and Filter Bank Design Toolkit Chapter 9 Wavelet Analysis History OF Wavelet Analysts quee ettet epe tiia c vaste atoms assi E AES 9 Conventional Fourier TTEansfOLfh iere roo ee teta ax tn ease ele egeo E RRRra esae eee 9 Innovative Wavelet Analysis eite retra itin Ele serene HER x Fee ai 9 3 Wavelet Analysis vs Fourier Analysis eese nennen eene nnne 9 7 National Instruments Corporation vii Signal Processing Toolset Contents Applications of Wavelet Analysis essen nnn nnn nnn nnns 9 0 Discontinulty De te CHOD 3 non Cada oun dco duse sso eme to p euer ee arde reque 9 0 Ivf ltiscale AMAL VSIS s o queres di ena T a Ces pe UI UNDIS 9 11 CCG sass cn cpl cianssospindnltns oatduouat nan anacecaRicancuan ea eeoaten a 9 12 DEDO o t 9 13 Pertornidtce 158068224 sorore eptap Rd Ee Riv ca EUR HD oS DP dod det at Odin A Ra fabu ads 9 13 Chapter 10
135. determines the maximum number of rows of the spectrogram pli k National Instruments Corporation 4 11 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS z i t STFT Spectrogram of frequency bins determines the number of columns of the spectrogram plillk from Equation 4 4 It must be a power of two plil k is the cone shaped distribution error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions Computes the STFT based spectrogram DBL DBL m z Em P Signal Processing Toolset am TK spect ear H of frequency bins x i is the time waveform r i is the analysis window function of rows determines the maximum number of rows of the spectrogram pLil k of frequency bins determines the number of columns of the spectrogram pli l k from Equation 4 3 It must be a power of two plil k is the STFT spectrogram error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions 4 12 National Instruments Corporation Chapter 4 Joint Time Frequency Analysis VIS PWVD Pseudo Wigner Ville Distribution Computes the windowed Wigner Ville distribution Analytical Signal j P EEA E E S r ll plik als wp sar PuVD sta H of rows H of frequency bins Analytical Signal determines whether to process the analytical signal 3
136. divisible by dM1 rows determines the number of elements for the second index n1 132 of the Gabor coefficients It must be a power of two ens synthesis 2 is the cluster for the analysis window function of the column Wo gynthesis 2 ha k 187 pa a dM zi cols alt 28 Signal Processing Toolset 4 6 National Instruments Corporation Chapter 4 Joint Time Frequency Analysis VIS h2 k is the synthesis window function for the column of x i k DBL KA dM2 is the Gabor time sampling interval The length of the synthesis function h2 i must be evenly divisible by dM2 cols determines the number of elements for the fourth index n2 of the Gabor coefficients It must be a power of two DBL y il k is the reconstructed 2D signal error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions Fast Dual Computes the dual function of a given function h i Lengths of signal and bf T hfi rli erar Lengths of signal and h i are the same T determines if lengths of the signal and the window function h i are the same If the length of h i is the same as the analyzed signal the dual function solution of the given function h i is much broader However if the length of the signal is very long the dual function solution might not be realistic TF DEL h i is the analysis or synthesis window function dM is the Gabor time sampling inter
137. e near 0 0 Gs is the minimum acceptable stopband attenuation or filter magnitude response In Figure 20 7 the stopband specification has a minimum attenuation of 40 dB between the frequencies of 0 and fs 1500 Hz and between the frequencies of fs 3000 Hz and 4000 Hz The following ranges define the stopband lowpass PiS S SJ aw 2 20 10 National Instruments Corporation highpass bandpass bandstop where Chapter 20 Digital Filter Design Application O lt fsfs OSfSS5 f52 Sf Sfeamp 2 fs Sf 32 fs is passband frequency 1 fS gt is passband frequency 2 samp 18 the sampling rate The Classical IIR Design panel estimates the minimum filter order required for the selected type and design to meet or exceed the modified filter specifications The DFD application automatically computes other appropriate filter parameters and designs and plots the IIR filter You see immediate graphical feedback to help you determine whether the filter meets your specifications Classical IIR Design Panel Controls and Displays Use the design panel DFD Menu to complete the following tasks e Save your filter specifications and coefficients e Load filter designs from previous work e Open the Analysis or the DAQ and Filter panels e Transfer the IIR design specifications to the Classical FIR Design panel e Transfer the poles and zeros to the Pole Zero Placement panel e Return to the Main Menu panel The graph in Figure
138. e As order increases the Gabor spectrogram converges to the Wigner Ville distribution Computing time is related to order The higher the order the longer the computation time For most applications choose an order between three and five x i is the time waveform either a real valued or complex signal r i is the analysis function r 1 must be the dual function of the normalized Gaussian function in Equation 4 2 dM is the Gabor time sampling interval The length of the analysis function r i must be evenly divisible by dM of frequency bins controls the number of columns of p i k When the analyzed signal x i is a real value the number of columns of p i k is determined by Equation 4 3 When x i is complex the number of columns of p i k is equal to of frequency bins The of frequency bins must be a power of two The length of the analysis function r i must be evenly divisible by of frequency bins The ratio of of frequency bins to dM is the oversampling rate which must be greater than or equal to 1 the number of frequency bins dM oversampling gt 1 National Instruments Corporation 4 15 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS tolerance controls the precision of the resulting Gabor spectrogram The smaller the tolerance the more computation time required The default value is 107 of rows determines the maximum number of rows of the spectrogram plill
139. e condition 0 lt fc lt fs 2 20021 OrderGTZeroErr The order must be greater than zero order must be The order must be greater than zero than zero 20031 EqRplDesignErr The filter cannot be designed with the specified input values National Instruments Corporation 14 1 Signal Processing Toolset Chapter 14 Wavelet Error Codes Table 14 1 LabVIEW VI and LabWindows CVI Function Error Codes Continued 2003 nse Mphenumbesot oot denn E T number of coefficients must be odd for this filter 20034 OddSizeErr The number of coefficients must be even for this filter 20038 IntervalsErr The number of intervals must be greater than zero 20039 MatrixMulErr The number of columns in the first matrix is not equal to the number of rows in the second matrix or vector 20040 SquareMatrixErr The input matrix must be a square matrix 20041 SingularMatrixErr The system of equations cannot be solved because the input matrix is singular 20062 MaxIterErr The maximum iterations have been exceeded 20065 Zero VectorErr The vector cannot be zero Signal Processing Toolset 14 2 National Instruments Corporation Part lll super Resolution Spectral Analysis Toolkit This section of the manual describes the Super Resolution Spectral Analysis toolkit National Instruments Corporation Chapter 15 Introduction to Model Based Frequency Analysis introduces the basic concepts of mode
140. e largest 25 percent wavelet transform coefficients to rebuild the original image Among them the majority 93 22 percent are from the low low sub array The remaining three sub arrays contain limited information If you repeat the wavelet transform to the low low sub array you can reduce the compression rate further Signal Processing Toolset 10 12 National Instruments Corporation Chapter 10 Digital Filter Banks symmetric Data Figure 10 10 2D Image Decomposition National Instruments Corporation 10 13 Signal Processing Toolset Using the Wavelet and Filter Bank Design Toolkit This chapter describes the architecture of the Wavelet and Filter Bank Design WFBD toolkit lists the design procedures and describes some applications you can create with the WFBD toolkit This chapter also describes how to use the WFBD toolkit to design a desired wavelet and filter bank Although you can use it without understanding the fundamentals of wavelets and filter banks introduced in the previous two chapters for the best results National Instruments highly recommends that you review those chapters before you run the WFBD toolkit You can run the application by selecting Start Programs National Instruments Signal Processing Toolset Wavelet and Filter Bank Designer Wavelet and Filter Bank Design Figure 11 1 lists the choices of wavelets and filter banks available in the WEBD toolkit The design of wavelets and filte
141. e color table of the spectrogram National Instruments Corporation 5 9 Signal Processing Toolset Chapter 5 Joint Time Frequency Analysis Applications Read Data Save Result a spectrum Signal Processing Toolset Inputting Data Click the Read Data button to select the data file that you want to analyze The data file must be a 1D text file If the file contains x index remove it with any word processor before you analyze the data The lt lt and gt gt buttons move you to the previous or next block of data respectively Saving Results By selecting Save Result you can save any displayed data such as the time waveform power spectrum and spectrogram as a text file All spectrograms display only the non negative points The Offline Analyzer automatically truncates negative points to zero If you use log scale the displayed spectrogram is further normalized However real spectrograms except for the STFT and the adaptive spectrograms might contain negative values Save Result saves the real spectrogram without truncating or normalizing Switching Between Conventional Power and Instantaneous Spectrum Select spectrum to switch the spectrum display between a conventional power spectrum and an instantaneous spectrum When you select instant spectrum as shown in Figure 5 7 the cursor controls the time instant A group of indicators below the spectrum displays the cursor position 5 10 National Instruments
142. e of the four design selections in the Main Menu panel the DFD application loads and runs the selected design panel You can use these design panels to design IIR or FIR filters save your design work and filter coefficients or load previous filter designs After designing your filter you can move from the design panels to the Analysis of Filter Design panel to view various frequency domain and time domain filter responses You can save these responses to text files for use in other applications You also can perform real world testing of your filter designs by moving to the DAQ and Filter panel which performs data acquisition and filtering in parallel with your filter designing National Instruments Corporation 20 3 Signal Processing Toolset Chapter 20 Digital Filter Design Application Common Controls and Features The following sections describe the controls and features of the DFD application Using the DFD Menu All four filter design panels the Analysis of Filter Design panel and the DAQ and Filter panel have a DFD pop up menu from which you can select a number of options Figure 20 3 shows the DFD pop up menu for the Classical IIR Design panel The following sections describe each DFD Menu option v DFD Menu cave Spec Load Spec Analysis DAC and Filter xr Classical FIR er Pole ero Main Menu Figure 20 3 DFD Pop Up Menu Saving Filter Specifications To save all your sp
143. e on the measurement displays of the front panel to make precise measurements 1 Setup VirtualBench DSA to display a waveform in one of the measurement displays 2 Select Dual or Harmonic Markers from the Display Settings control to turn on markers on the display 3 Move the cursors on the display by dragging them with the mouse or use the Marker control for fine positioning With Harmonic Markers you can move only marker m1 Markers m2 m3 and so on appear automatically at the second third and so on harmonic frequency Marker ml is considered the fundamental frequency With Dual Markers you can move both m1 and m2 You can use the Marker display to determine the exact positions of markers m1 and m2 and the distance between them on the x axis and y axis Loading Reference Waveforms Waveforms that you have saved to disk are called reference waveforms They can be loaded into either measurement display of the front panel To do so complete the following steps 1 Click on Run or Single to stop data acquisition 2 Select File Load Reference Waves 3 Select the name of the reference waveform file Click OK Signal Processing Toolset 31 10 National Instruments Corporation Chapter 31 VirtualBench DSA 4 Select a measurement display for each reference waveform in the file in the Load Reference Waveforms dialog box as shown in Figure 31 8 Notice that you can load only one reference waveform into a measurement displ
144. e phase The parameter number of samples determines the size of the data set The model based analysis heavily uses matrix computation which is computationally expensive National Instruments highly recommends that you limit the number of samples to less than a few hundred because of the computing time and memory space considerations As shown in Figure 18 6 you can adjust the intensity of the additive Gaussian white noise by using the Gaussian white noise control As mentioned in Chapter 15 Introduction to Model Based Frequency Analysis the results of model based analysis are sensitive to the intensity National Instruments Corporation 18 5 Signal Processing Toolset Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation Signal Processing Toolset and type of noise The performance of model based analysis deteriorates substantially as the intensity of noise increases or the noise is other than Gaussian white noise Once you click the Quit button or change the set of the Select Test Data ring control in the main panel the Synthetic Data panel automatically disappears The default value of number of samples is 50 Table 18 1 lists the default sinusoid parameters Table 18 1 Default Sinusoid Parameters Damping Sinusoid Amplitude Phase Factor Frequency When number of samples is 50 you can see that both FFT based and model based methods separate two different frequencies well If you reduce number of sa
145. e to build in block diagram form Segment of time domain data G 4 National Instruments Corporation front panel function global variable GPIB H halfband filter Help Help window National Instruments Corporation G 5 Glossary Interactive user interface of a VI Modeled after the front panel of physical instruments it is composed of switches slides meters graphs charts gauges LEDs or other controls or indicators Built in execution element comparable to an operator function or statement in a conventional language Graphical programming language used to develop LabVIEW and Bridge VIEW applications Non reentrant subVI with local memory that uses an uninitialized shift register to store data from one execution to the next The memory of copies of these subVIs is shared and thus can be used to pass global data between them General Purpose Interface Bus Common name for the communications interface system defined in ANSI IEEE Standard 488 1 1987 and ANSI IEEE Standard 488 2 1987 A filter with a cut off frequency at a half of the frequency band Online instructions that explain how to use a Windows application The Help menu displays specific Help topics Pressing lt F1 gt displays a list of Help topics Special window that displays the names and locations of the terminals for a function or subVI the description of controls and indicators the values of universal constants and descriptions
146. e you run time control over the format of the x scale and y scale markers You use the remaining three buttons to control the operation mode for the graph The plus or crosshatch indicates that you are in standard operate mode In operate mode you can click in the graph to move cursors around When you click the Panning Tool you switch to a mode in which you can scroll the visible data by clicking and dragging sections of the graph When you click the Zoom Tool you can zoom in on a section of the graph by dragging a selection rectangle around that section If you click the Zoom Tool a pop up menu opens in which you can choose other methods of zooming Figure 20 5 shows this menu Zoom Figure 20 5 Zoom Tool Pop Up Menu The Zoom Tool pop up menu contains the following buttons Zoom by rectangle Zoom by rectangle with zooming restricted to x data The y scale remains unchanged Zoom by rectangle with zooming restricted to y data The z scale remains unchanged Undo last zoom Resets the graph to its previous setting Zoom in about a point If you click and hold the mouse button on a specific point the graph continuously zooms in until you release the mouse button Shift click to zoom in the opposite direction Zoom out about a point If you click and hold the mouse button on a specific point the graph continuously zooms out until you release the mouse button Shift click to zoom in the opposite direction 2
147. easing N dramatically increases the time needed to compute the FFT and makes the Third Octave Analyzer impractical Therefore you should reduce the sampling frequency for lower frequency bands Most data acquisition devices have a limited choice of sampling frequencies At any given time only one sampling frequency is chosen The hardware sampling frequency should be selected according to the highest center frequency that you analyze as shown in Table 26 1 26 2 National Instruments Corporation Chapter 26 Third Octave Analysis Design After you select the hardware sampling rate the Third Octave Analyzer uses a lowpass filter to remove unwanted high frequencies and then takes every 10th data point to lower the sampling frequency This process is called decimation For example a 100 point data block would contain only 10 points after decimation Table 26 2 shows how different sampling rates apply to the different third octave filters Table 26 2 also shows the frequency resolution in each group assuming that you used a 512 point FFT size Table 26 2 Different Sampling Frequencies Sampling Frequencies Group 3 ANSI 7 16 ANSI 10 19 ANSI 13 22 first 10 filters f 128 Hz f 256 Hz J 512 Hz Af 0 25 Hz Af 0 5 Hz Af 1 Hz Group 2 ANSI 17 26 ANSI 20 29 ANSI 23 32 middle 10 filters f 1 28kHz f 2 56kHz f 5 12 kHz Af 2 5 Hz Af 5 Hz Af 10 Hz Group 1 ANSI27 37 ANSI30 40 ANSI 33 43 last 11 filters f 212 8kHz
148. ecifications for the present filter design panel select DFD Menu Save Spec The DFD application prompts you for the name of the filter specification file to save National Instruments suggests that you name your spec files appropriately for a given filter design For example if you design a lowpass IIR filter name the file lowpass iir Or lowpl iir if this design is the first of many lowpass IIR designs Table 20 1 lists suggested filename extensions for the four filter design panels These names have no effect on how the DFD application interprets the file contents Signal Processing Toolset 20 4 National Instruments Corporation Chapter 20 Digital Filter Design Application Table 20 1 Suggested Specification Filename Extensions Design Panel Filename Loading Filter Specifications To load a filter specification file into the present filter design panel select DFD Menu Load Spec The DFD application prompts you for the location of the filter specification file to load If the selected spec file is the same type design as the present design panel the DFD application loads the specification from the selected file into the present design panel for viewing editing or analysis If you designed the selected spec file in a different design panel than the present panel the DFD application prompts you to open the appropriate design panel for that specification file For example if you are using the Pole Zero Placement panel a
149. econd order stages You can view the N z and D z polynomials for other stages by incrementing the index shown in the upper left side of the H z display H z for FIR Filters H z is the z transform of the designed digital filter as shown in Figure 20 31 You can scroll through H z using the scroll bar Hiz 0 00635 0 008832 1 0 028482 2 045272 7 3 0 04104z 4 0 11146z 5 0 014132 6 0 181082 0 059852 6 n nunmo3s 9 AACA an NICIO 14 Figure 20 31 H for FIR Filters 20 34 National Instruments Corporation Chapter 20 Digital Filter Design Application For an FIR filter H z can be represented as a polynomial in z order 1 H z hz where j 0 1 order 1 h represents the FIR filter coefficients order is the number of FIR coefficients DAQ and Filter Panel Figure 20 32 shows the DAQ and Filter panel Use this panel if you have a National Instruments DAQ device and you want to see how the current filter design performs on real world signals or if you want to check the performance of your filter with a simulated signal In this panel you can configure your DAQ device and acquire real signals The acquired data passes through the designed filter and the DFD application plots the input and output waveforms and spectrums I DAO and Filter File Edi Operate Project Windows Help DFD Menu Y gs MATIOMAL Eae TRU EH TE Input Time Output Time Filter De
150. ed has two forms one for real and the other for complex valued samples The real VIs work only for real valued data sets and the complex VIs work for both real and complex samples Using a complex VI on the real valued samples is at least two times slower than using the real VIs As shown in Figure 17 1 the real and complex VIs have except for the data type of the input array x n the same inputs and outputs The icons for the complex VIs include the letter C in the upper left corner This chapter includes only the VIs for real valued samples You can find descriptions of error codes in Appendix B Error Codes of the LabVIEW Function and VI Reference Manual n AR coefficients 4I C AR coefficients AR order cova roots AP arder cover rante nose estimation Hose estimatian covariance Yi Complex Covariance vi Figure 17 1 Real and Complex Covariance VIs Computes the AR coefficients and the corresponding roots by the covariance method s n AH coefficients AR order cova a nose estimation DEL x n is the time waveform AR order determines the order of the auto regressive model The selection of the AR order is crucial and directly affects the accuracy of the National Instruments Corporation 17 1 Signal Processing Toolset Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs DBL COB E estimation However you can apply the MDL vi to estimate the AR order if you are not sure wha
151. ee an E OEE 3 9 Cone Shaped Dist Dit OM ee o ertt e n Op a dene vsu Uo EI e RE 3 10 Gabor Speco Falls or samen Saad e esocec voto sro Shan oeesennewaiudeenvanstanaku ec LUE do Maca Deque 3 11 Adaptive Spectosra M ereman EE lobos odoris uta bio rasa PRSE UR 3 13 Chapter 4 Joint Time Frequency Analysis VIs Adaptive TEOBSEOEDIES e Gast vibus bbs Penieesoct i ta gach EO i cues Una e Unda e ie DEM ees RE 4 IiversezXdapttve LranstfOEIIs odio ico od e ep bate tope Lu e a o eue S ue eect tates 4 2 Short Time Fourier Transform 00 00ss0esseeessseessssssseesseecessceeeseceeeeeceeeerecensecenss 4 3 Gabor EX Pans 1 OM cients weiter esee ceecauoe D LOAD ed EM S Ln uas eds n tiec LA dE 4 4 4 B sd Ocul REED N AEEA A EEN 4 4 PIBEGeda qoot T A TT 4 6 DaSpDUdl od ocuto d Ei dS e NIME ESL cm reer ere Teeter err DC MIS DLE 4 7 Normalized Gaussian Window Function ccccccccccccccecceceeeceeeceeeeeeeeseseaeseeeaeeeaaeaaaaaaas 4 8 Adap ive SPEC TOSTA sii aa betont E bote teftc me tanto UMP apa uis 4 9 OMENS CASS mr 4 10 CWD Choi Williams Distribution 20 0 0 cece cceeccceesecccesecceesscceeescseseeccsseessseueseseenss 4 10 Cone haped DISEHDULIOT 55 oie as sss eres saa estes E eae antes 4 11 STEF SPC CO Sian oeno ortu Union nE ENEON 4 12 PWVD Pseudo Wigner Ville Distribution eeseeeeeeeeeeeen 4 13 Gabor Spectrogram Gabor Expansion Based Spectrogram suus 4 14 TimesBrequency Distribu
152. el Use this panel to design arbitrary magnitude FIR digital filters Enter or modify the array magnitude response points frequency and magnitude From these points the DFD application forms a desired magnitude response that covers the entire frequency range from 0 0 to Nyquist half the sampling rate The DFD application then processes this desired response along with the filter order and uses the Parks McClellan algorithm to design an optimal equiripple FIR filter The Parks McClellan algorithm minimizes the difference between the desired and actual filter response across the entire frequency range To design arbitrary magnitude FIR filters enter or modify the desired frequency magnitude points and choose an interpolation type to generate National Instruments Corporation 20 25 Signal Processing Toolset Chapter 20 Digital Filter Design Application DFO Menu Signal Processing Toolset the desired response between your specified points The DFD application automatically designs and plots the equiripple FIR filter You see immediate graphical feedback to help you determine whether the filter meets your specifications Arbitrary FIR Filter Design Panel Controls and Displays Use the design panel DFD Menu to complete the following tasks e Save your filter specifications and coefficients e Load filter designs from previous work e Open the Analysis or the DAQ and Filter panels e Return to the Main Menu panel The graph
153. elay Figure 12 4 shows how to build a two channel perfect reconstruction system using the Decimation Filter VI and the Interpolation Filter VIs The x i and y i arrays are the same In this example the initial condition and final condition arrays are constructed as zero padding You can construct any values in initial condition and final condition as long as the sizes meet the requirements previously mentioned If these requirements are met you receive the same y i as x i Ej Initial Condition and Final Condition arrays 2 channel analysis 2 channel synthesis filter bank filter bank 2 IP Highpass Analysis Filter Bank Synthesis Filter Bank Figure 12 4 Two Channel Perfect Reconstruction System This VI is a subVI of the 2 Channel Analysis Filter Bank VI which limits the initial condition and final condition to two cases zero padding and symmetric extension Truncated Decimation Filter VI This VI performs a truncated decimation filter extension w i h k decimate factor extension decides the initial condition and final condition extension has two options 0 zero padding changes all the initial conditions and final conditions to zeros 1 symmetric extension extends signal x i symmetrically as the initial condition and final condition National Instruments Corporation 12 13 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Refer to the Analysis Filter Bank VI for
154. ency and magnitude indicators display the location of the 275000 13 304 tracking transparent square cursor This cursor is locked to the frequency response H f so moving this cursor updates the frequency and magnitude digital displays with data points from H f National Instruments Corporation 20 17 Signal Processing Toolset Chapter 20 Digital Filter Design Application Signal Processing Toolset You can enter the complete filter specifications using the text entry portion of the design panel as shown in Figure 20 12 passband resp 5 0000 passband freq 1900 00 2600 00 stopband atten 40 00 stopband freq 1500 00 3000 00 sampling rate 8000 00 type bandpass Figure 20 12 Text Based Interface The passband response is the minimum gain in the passband The horizontal blue cursor line represents this response in the Magnitude vs Frequency plot In the passband the filter gain is guaranteed to be at least as high as the specified passband response Gp IH f 2 Gp The first passband frequency defines one frequency edge of the passband The first vertical blue cursor line represents this frequency in the Magnitude vs Frequency plot The second passband frequency defines the second frequency edge of the passband The second vertical blue cursor line represents this frequency in the Magnitude vs Frequency plot The stopband attenuation is the minimum attenuation in the stopband The horizontal
155. ency bins is not evenly divided by the window length The oversampling rate N dM is less than one 2082 GaborOversamplErr The oversampling rate N dM is less than one 2083 JTFANoSolutionErr The dual function does not exist 2084 JTFAWindowErr The window length is not an integral multiple of the number of frequency bins N 2085 JTFAParametErr The order of the Gabor spectrogram is less than zero The number of terms of the adaptive transform is less than zero 2086 JTFATimeSamplErr The Gabor coefficient array is empty 2087 JTFAHilbertErr The sample length is not equal to the length of the corresponding Hilbert transform 2088 JTFADecimatErr The time decimation is greater than the sample length 2001 The matrix is near ill condition The matrix is near ill condition is near ill condition National Instruments Corporation 8 1 Signal Processing Toolset Part ll Wavelet and Filter Bank Design Toolkit This section of the manual describes the Wavelet and Filter Bank Design toolkit e Chapter 9 Wavelet Analysis describes the history of wavelet analysis compares Fourier transform and wavelet analysis and describes some applications of wavelet analysis e Chapter 10 Digital Filter Banks describes the design of two channel perfect reconstruction filter banks and defines the types of filter banks used with wavelet analysis e Chapter 11 Using the Wavelet and Filter Bank Design Toolk
156. ents SynthesisFilter FilterBankPtr The structure that holds the synthesis filter bank coefficients If this pointer is set to NULL the function does not read the synthesis filter bank coefficients Return Value Aus 08 XN Rese AEN 1 to Chapter 14 Wavelet Error Codes for a description of the error National Instruments Corporation 12 37 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Synthesis2DArraySize long status Synthesis2DArraySize long nsize 8 long nl long nh long rows long cols Computes the size of the 2D output array for SynthesisFilterBank2D Call this function to compute the sizes for the output array before calling SynthesisFilterBank2D Parameters Input long integer array The array contains all the size information of four input arrays for the SynthesisFilterBank2D The array size of nsize must be 8 Assume the four input arrays are low low low high high low and high high then nsize 0 the number of rows of array low low nsize 1 the number of columns of array low low nsize 2 the number of rows of array low high nsize 3 the number of columns of array low high nsize 4 the number of rows of array high low nsize 5 the number of columns of array high low nsize 6 the number of rows of array high high nsize 7 the number of columns of array high high Signal Processing Toolset 12 38 National Instruments Corporation Chapte
157. eous Spectrum Display essen 5 11 Figure 6 1 STFT Spectrogram Hanning Window essen 6 4 Figure 6 2 Gabor Spectrogram Order Four sese 6 5 Figure 9 1 Sum of Two Truncated Sine Waveforms ssseeeeeeeee 9 2 Fear oe Wavelet ci oie dt ND apte E i a ORE compo Seu E 9 4 Dibure 9 5 Wave Analysis ses auno Ubaldo rep e Le sanete Ioa bat eee 9 6 Figure 9 4 Short Time Fourier Transform Sampling Grid sssss 9 7 Figure 9 5 Wavelet Transform Sampling Grid sess 9 8 Figure 9 6 Comparison of Transform Processes ccccccccccccccceceeeeeeesesseeentneeeeeeees 9 9 Pioure9 7 JDetecton or DIScont tulby oor quse sue edie ae FU Oa Edad 9 10 Pieure 9 8 Multiscale Analysts eode rice tox Desa st ves eed qx cba ere eR Ue eon UE 9 11 Lieure 9 9 Denen hex deieniv hotte tC ep D Dpto ubl ete ep D Eolo fnt ibn Und 9 12 Pede 910 Denoi Grea el wien hoa etn ema 9 13 Figure 10 1 Two Channel Filter Bank essiccare E E AAS 10 1 Figure 10 2 Relationship of Two Channel PR Filter Banks and W avelet Transfo si ede cue terio a UN IE T LUR ES toe iduads 10 2 Figure 10 3 Filter Bank and Wavelet Transform Coefficients 10 3 Fiege 0 4 Hallband Ee dioi eb ipsun nexus toda Deus Roe a ee WEN RU UNR URS 10 6 Figure 10 5 Zeros Distribution for 1 Z Q Z cccecccesscesscssecesecssecsseessees
158. er Ville Distribution The pseudo Wigner Ville distribution is fast and provides high time frequency resolution However it might suffer from serious crossterm interference if the analyzed signal consists of multiple components You can lessen the crossterm interference two ways First you can take the pseudo Wigner Ville distribution with respect to the analytical function by setting analytic to ON However this approach destroys the low frequency portion of the signal s time dependent spectrum Second you can reduce Gauss window var to eliminate the crossterm caused by a pair of autoterms separated in time However reducing Gauss window var deteriorates time frequency resolution Choi Williams Distribution The Choi Williams distribution is designed to reduce crossterm interference while preserving as many useful Wigner Ville distribution properties as possible Like the pseudo Wigner Ville distribution you can take the Choi Williams distribution with respect to the analytical function by setting analytic to ON The resulting spectrogram has reduced crossterm interference You also can lessen crossterm interference by setting the control paramet In general the smaller the paramet value the less crossterm interference but the poorer the time frequency resolution paramet defaults to a value of 1 5 14 National Instruments Corporation Chapter 5 Joint Time Frequency Analysis Applications Cone Shaped Distribution eth
159. ernal Data Averaging section in Chapter 26 Third Octave Analysis Design for more information Click OK to accept the new internal average settings or Cancel to go back to the original setting Running the Third Octave Analyzer When you finish setting all the parameters in the Setup dialog box click the Done button Then the analyzer begins to acquire data performs third octave analysis and displays the power results on the front panel The analyzer shows both the power values and the corresponding center frequencies The Third Octave Analyzer displays the graphs only for the channels you choose Figure 25 3 shows a four channel analyzer panel Only one two or three graphs appear if you choose only one two or three channels National Instruments Corporation 25 5 Signal Processing Toolset Chapter 25 Operating the Third Octave Analyzer You can use the Operating Tool to position the cursors shown as thin vertical lines with an asterisk in each channel chart in Figure 25 3 Move the cursors left and right to display the power value in each band Two indicators show the center frequency of each band and the corresponding power value Center Power Frequency Value Cursor ea pe Third Octave Analyzer olx File Edi Operate windows Help 2000 0 Hz 57 01 dB Cho 1250 0 Hz 5714 dB Chi 0 A0 100 150 EL m 3150 Hz 57 25 dB Ch 2000 0 Hz 56 B dB Ch3 start 10 0Hz stop 10 0 kHz Figure
160. esee 20 6 Returning to the Main Menu sse 20 7 Panning and Zooming Options cccccccccccccecccceceecececeeeeeeeseeeeeeeeeess 20 7 Graph CUPS OLS RP n T vp S 20 9 Signal Processing Toolset X National Instruments Corporation Contents Classical HR Filter Desire T pui dedi RED B DUE PR CO P pua cuo eec ue URNA 20 9 Classical IIR Design Panel Controls and Displays 20 11 Classical EIR IDOSIPTL oo oreet ou obe eon odds domu edes ce Eve URN Rt Nd E Rap ews 20 14 Classical FIR Design Panel Controls and Displays 20 16 Pole Zero Placement Filter DeSsio9Tis i i REED D EMI AEEA aa 20 19 Pole Zero Placement Panel Controls and Displays 20 21 Arbi Tay PUR Pru c 20 25 Arbitrary FIR Filter Design Panel Controls and Displays 20 26 Analysis of Filter Desren Pahbeli cuo it ob ovest qus Peur RS RI EE EPprE us 20 30 Apalysis DIS play Tr T 20 32 Magnit de Response o ex vom eerte a a ses 20 32 Phase RESPONSE osadena qu de kate obuia is 20 32 Impulse RESPONSE Sont Eo B D RR Doo CO ERA 20 33 SIEDReSDODSG catt etus eo Co pup Ev DUE ct dod edet ed boe Ue La PR Rie 20 33 Ze Plane PIOUsosc nb DM Moldau nta ed cM 20 33 HOO TOF HRPICGES 2 titio ERE IE Noe ad Ded eodeni 20 34 HO HOLBIR FIE SS ovecdio reo etn eevee 20 34 DAC and pter Tale i565 meist neci os acantecel tease AA 20 35 Chapter 21 IIR and FIR Implementation Hinte Impulse Response Filte
161. estrictions On the other hand it is not unique Unlike the case of conventional Fourier transform in which the basis functions must be complex sinusoidal functions you can select from an infinite number of mother wavelet functions Therefore the biggest issue of applying wavelet analysis is how to choose a desired mother wavelet y t It is generally agreed that the success of the application of wavelet transform depends on the selection of a proper wavelet function e Because the scale factor m could go from negative infinity to positive infinity it is impossible to make the time index of the wavelet function 2 t n2 an integer number simply by digitizing t as i where A denotes the time sampling interval This problem prohibits us from using digital computers to evaluate wavelet transform Fortunately researchers discovered a relationship between wavelet transform and the perfect reconstruction filter bank a form of digital filter banks You can implement wavelet transform with specific types of digital filter banks known as two channel perfect reconstruction filter banks Chapter 10 Digital Filter Banks describes the basics of two channel perfect reconstruction filter banks and the types of digital filter banks used with wavelet analysis Signal Processing Toolset 9 14 National Instruments Corporation Digital Filter Banks This chapter describes the design of two channel perfect reconstruction filter banks and
162. et the following condition ni nf nl nh 2 1 where nl is the size of the analysis lowpass filter nh is the size of the analysis highpass filter You can use this function to build a 2 channel analysis filter bank Signal Processing Toolset 12 32 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference FreeCoeffWFBD long err FreeCoeffWFBD FilterBankPtr fptr Use this function to free the WFBD filter bank coefficients structure and all of its coefficients arrays Parameters Input fpe FilterBankPtr Pointer to allocated filter bank structure Return Value err integer Refer to Chapter 14 Wavelet Error Codes for a description of the error National Instruments Corporation 12 33 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference InterpolationFilter long status InterpolationFilter double x long nx double coef long nf long interfact double y long ny Performs an interpolation filter It performs the same operation as the Interpolation Filter VI Refer to the description for that VI for more information You can use this function to build a 2 channel synthesis filter bank Parameters Input X double precision The input data array array double precision The array of filter coefficients array ny long integer The size of output array y it must be nx x interfact nf 1 Output e double precision Teen enone output from the interpolat
163. ets and filter banks by using the Design Panel To access the Design Panel open WaveMain 11b and open Design Panel This VI opens the panel shown in Figure 11 6 If you do not have LabVIEW run wfbd exe The first panel to appear is the Design Panel Use the Design Panel to complete the three steps in the following Designing Wavelets and Filter Banks section Refer to Chapter 10 Digital Filter Banks for background information on wavelets and filter banks Design Panel Step 1 Type of Filter Banks i Frequency Response 0 6 0 8 1 0 7 of Go z and G z zero pairs at 7r Step 2 Type of Po z Step 3 1 00 Zero Distribution 405 ooo 100 200 319 x Go z zeros at T 4 I 5 5 55 o Ho z zoom jj vt sess Figure 11 6 Design Panel Signal Processing Toolset 11 6 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Designing Wavelets and Filter Banks The three steps in designing wavelets and filter banks are as follows 1 Select the type of filter bank You can select from two types of wavelets and filter banks orthogonal and biorthogonal You can design orthogonal filters and wavelets easily because they involve fewer parameters but the filter banks cannot be linear phase Find the product Po 2 Po z denotes the product of Go z and Ho 2 Po z Go z Ho Z i Note In the WF BD toolkit G denotes an a
164. f 225 6kHz f 251 2 kHz Af 25 Hz Af 50 Hz Af 100 Hz The frequencies in Group 1 are actual hardware sampling rates and the other groups show rates obtained by using the decimation technique The filters in Group 2 have one tenth the sampling rate of those in Group 1 and the filters in Group 3 have one tenth the sampling rate of the Group 2 filters By reducing the sampling frequency in this way there is enough frequency resolution for all the octave filters The size of the FFT N remains fixed at 512 points When you run the analyzer it gathers 51 200 data points at the higher frequencies and computes a 512 point FFT The analyzer modifies the frequency data from the FFT according to a predetermined weighting function to obtain the output of the 11 third octave filters in Group 1 The analyzer then decimates the data block to get the data at the next lower sampling frequency and computes the second 512 point FFT Finally it decimates the data block again to get the data at the lowest frequencies and computes National Instruments Corporation 26 3 Signal Processing Toolset Chapter 26 Third Octave Analysis Design the third 512 point FFT In this way the analyzer obtains and displays 31 bands of power output Figure 26 1 shows this design procedure i Lowpass Filter Display 512 point FFT 20kHz 11 Weighting Functions Figure 26 1 Multistage Third Octave Analyzer Design Using FFT With the analyzer you a
165. f wavelet analysis originally was motivated by the desire to overcome the drawbacks of traditional Fourier analysis and short time Fourier transform STFT processes Fourier transform characterizes the frequency behaviors of a signal but not how the frequencies change over time STFT or windowed Fourier transform simultaneously characterizes a signal in time and frequency You can encounter a problem because the signal time and frequency resolutions are fixed once you select the type of window However signals encountered in nature always have a long time period at low frequency and a short time period at high frequency This suggests that the window should have high time resolution at high frequency To understand the fundamentals of wavelet analysis start with an artificial example National Instruments Corporation 9 1 Signal Processing Toolset Chapter 9 Wavelet Analysis Signal Processing Toolset Figure 9 1 shows a signal s t that consists of two truncated sine waveforms The first waveform spans 0 second to 1 second and the second waveform spans 1 second to 1 5 seconds In other words the frequency of s t is 1 Hz for O lt t lt 1 and 2 Hz for 1 lt t lt 1 5 Figure 9 1 Sum of Two Truncated Sine Waveforms When describing frequency behavior you traditionally compare s t with a group of harmonically related complex sinusoidal functions such as expl j27kt T Here the term harmonically related complex sinusoidal fu
166. fficients poln is odd N 1 Signal Processing Toolset 10 6 National Instruments Corporation Chapter 10 Digital Filter Banks Figure 10 5 plots the zeros distribution of a maximum flat filter Po z for p 3 2 bl 2 00 1 50 1 00 0 50 a 1 107 l l l l l l l l l l 2 00 1 50 1 00 0 50 0 00 0 50 1 00 1 50 200 250 3 00 Figure 10 5 Zeros Distribution for 1 z 6Q z There are six zeros at 7 In this case the order of the unique polynomial Q z 1s four which contributes another four zeros not on the unit circle If you let three zeros at T go to Go z according to the formula Gy ez y and the rest of the zeros go to Ho z you obtain B spline filter banks The coefficients of go n and g n and the corresponding scaling function and mother wavelet are plotted in Figure 10 6 Both the scaling function and mother wavelet generated by eo n and g n are smooth Scaling Functian r Mother Wavelets Figure 10 6 B Spline Filter Bank National Instruments Corporation 10 7 Signal Processing Toolset Chapter 10 Digital Filter Banks Figure 10 7 depicts the dual filter bank Ag n and h n and corresponding scaling function and mother wavelet You also can use Aig n and h n for analysis In Figure 10 7 the tree filter banks constituted by Ag n and h n do not converge Scaling Func
167. ficients Figure 11 15 Implementation of a Wavelet Packet National Instruments Corporation 11 19 Signal Processing Toolset WFBD Toolkit Function Reference This chapter describes the VIs in the WFBD toolkit the instrument driver for LabWindows CVI and the functions in the DLLs LabVIEW VI Applications This section contains the VIs you can use when operating the WFBD toolkit with LabVIEW Analysis Filter Bank VI This VI computes the outputs of an analysis filter bank fi Analysis Filter Bank extension perfect reconstruction 7 eee x i is the input data array DEL Analysis Filter Bank contains the analysis filter bank coefficients DEL Lowpass contains the lowpass analysis filter coefficients GO DBL Highpass contains the highpass analysis filter coefficients Gl extension decides the initial condition Xi and final condition Xf extension has two options 0 zero padding changes all the initial conditions and final conditions to zeros 1 symmetric extension extends signal x i symmetrically as the initial condition and final condition National Instruments Corporation 12 1 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference TE perfect reconstruction determines if the results can be reconstructed yl is the output of analysis highpass filter y0 is the output of analysis lowpass filter error Refer to Chapter 14 Wavelet Error Codes for a description of the er
168. g part of this manual Signal Processing Toolset The Signal Processing Toolset contains the Joint Time Frequency Analysis toolkit the Wavelet and Filter Bank Design toolkit the Super Resolution Spectral Analysis toolkit the Digital Filter Design toolkit the Third Octave Analysis toolkit and the VirtualBench DSA This software performs various specialized signal processing tasks such as finding the power spectrum of a signal representing signals in the joint time frequency domain and interactively designing digital filters and wavelets You can use the Signal Processing Toolset with programming environments such as LabVIEW LabWindows CVI or Microsoft Visual Basic The diverse applications for the toolset include acoustics radar sonar seismology remote sensing instrumentation and vibration analysis Joint Time Frequency Analysis Toolkit Using the Joint Time Frequency Analysis toolkit you can enhance computer based signal processing on nonstationary signals Applications include speech processing sound analysis sonar radar machine testing vibration analysis and dynamic signal monitoring The Joint Time Frequency Analysis toolkit provides several algorithms for applications in which the frequency content of a signal varies with time These algorithms include the award winning and patented Gabor spectrogram the Wigner Ville distribution the Choi Williams National Instruments Corporation 1 1 Signal Processing Toolse
169. gnals However it is unclear based on a alone when the 1 Hz or the 2 Hz components exist in time There are many ways of building the frequency tick marks to measure the frequency behavior of a signal By using complex sinusoidal functions not only can you analyze signals but you also can reconstruct the original signal with the Fourier coefficient a For example you can write s t in terms of the sum of complex sinusoidal functions according to the following formula traditionally known as Fourier expansion s t y aye 0 y aeroj jZ 9 1 k 00 ESEA where a is the Fourier coefficient and 27k T is the frequency tick mark In this equation because a is not zero for all k you must use an infinite number of complex sinusoidal functions in Equation 9 1 to restore s t in Figure 9 1 Innovative Wavelet Analysis Looking at s f more closely you find that to determine the frequency contents of s t you need information regarding only one cycle such as the time span of one cycle With this information you can compute the frequency with the following formula 1 frequency time span of one cycle According to this equation the higher the frequency the shorter the time span Therefore instead of using infinitely long complex sinusoidal functions you can use only one cycle of a sinusoidal waveform or a National Instruments Corporation 9 3 Signal Processing Toolset Chapter 9 Wavelet
170. gth algorithm introduced later in this chapter Because AR based algorithms have been better understood and are more popular than their counterparts the rest of this section of the manual limits the discussion to AR based methods Model Coefficients and Power Spectra Taking the z transform of Equation 16 1 yields a rational transfer function q 1 bz _ BR _ m 1 E z xa n n HG 16 6 az It can be proved that the power spectrum P f is P z evaluated along the unit circle where B z B 1 27 2 A z A 1 z P z H 2 H 1 z o 16 7 where denotes the complex conjugate For the AR model the power spectrum is 2 aE 16 8 d i2 A ZTU us y e f k 1 which implies that once you compute the coefficients a of the AR model you readily can obtain the power spectrum by taking the reciprocal of the fast Fourier transform FFT of a If A z is the z transform of the coefficients a as shown in Equation 16 6 it can be shown that p A 1 z 1 V ap z k 1 National Instruments Corporation 16 3 Signal Processing Toolset Chapter 16 Model Based Frequency Analysis Algorithms While A z X z forms the forward prediction A 1 z X z constitutes a backward prediction P x n X a x n k for0 lt n lt N 16 9 k 1 which uses future data to predict the data that was sampled at p steps before The formula in Equation 16 9 of the backward prediction can be written as x 1 x 2
171. h n contains the FIR filter coefficients new file path is the file path to the coefficient file read If coefficient file path is empty the new file path contains the path to the file selected from the open file dialog file error is set to TRUE if an error has occurred while reading or interpreting the coefficient file 22 2 National Instruments Corporation DFD Filter Chapter 22 Using Your Coefficient Designs with DFD Utilities Filters the input array X using the DFD coefficient cluster Use the Read DFD Coefficients VI to read your DFD DBL zm DBL DBL coefficient files and properly initialize the input Coefficient Cluster ls g Filtered X Coefficient Cluster SA n init cont nit F X contains the array of input samples to filter Coefficient Cluster is the cluster of coefficient information read from the coefficient file The Coefficient Cluster contains the following parameters coefficient type is either O IIR or 1 FIR sampling rate is the sampling rate in hertz IIR Filter Cluster is the cascade IIR filter cluster h n specifies the FIR filter coefficients init cont init F controls the initialization of the internal filter states When init cont init F is FALSE default the internal states are initialized to zero When init cont init F is TRUE the internal filter states are initialized to the final filter states from the previous call to this instance of this VI To fi
172. h the same frequency center crossterm 1 The cone shaped distribution is faster than the CWD method current data gauss3 t t gaussi tst Est data length sec 1 28E zl spectrum E 4 0E 2 3 0E 2 2 0E 2 1 0E 2 0 0E 0 2 DE 0 HET 0 sec a 01E 2 Hz sec l ro DE 4D 2 0E 2 4 JE 2 6 0E 2 5 0E 2 1 0E 1 1 3E 1 EAr t contral Figure 3 7 Cone Shaped Distribution 1 for the Three Tone Test Signal Signal Processing Toolset 3 10 National Instruments Corporation Chapter 3 Joint Time Frequency Analysis Algorithms Gabor Spectrogram In addition to applying the Pseudo Wigner Ville distribution window method you can apply the Gabor expansion to a signal to identify the significance of each term to the signal s energy at point i k You can then preserve those terms that have major contributions at point i k and remove those terms that have a negligible influence on the signal s energy Because it is a Gabor expansion based spectrogram the resulting method is the Gabor spectrogram The Gabor spectrogram is defined by GSpli k y C C m n m n WVD i k Im m in n lt D where WVD i k denotes the cross WVD of frequency modulated Gaussian functions The order of the Gabor spectrogram D controls the degree of smoothing For D 0 GSo i k is non negative and similar to the STFT spectrogram As D goes to infinity the Gabor spectrogram converges to
173. hapter 21 IIR and FIR Implementation IIR filters are also known as recursive filters or autoregressive moving average ARMA filters Refer to Chapter 23 DFD References for additional references for information about this topic Cascade Form IIR Filtering Filters implemented using the structure Equation 21 1 defines directly are known as direct form IIR filters Direct form implementations often are sensitive to errors introduced by coefficient quantization and by computational precision limits Additionally a filter designed to be stable can become unstable with increasing coefficient length which is proportional to filter order You can obtain a less sensitive structure by dividing the direct form transfer function into lower order sections or filter stages The direct form transfer function of the filter given by Equation 21 1 with ag 1 can be written as a ratio of z transforms N S 7 botb z by az 21 2 i N 1 az t y jZz By factoring Equation 21 2 into second order sections the transfer function of the filter becomes a product of second order filter functions N 1 2 boy t bigz b H z 21 3 cay L ay Z td where N N 2 is the largest integer less than or equal to N 2 and N 2 N This new filter structure can be described as a cascade of second order filters as shown in Figure 21 1 Figure 21 1 Cascaded Filter Stages You can implement each second order
174. he 31 filters You can obtain these same results by using a third octave filter The number of bins used for each octave filter varies depending on the center frequency of the octave filter Typically higher frequencies require more bins than lower frequencies National Instruments Corporation 26 1 Signal Processing Toolset Chapter 26 Third Octave Analysis Design Table 26 1 shows the three possible sampling rates the Third Octave Analyzer uses Each sampling rate covers 31 ANSI third octave bands as listed in Table 24 1 Filter Bands for ANSI S1 11 in Chapter 24 Overview of the Third Octave Analysis Toolkit Table 26 1 Third Octave Analyzer Sampling Rates ANSI Bands and Center Frequencies Sampling Rate ANSI Band Center Frequencies 12 8 KHz 5 Hz 5 kHz 25 6 kHz 10 40 10 Hz 10 kHz 51 2 kHz 13 43 20 Hz 20 kHz Multistage Decimation Techniques Signal Processing Toolset Given an N point FFT and a sampling frequency fs you can find the frequency resolution by using the following formula _ fs UN Assume you have selected fs 12 8 kHz for N 512 Therefore f 128 kHz L 0 025 kHz 25 Hz 512 A 25 Hz frequency resolution is sufficient for higher frequency bands but not for lower frequency bands For example the center frequencies for ANSI bands 7 and 8 are only 1 3 Hz apart Therefore you must reduce f for lower frequency bands You can reduce f by increasing N or by reducing the sampling frequency fs Incr
175. he selected function is displayed The time waveform power spectrum coherence and impulse response functions do not have a phase result Use the Magnitude Unit control to set the unit for the magnitude result of the selected function These units include Vrms Vpk Vrms Vpk Vrms rtHz Vpk rtHz Vrms Hz and Vpk Hz Dual channel measurements like coherence and frequency response are not expressed in units As a result no unit appears on the measurement display Furthermore if you select an inappropriate unit for a function VirtualBench DSA overrides the selection and chooses the correct units Use the Log Linear Mode control to select linear or decibel dB modes for the y axis of the magnitude display If you select dB mode VirtualBench DSA uses dBV rms or dBVpk for the display for amplitude auto power and cross power spectra where the reference is Vrms or 1 Vpk respectively dB is used for the amplitude spectrum because it is already a ratio Coherence impulse response and time waveform are never shown in dB If dBm is selected the reference is 0 78 V for amplitude power and cross power spectrums Use the Phase Unit control to select the unit degrees or radians for the phase result of the selected function The time waveform power spectrum coherence and impulse response functions do not have a phase result Use the Markers control to turn markers on and off for the selected display Options are Off Dual and Ha
176. he trace to the negative edge of the graph With the last option you can set a specific trace of the strip chart to fill e Interpolation options are X or Y Stepwise No or Linear interpolation e Color sets the color for the trace The foreground color determines the color for the point if you select a point style The background color determines the color for the line if you select interpolation Use the following Palette controls to change the display of each channel e X axis Autoscale autoscales the x axis of the display once You can enable x axis autoscaling permanently by clicking the switch to the left of this button e X axis Formatting accesses the Format Precision and Mapping Mode of the x axis With Format you select notation for the axis Some options are Octal Decimal and Hexadecimal 31 3 Signal Processing Toolset Chapter 31 VirtualBench DSA Precision controls the number of digits after the decimal Mapping Mode controls whether the data is displayed using a linear or logarithmic scale e Zoom Mode accesses different types of zooming which include zoom by rectangle zoom in about a point zoom out about a point and undo zoom e Standard Mode changes the mode of the display from zoom or pan to standard mode e Y axis Autoscale autoscales the y axis of the display once You can enable y axis autoscaling permanently by clicking the switch to the left of this button e Y axis Formatting accesses the For
177. ication or as an add on toolkit for LabVIEW The toolkit also provides the instrument driver for LabWindows CVI users and dynamic link libraries DLLs for Windows users Description of an Octave Analyzer An octave analyzer is a parallel connected filter bank with a set number of filters Each filter is tuned to a special frequency band and has a designated center frequency and bandwidth The following formula determines the center frequencies of a pair of two adjacent filters where f is the designated center frequency in the ith filter band and fj is the designated center frequency of the next higher band The parameter b is the bandwidth designator for the particular octave analyzer of interest Therefore 5 1 for an octave analyzer b 1 3 for a one third octave analyzer also called a third octave analyzer b 1 6 for a one sixth octave analyzer and so on Notice that the following equation also is expressed in b octaves often log 7 b fi where log represents the base 2 logarithm In the case of a third octave analyzer the center frequencies of any two adjacent filters are related by a factor of 2 5 or one third of an octave National Instruments Corporation 24 1 Signal Processing Toolset Chapter 24 Overview of the Third Octave Analysis Toolkit Introduction to the Third Octave Analysis Toolkit Third octave analysis is a special type of octave analysis widely used in acoustical analysis and audio signal
178. ilter Design Toolkit Part V Third Octave Analysis Toolkit Part VI VirtualBench DSA Conventions Used in This Manual Related Documentation Customer Communication Chapter 1 signal Processing Toolset Overview Signal Processing Toolset Joint Time Frequency Analysis Toolkit Wavelet and Filter Bank Design Toolkit Super Resolution Spectral Analysis Toolkit Digital Filter Design Toolkit Third Octave Analysis Toolkit VirtualBench DSA System Requirements Installation Part Joint Time Frequency Analysis Toolkit Chapter 2 The Need for Joint Time Frequency Analysis Review of the Classical Fourier Transform The Need for JTFA Basic Approaches to JTFA National Instruments Corporation V Signal Processing Toolset Contents Chapter 3 Joint Time Frequency Analysis Algorithms Hnc EE ACA TGOm MIs S oo itcm sir dines dude cise Cada br reti idm Sat bn de oo e Ru ERR LUS 3 Gabor Expanstom and DEG sonent teo A oiv ues Cus Ue ME bests Uto UU Que 3 Adaptive Representation and Adaptive Transform eeeseeeeeeee 3 2 Quadratec ITEA AIS ONTEM Sororis iie antes ues dipuec cada du uo ced nto dua Coa res SE noue dated e Pub o bans 3 3 SIPC SPec OSTA satio rie desit cotes de Pato Data teu ict eu E PORE EO S Edd 3 3 Wigner Ville Distribution and Pseudo Wigner Ville Distribution 3 5 Conor e dT ee coe eases acanscuas sstetaheet E iaaweeceate 3 8 Choi Williams DISCIDUEBOR oii coveneacesPaeed inden n
179. ilter order until it finds the minimum order that meets or exceeds the filter specifications The message window displays errors that occur during the FIR design procedure These errors occur when the filter specifications are inconsistent with the chosen filter type Pole Zero Placement Filter Design Figure 20 13 shows the Pole Zero Placement filter design panel The panel includes a graphical interface with the z plane pole and zero cursors and the Magnitude vs Frequency plot on the left side and a text based interface with digital controls on the right side National Instruments Corporation 20 19 Signal Processing Toolset Chapter 20 Digital Filter Design Application I Pole Zero Placement Eile Edit Signal Processing Toolset Operate Project Windows Help DFO Menu v PEhSTkUMEHT z plane rectangular coordinates selected TIN 433093034571 EE order C08 value 20 1301 3151 i real order Magnitude vs Frequency E NN sampling rate 8 0000E 3 gain I 8150E 2 EE i TE l l l 3 l 1000 0 2000 0 3000 0 aooaa Mi 33 Figure 20 13 Pole Zero Placement Filter Design Panel Use the Pole Zero Placement filter design panel to design IIR digital filters by manipulating the filter poles and zeros in the z plane The poles and zeros initially might have originated from classical IIR designs Use this panel to move existing poles and zeros directly on the z plane plot You can add and delete poles an
180. imation by Matrix Pencil Method 15 5 Super Resolution Power Spectra with Order 10 tor Sur Of TVO SIDnusolds uidi etie etos todas doe o eeu pU qa ER a 15 6 Real and Complex Covdrance VIs urcoid Lo n OU E aC 17 1 Super Resolution and Modal Panel sees 18 1 Wavetormpror Test Satmpleuie vectes aa a PUDE 18 2 EPT DasedMEtBOUOUS uus ied top rear p peu tbe pedo Eoo mar Publ anus 18 3 Saper Resolution Speca oce eser cope o edet Me suse taa A 18 4 Estimation of Damped SinUSGIdS icit e at cie dn pta e gn 18 4 Synthetic Data Panel oed bedttk da tattoo toU muU aaa Set 18 5 National Instruments Corporation XV Signal Processing Toolset Contents Figure 20 1 Figure 20 2 Figure 20 3 Figure 20 4 Figure 20 5 Figure 20 6 Figure 20 7 Figure 20 8 Figure 20 9 Figure 20 10 Figure 20 11 Figure 20 12 Figure 20 13 Figure 20 14 Figure 20 15 Figure 20 16 Figure 20 17 Figure 20 18 Figure 20 19 Figure 20 20 Figure 20 21 Figure 20 22 Figure 20 23 Figure 20 24 Figure 20 25 Figure 20 26 Figure 20 27 Figure 20 28 Figure 20 29 Figure 20 30 Figure 20 31 Figure 20 32 Figure 20 33 Figure 21 1 Figure 21 2 Figure 21 3 Figure 25 1 Figure 25 2 Figure 25 3 Figure 25 4 Signal Processing Toolset Conceptual Overview of the Digital Filter Design Toolkit 20 2 ITD Wain Memik Panels inten a eodeni e aab n 20 2 IPD BP O
181. infinite impulse response filters See IIR filters installation Signal Processing Toolset 1 4 internal data averaging Third Octave Analysis toolkit 26 5 to 26 6 Interpolation Filter VI 12 14 to 12 15 InterpolationFilter function 12 34 to 12 36 Inverse Adaptive Transform VI 4 2 to 4 3 J joint time frequency analysis algorithms 3 1 to 3 13 choosing an algorithm 6 2 to 6 3 differences between linear and quadratic methods 6 1 linear algorithms 3 1 to 3 2 adaptive representation and adaptive transform 3 2 Gabor expansion and STFT 3 1 to 3 2 quadratic algorithms 3 3 to 3 13 adaptive spectrogram 3 13 National Instruments Corporation Index Choi Williams distribution 3 9 Cohen s class 3 8 to 3 9 cone shaped distribution 3 10 Gabor spectrogram 3 11 to 3 12 STFT spectrogram 3 3 to 3 4 Wigner Ville distribution and Pseudo Wigner Ville distribution 3 5 to 3 8 joint time frequency analysis applications 5 to 5 15 linear algorithm examples 5 1 to 5 6 denoise 5 1 to 5 3 image analysis 5 3 to 5 6 time dependent spectrum analysis examples 5 6 to 5 15 Offline Joint Time Frequency Analyzer 5 8 to 5 15 Online STFT Spectrogram Analyzer 5 7 to 5 8 joint time frequency analysis JTFA basic approaches to 2 6 to 2 7 classical Fourier transform review 2 to 2 3 comparison of FFT JTFA wavelets and model based methods table 15 7 error codes 8 1 frequently asked questions 6 1 to 6 6
182. inning the EDS Electronic Design News 1992 Software Award and the 1993 R amp D 100 award Signal Processing Toolset 3 12 National Instruments Corporation Chapter 3 Joint Time Frequency Analysis Algorithms Adaptive Spectrogram The adaptive spectrogram method is an adaptive representation based spectrogram refer to Equation 3 2 computed by li il k Di TE 2 TEENS AS i n 2 X A exp 2x ain f B Gi i 3 9 k 0 The adaptive spectrogram achieves the best joint time frequency resolution if the analyzed signal is a sum of linear chirp modulated Gaussian functions For example Figure 3 9 shows that the adaptive spectrogram effectively describes the three tone test signal Unfortunately the computation speed of the adaptive spectrogram increases exponentially with the analyzed data size current data gauss3 txt gauss3 tst but data length sec 1 28E 1 spectrum EO 4 0E 2 3 0E 2 2 0E 2 1 0E 2 D DE 0 2 DE 0 1 0E 0 B OUE 2 sec 15E 2 Hz 0 0E 0 1 0E 0 1 7E 0 ec 0 DE 0 20E 2 406 2 60E 2 amp E2 1 0E 1 1 36 1 aE contral Figure 3 9 Adaptive Spectrogram for the Three Tone Test Signal Scientists at National Instruments and Mallat and Zhang 1993 independently developed the adaptive representation also known as the matching pursuit The adaptive methods in this toolkit were implemented with the adaptive oriented orthogonal projective decomposition algorithm
183. inusoids ARMA MA and AR Models As mentioned previously model based frequency analysis is suitable only for certain types of data In general it has to be generated by exciting a linear shift invariant causal pole zero filter rational transfer function with white noise In other words the data sample x n has to fit the following model P q x n 23 ayx n k b w n m for O n N 16 1 kal m 0 where by 1 and w n is the white noise with zero mean and variance 0 Equation 16 1 is traditionally called the auto regressive and moving average ARMA model There are two special cases of Equation 16 1 one is a O for all k Consequently it reduces to q x n b w n m for0 lt n lt N 16 2 m 0 National Instruments Corporation 16 1 Signal Processing Toolset Chapter 16 Model Based Frequency Analysis Algorithms Signal Processing Toolset which is called a moving average MA model The second is b 0 for m gt Q In this case the ARMA model in Equation 16 1 becomes p x n ay x n k w n for O n N 16 3 k 1 which is called an auto regressive AR model According to Equation 16 3 you can use currently known data samples to predict the future data with error w n Let the predicted data be x n then P x n a x n k for p lt n lt N 16 4 kc Or x p 1 x p 2 x 0 dj x p x p x p 1 x 1 aj _ _ x p 1 16 5 x N 2 xIN 1 xIN p
184. ion National Instruments Corporation 1 3 Signal Processing Toolset Chapter 1 Signal Processing Toolset Overview System Requirements You must use the Third Octave Analysis toolkit with one of the National Instruments data acquisition devices The Third Octave Analysis toolkit can analyze signals correctly only when the signal does not have any aliasing You should use a device that has a built in anti aliasing filter The National Instruments Dynamic Signal Acquisition boards have these built in filters Installation Complete the following steps to install the Signal Processing Toolset 1 Insert the CD of the Signal Processing Toolset into your CD ROM drive and double click setup exe 2 Follow the instructions on your screen Once you have completed the on screen installation instructions you are ready to run the toolkits in the Signal Processing Toolset Signal Processing Toolset 1 4 National Instruments Corporation Part I Joint Time Frequency Analysis Toolkit This section of the manual describes the Joint Time Frequency Analysis JTFA toolkit National Instruments Corporation Chapter 2 The Need for Joint Time Frequency Analysis explains the need for and the approaches to joint time frequency analysis JTFA Chapter 3 Joint Time Frequency Analysis Algorithms describes the algorithms the JTFA VIs use The JTFA algorithms implemented in this package fall into two categories linear and quadratic
185. ion of 40 dB between the frequencies of 0 and fs 2 1500 Hz and between the frequencies of fs 3000 Hz and 4000 Hz National Instruments Corporation 20 15 Signal Processing Toolset Chapter 20 Digital Filter Design Application The following ranges define the stopband lowpass Isi Sf SS samp 2 highpass O lt fsfs bandpass VSS SSi SaS S camp 2 bandstop fs Sf s2 where fs is passband frequency 1 fsa is passband frequency 2 JP samp 18 the sampling rate The Classical FIR Design panel estimates the minimal filter order required for the selected type and design to meet or exceed the modified filter specifications The DFD application automatically computes other appropriate filter parameters and designs and plots the FIR filter You see immediate graphical feedback to help you determine whether the filter meets your specifications Classical FIR Design Panel Controls and Displays These controls are similar to those in the Classical IIR Design panel with two additions a minimize filter order button and an error message display box Use the design panel DFD Menu to complete the following tasks e Save your filter specifications and coefficients e Load filter designs from previous work e Open the Analysis or the DAQ and Filter panels e Transfer the FIR design specifications to the Classical IIR Design panel e Return to the Main Menu panel The graph in Figure 20 11 plots the frequency response H f magnitude of
186. ion filter array Return Value status integer Refer to Chapter 14 Wavelet Error Codes for a description of the error Signal Processing Toolset 12 34 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference Example Example 4 How to build 2 channel synthesis filter bank using InterpolationFilter include wfbd h test FilterBankPtr anaptr synptr double x V0 tyl tmo X0 Long err nx nyU nyl mLb nh npad anaptr AllocCoeffWFBD allocate filter bank structure TfT lanaptrtr return synptr AllocCoeffWFBD TIEThSympEX 4 free anaptr return err ReadCoeffWFBD coef dat anaptr synptr Read filter bank coefficients T7 if err goto errend nl anaptr gt nl nh anaptr gt nh x double malloc nx sizeof double if x goto errend Compute the size of output arrays and allocate memory for them ny ocerbLbTO b inxtensputr onh li4133 yO double malloc nyO sizeof double if y0 goto erreng ny perL00 5 00hansobEP onl LyJs yl double malloc nyl sizeof double a oak any 4 free y0 goto errend err AnalysisEFilterBank x nx anaptr 0 y0 nyU0 yl nyl g if err free y0 free y1 goto erreng National Instruments Corporation 12 35 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Allocate memory for the output of synthesis filter bank x0 double malloc
187. ired signal as shown in the top plot in Figure 2 6 You then can apply the inverse transformation to recover the noiseless time waveform The lower plot of Figure 2 6 illustrates the noisy and reconstructed signals When the SNR is very low as with many satellite signals JTFA might offer the only opportunity to detect the signal of interest 0 00 0000 0o20 0040 ooo O50 0100 0120 145 ms O 000 0 020 0 040 0 060 0 080 0100 0 120 0 145 Figure 2 6 Reconstructed Signal National Instruments Corporation 2 5 Signal Processing Toolset Chapter 2 The Need for Joint Time Frequency Analysis Basic Approaches to JIFA The development of JTFA began more than a half century ago The most straightforward approach of characterizing the frequency of a signal as a function of time was to divide the signal into several blocks that could be overlapped Then the Fourier transform was applied to each block of data to indicate the frequency contents of each This process has become known as the short time Fourier transform STFT and roughly reflects how frequency contents change over time The size of the blocks determines the time accuracy The smaller the block the better the time resolution However frequency resolution is inversely proportional to the size of a block While the small block yields good time resolution it also deteriorates the frequency resolution and vice versa Traditionally this phenomena is known as the window effect
188. is manual including the page where you can find each one Conventions Used in This Manual lt gt bold bold italic italic Signal Processing Toolset The following conventions are used in this manual Angle brackets enclose the name of a key on the keyboard for example lt shift gt Angle brackets containing numbers separated by an ellipsis represent a range of values associated with a bit or signal name for example DBIO lt 3 0 gt The symbol leads you through nested menu items and dialog box options to a final action The sequence File Page Setup Options Substitute Fonts directs you to pull down the File menu select the Page Setup item select Options and finally select the Substitute Fonts option from the last dialog box This icon to the left of bold italicized text denotes a note which alerts you to important information Bold text denotes the names of menus menu items parameters dialog boxes dialog box buttons or options icons windows Windows 95 tabs panels controls or LEDs Matrices are in uppercase bold letters Vectors are in lowercase bold letters Bold italic text denotes a note Italic text denotes variables elements of a matrix emphasis a cross reference or an introduction to a key concept This font also denotes text from which you supply the appropriate word or value XXII National Instruments Corporation About This Manual monospace Text in this font denotes
189. is identical to the original signal X z except for the time delay Such a system is commonly referred to as two channel PR filter banks Go z and G z form an analysis filter bank whereas Ho z and H z form a synthesis filter bank i Note G z and H z can be interchanged For instance you can use H z and H z for analysis and G z and G z for synthesis H z and H4 z are usually considered as the dual of Go z and G z and vice versa Signal Processing Toolset Traditionally Go z and Ho z are lowpass filters while G z and H z are highpass filters where the subscripts O and 1 represent lowpass and highpass filters respectively Because the two channel PR filter banks process Yo z and Y z at half the sampling rate of the original signal X z they attract many signal processing applications If you assume the following convention then the relationship between two channel PR filter banks and wavelet transform can be illustrated by Figure 10 2 Figure 10 2 Relationship of Two Channel PR Filter Banks and Wavelet Transform 10 2 National Instruments Corporation Chapter 10 Digital Filter Banks It has been proved Qian and Chen 1996 that under certain conditions two channel PR filter banks are related to wavelet transform in two ways e The impulse response of the lowpass filters converges to the scaling function 0 t Once you obtain 0 f yo
190. it describes the architecture of the Wavelet and Filter Bank Design WFBD toolkit lists the design procedures and describes some applications you can create with the WFBD toolkit e Chapter 12 WFBD Toolkit Function Reference describes the VIs in the WFBD toolkit the instrument driver for LabWindows CVI and the functions in the DLLs e Chapter 13 Wavelet References lists reference material that contains more information on the theory and algorithms implemented in the WFBD toolkit e Chapter 14 Wavelet Error Codes lists the error codes LabVIEW VIs and LabWindows CVI functions return including the error number and a description National Instruments Corporation Il 1 Signal Processing Toolset Wavelet Analysis This chapter describes the history of wavelet analysis compares Fourier transform and wavelet analysis and describes some applications of wavelet analysis History of Wavelet Analysis Although Alfred Haar first mentioned the term wavelet in a 1909 thesis the idea of wavelet analysis did not receive much attention until the late 1970s Since then wavelet analysis has been studied thoroughly and applied successfully in many areas Some people think current wavelet analysis is no more than the recasting and unifying of existing theories and techniques Nevertheless the breadth of applications for wavelet analysis is more expansive than ever was anticipated Conventional Fourier Transform The development o
191. ive less crossterm than PWVD less crossterm interference than PWVD or CWD Gabor spectrogram good resolution moderate robust minor crossterms extremely high resolution for fast a few types of signals severe crossterms STFT spectrogram poor resolution fast robust non negative If the frequency contents of the analyzed signal do not change rapidly try the STFT spectrogram first You can apply a relatively long window function to obtain a good frequency resolution with tolerable time resolution deterioration Because the STFT spectrogram is fast it is suitable for online analysis 6 2 National Instruments Corporation Chapter 6 Frequently Asked Questions The other algorithms generally have better joint time and frequency resolution than the STFT spectrogram but they require more computation time which is suitable for offline analysis only If you need a higher resolution use the third or fourth order Gabor spectrogram to reduce crossterm interference and achieve faster processing speeds National Instruments recommends that you use the following procedure when analyzing a signal 1 Begin with the STFT and determine which analysis window is best wideband mediumband or narrowband 2 Use STFT if you are satisfied with the results If not continue with step 3 3 Try the Gabor spectrogram if the STFT does not produce satisfactory results Regardless of the analysis window used the Gabor spectrogram converges t
192. k plil k is the Gabor spectrogram m z E P error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions Signal Processing Toolset 4 16 National Instruments Corporation Joint Time Frequency Analysis Applications This chapter introduces some JTFA applications Because JTFA is relatively new it is less known among practicing engineers and scientists unlike the well known Fourier analysis The examples in this chapter reveal only the potential of JTFA The power of JTFA has not been fully explored These examples can help you learn and apply JTFA to your applications Unlike the traditional analysis in which you can analyze a signal only in the time domain or frequency domain JTFA defines a signal in the joint time and frequency domain Consequently you can better understand and process the signal in which you are interested The examples in this chapter demonstrate VIs based on linear or quadratic algorithms You can find all examples in Examples 11b in the Examples Signal Processing Toolset Joint Time Frequency Analysis directory in your LabVIEW directory You can run the application by selecting Start Programs National Instruments Signal Processing Toolset Joint Time Frequency Analyzer Linear Algorithm Examples Denoise The following two linear algorithm examples demonstrate noise reduction denoise and image analysis Noise reduction is
193. l Signal Processing Toolset 11 10 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit The following sections describe the controls on the 1D_Test panel Extension Type determines the padding method for the data You have the following choices zero padding adds zeros at the beginning and end of the original data symmetric extension symmetrically adds the input data at the beginning and end of the original data In both cases you can add the number of points at the beginning and the end of the original data with the following formula Nc M ae 2 2 where N is the number of coefficients of Po z N is the number of coefficients of filter Go z and N is the number of coefficients of filter Ho z Display shows either a time waveform or a histogram Data provides the following choices National Instruments Corporation Read from file reads 1D input data from a text file Acquire Data uses the data acquisition board specified in the DAQ Setup panel to acquire a block of data and then analyze it You must run the DAQ Setup panel before you acquire any data 11 11 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit e DAQ Setup invokes the DAQ Setup panel shown in Figure 11 9 Use this panel to configure your data acquisition board DAQ Setup trigger type no trig sampling rate jt of samples na trigger o 8000 00 H
194. l Instruments Corporation control CWD D DAQ data acquisition data type datalog file Daubechies wavelet and filter bank dB decimation filter denoise developer DFD DFT DGT National Instruments Corporation G 3 Glossary Front panel object for entering data to a VI interactively or to a subVI programmatically Choi Williams distribution See data acquisition DAQ Process of acquiring data typically from A D or digital input plug in boards Format for information In Bridge VIEW acceptable data types for tag configuration are analog discrete bit array and string In LabVIEW acceptable data types for most functions are numeric array string and cluster File that stores data as a sequence of records of a single arbitrary data type that you specify when you create the file While all the records in a datalog file must be of a single type that type can be complex for instance you can specify that each record is a cluster containing a string a number and an array Wavelet and filter bank that has a maximum number of zeros at m The wavelet and filter bank was initially developed by Ingrid Daubechies Decibels A logarithmic unit for measuring ratios of amplitude levels If the amplitudes are specified in terms of power then I dB 10xlog10 P Pr where P is the measured power and Pr is the reference power If the amplitudes are specified in terms of voltage then 1 dB 20 xlog10 V Vr
195. l based frequency analysis Chapter 16 Model Based Frequency Analysis Algorithms outlines the theoretical background of model based frequency analysis and describes the relationship among the model coefficients the power spectra and the parameters of damped sinusoids Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs describes VIs used to perform super resolution and parameter estimation Each algorithm included has two forms one for real and the other for complex valued samples The real VIs work only for real valued data sets and the complex VIs work for both real and complex samples Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation describes a comprehensive testing example application included with the Super Resolution Spectral Analysis toolkit This example software is designed to help you learn about model based analysis Chapter 19 Super Resolution Spectral Analysis References lists reference material that contains more information on the theory and algorithms implemented in the Super Resolution Spectral Analysis toolkit III 1 Signal Processing Toolset Introduction to Model Based Frequency Analysis This chapter introduces the basic concepts of model based frequency analysis Spectral analysis usually consists of two methods non model based methods such as the fast Fourier transform FFT based methods and model based methods Compared to the FFT based
196. learn about model based analysis This software runs with or without LabVIEW By using this comprehensive testing software you can try different algorithms for the data samples without programming You can run the application by selecting Start Programs National Instruments Signal Processing Toolset Super Resolution Spectral Analyzer Super Resolution and Modal Analysis File Edt Operate Project Windows Help Test File Rectangular NM SN C 00 UA Covariance y amp 3 00 x o26 h AR orders 14 fs a 1 0530 Estimated Parameters amplitude phase damping frequency PE as ooo ooo 25 0 50 0 00 o oo 0 11 4 complex sinusoids Prony s Method Figure 18 1 Super Resolution and Modal Panel National Instruments Corporation 18 1 Signal Processing Toolset Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation Figure 18 1 illustrates the main panel of the testing software which contains the following three major plots e The upper left plot is the waveform of the test sample e The upper right plot is the FFT based spectrum e The lower right plot is the model based super resolution spectrum The table in the lower left portion of the panel lists the parameters associated with each damped sinusoid The following sections describe how to use this built in software Sampling Frequency The control fs sampling frequency located below the time wavefor
197. lection of Super Resolution Spectra Algorithms eeeeeeeeeeesseeeeeenee 18 4 Estimation or Damped Sinusoids edic brace srt eio nota Dr boni eres d ut Peatg Le URS 18 4 Syothene Data P PR 18 5 Chapter 19 Super Resolution Spectral Analysis References Part IV Digital Filter Design Toolkit Chapter 20 Digital Filter Design Application IVA CUT IST seen tonto daa a E tenets daanannaaseuassass een nid calda of tua e eese D ioa OUR 20 2 Opening the Filter Design Panels ertet edet Ub e ELITR UE dU Re ruis 20 3 Directly Loading a Filter Specification File sesseeeseeeeeeeeeeeees 20 3 Editing the DED PrererenCe Sis ni Ide tee ota Re E CERE iuto 20 3 Quitting the DFD Application eeeesssssssssseeeeeeeeeeenenenem nennen 20 3 Dreital Filter Desien Panels i avers Mese pee Re PU Passes s eo eser Siar 20 3 Common Controls and Peatures iee doeet e ea eia tenu sE e dose Rn rode chen eis 20 4 Usine the DED Men ode ee Ue eer on e up a RUEE 20 4 Saving Filter Specifications sse 20 4 Loading Filter Specifications eeesssssss 20 5 Saving Filter Coefficients sse 20 5 Analyzing Filter Designs eeeeeeeeeeeseeeeeeee 20 6 DAQ and Filter Real World Testing 20 6 Simulated DAQ and Filter Testing ssesse 20 6 Transferring Filter Designs
198. les 5 1 to 5 6 denoise 5 1 to 5 3 image analysis 5 3 to 5 6 Gabor expansion and STFT 3 1 to 3 2 MA filters See FIR filters MA moving average model 16 1 manual See documentation matching pursuit 3 2 matrix pencil method 16 8 Matrix Pencil Method VI 17 6 to 17 7 minimum description length algorithm 16 8 Minimum Description Length VI 17 7 model based frequency analysis 15 1 to 15 8 See also super resolution spectral analysis and parameter estimation algorithms 16 5 to 16 8 covariance method 16 5 to 16 6 matrix pencil method 16 8 minimum description length 16 8 principle component auto regressive method 16 6 to 16 7 Prony s method 16 7 applications comparison of FFT JTFA wavelets and model based methods table 15 7 proper use of 15 6 to 15 7 types of 15 6 AR model and damped sinusoids 16 4 to 16 5 National Instruments Corporation l 7 Index ARMA MA and AR models 16 1 to 16 3 compared with fast Fourier transform 15 1 to 15 6 estimating parameters of damped sinusoids 15 4 to 15 5 model coefficients and power spectra 16 3 to 16 4 uses for 15 1 to 15 6 Mother Wavelet and Scaling Function VI 12 16 moving average MA model 16 1 multiscale analysis application wavelet analysis 9 11 multistage decimation techniques Third Octave Analysis toolkit 26 2 to 26 4 noise reduction JTFA application denoise 5 1 to 5 3 Normalized Gaussian Window Function VI 4 8 0 octave analyze
199. les to perform frequency analysis is to ensure that the spectral characteristics of a signal do not change over the duration of the data record This is also a primary motivation of developing the joint time frequency analysis JTFA and wavelet transform At this point a natural question might be Which technique is the best The answer is that each method has advantages and disadvantages None is superior to all others in every application Table 15 2 compares model based methods with FFT JTFA and wavelets There is no assumption about the analyzed signal for FFT JTFA and wavelet analysis whereas the model based methods work only for certain type of signals Moreover the performance of model based frequency analysis is quite sensitive to noise though there are some variations for different algorithms For example the principle component auto regressive PCAR method in Figure 15 5 has better noise immunization than that of the covariance method Table 15 2 FFT JTFA Wavelets and Model Based Methods Data Frequency Noise Method Signal Model Stationary Length Resolution Sensitivity Speed Finally the computation of the super resolution power spectra is much more expensive than that of FFT JTFA and wavelet transform When the number of data samples is more than a few hundred it is no longer appropriate to use model based methods because of the computation time involved and numerical inaccuracies that might result
200. lset Chapter 12 WFBD Toolkit Function Reference outsize 5 the number of columns of array high_low it must be ceil cols nl 1 2 outsize 6 the number of rows of array high high it must be ceil rows nl 1 2 outsize 7 the number of columns of array high high it must be ceil cols nl 1 2 For all equations nl is the size of the lowpass filters and nh is the size of the highpass filters in the Analysis Filters ieee low Em precision aBeuaeric Sub ae ome upper left subimage from the analysis 2D array filter bank low_high double precision The upper right subimage from the 2D array analysis filter bank high_low double precision The lower left subimage from the analysis 2D array filter bank high_high double precision The lower right subimage from the 2D array analysis filter bank Return Value sae EE Doc Reco coer Neas 31 to Chapter 14 Wavelet Error Codes for a description of the error Signal Processing Toolset 12 26 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference Example Example 2 How to call function AnalysisFilterBank2D finclude wfbd h PYlterBankPtr anaptr synptr doubler Ase I TL b n long err rows cols nsize 8 anaptr AllocCoeffWFBD allocate filter bank structure if anaptr return synptr AllocCoeffWFBD LE ClSynoc re x free anaptr return err ReadCoeffWFBD coef dat
201. lso can choose to have 256 point FFT This is not as accurate as using 512 point FFT but it requires less memory and runs faster If you choose to use 256 point FFT the analyzer acquires a total of 28 680 points Signal Processing Toolset 26 4 National Instruments Corporation Chapter 26 Third Octave Analysis Design Internal Data Averaging Figure 26 2 shows a diagram of how internal data points are used in each processing stage Stage 1 overlapping case lt AN gt lt n gt s N e decimate I M Mn y H Stage 2 E 4 AN non overlapping case Figure 26 2 Internal Data Averaging Procedure As described previously there are three filter groups The original M points are acquired by hardware M 54280 if N 512 and M 28680 if N 256 The decimation filters are successively applied to obtain approximate M 10 points and M 100 points in the second and third stages In the first stage there are roughly 100 blocks of data In the second stage there are approximately 10 blocks of data each is N points Thus averaging is applicable in the first and second stages The last stage has exactly N points Therefore no average is available at this stage The Internal Data Averaging array controls the number of averaging blocks in each stage The first element controls the first stage and the second element controls the second stage Assuming the value of one element in the
202. lter a large data sequence that has been split into smaller blocks set this control to FALSE for the first block and to TRUE for continuous filtering of all remaining blocks Filtered X is the array of filtered output samples error is the error code returned from the filtering VIs You can wire this output to the Find First Error VI to produce an error cluster Then you can wire this cluster to the Simple Error Handler VI or the General Error Handler VI for an immediate report on any errors You can find descriptions of error codes in Appendix B Error Codes of the LabVIEW Function and VI Reference Manual National Instruments Corporation 22 3 Signal Processing Toolset Chapter 22 Using Your Coefficient Designs with DFD Utilities LabWindows CVI Utilities This section contains descriptions of the DFD utilities you can use within your LabWindows CVI applications to read DFD filter coefficient files and filter your data using the coefficients The DFD Instrument Driver The DFD toolkit provides a LabWindows CVI instrument driver file named DFDUTILS FP You can find this file in the CVI Support instr subdirectory of your Digital Filter Design installation directory The DED utility functions contained in the instrument driver DFDUTILS FP use a filter coefficient structure that holds the filter coefficients The header file DFDUTILS H contains this filter structure and the four DFD utility function prototypes define intnum long
203. lumns of input array x AnalysisFilters FilterBankPtr The structure that holds the analysis filter bank coefficients long integer The type of padding used at the beginning and the end of the input data 0 zero padding 1 symmetric extension Signal Processing Toolset 12 24 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference outsize long integer array Contains the size information for four output arrays Call the Analysis2DArraySize function to compute this array outsize 0 the number of rows of array low_low it must be ceil rows nh 1 2 outsize 1 the number of columns of array low low it must be ceil cols nA 1 2 outsize 2 the number of rows of array low high it must be ceil rows nl 1 2 outsize 3 the number of columns of array low high it must be ceil cols nA 1 2 outsize 4 the number of rows of array high low it must be ceil rows nh 1 2 outsize 5 the number of columns of array high low it must be ceil cols nl 1 2 outsize 6 the number of rows of array high high it must be ceil rows nl 1 2 outsize 7 the number of columns of array high high it must be ceil cols nl 1 2 For all equations nl is the size of the lowpass filters and nh is the size of the highpass filters in the Analysis Filters National Instruments Corporation 12 25 Signal Processing Too
204. m Signal Processing Toolset 6 4 National Instruments Corporation Chapter 6 Frequently Asked Questions a current data testdat data length sec 3 0DE 1 x spectrum 5 0E 1 aE z 5 0E 1 0 00E 0 sec PA 3 48E 2 Hz 3 sec Q0E40 50E2 106 1 156 1 2061 256 1 3061 CUm contral Figure 6 2 Gabor Spectrogram Order Four What Can I Do If the Time Dependent Spectrum Shows a Line Only at DC If the analyzed signal is non negative such as an ECG or the stock index or if it contains a large DC offset the resulting time dependent spectrum is dominated by a single line in the vicinity of DC You might not be able to see more interesting frequency patterns To suppress the DC component you have to apply certain types of preprocessing However the methods for removing the DC components or detrending are application dependent No general method works in all cases Common techniques of detrending include lowpass filtering and curve fitting However a more promising technique is the wavelet transform Refer to Part II Wavelet and Filter Bank Design Toolkit of this manual for information on wavelet based detrending National Instruments Corporation 6 5 Signal Processing Toolset Chapter 6 Frequently Asked Questions Can I Use Other Software to Plot the Time Dependent Spectrum Yes Save the time dependent spectrum to a text file The resulting text file contains only Z values and does not
205. m as your password The support files and documents are located in the support directories National Instruments Corporation A 1 Signal Processing Toolset Fax on Demand Support Fax on Demand is a 24 hour information retrieval system containing a library of documents on a wide range of technical information You can access Fax on Demand from a touch tone telephone at 512 418 1111 E Mail Support Currently USA Only You can submit technical support questions to the applications engineering team through e mail at the Internet address listed below Remember to include your name address and phone number so we can contact you with solutions and suggestions support natinst com Telephone and Fax Support National Instruments has branch offices all over the world Use the list below to find the technical support number for your country If there is no National Instruments office in your country contact the source from which you purchased your software to obtain support Country Australia Austria Belgium Brazil Canada Ontario Canada Qu bec Denmark Finland France Germany Hong Kong Israel Italy Japan Korea Mexico Netherlands Norway Singapore Spain Sweden Switzerland Taiwan United Kingdom United States Signal Processing Toolset Telephone 03 9879 5166 0662 45 79 90 0 02 757 00 20 011 288 3336 905 785 0085 514 694 8521 45 76 26 00 09 725 725 11 01 48 14 24 24 089 741 31 30 2645 3186 03
206. m plot shown in Figure 18 2 determines the sampling frequency The default value is Hz Text File AR orders 14 fs i 1 0E 0 Figure 18 2 Waveform of Test Sample Select Test Data The Select Test Data ring control shown in Figure 18 2 is located in the upper left of the panel and provides two choices input data from built in Synthetic Data panel or from a text file If you are a first time user start with the Synthetic Data which gives you a better idea of how to properly apply the model based analysis Once you select the input data from Synthetic Data the Synthetic Data panel automatically opens Signal Processing Toolset 18 2 National Instruments Corporation Chapter 18 Applying Super Resolution Spectral Analysis and Parameter Estimation The Upper Bound AR Order One of the most important efforts for effectively applying the model based analysis is the proper choice of the order of the AR model Usually each complex sinusoid counts as one order and each real valued sinusoid counts as two orders Unfortunately in many cases you might not know how many sinusoids the sample contains To help you to determine the order of the AR model this testing software uses the maximum description length algorithm to estimate the order of the AR model for the sample data To automatically estimate the order of AR model however you need to define the upper bound of the order The control of the upper bound AR order is
207. m Analyzer 5 7 to 5 8 Time Frequency Distribution Series VI 4 15 to 4 16 Truncated Decimation Filter VI 12 13 to 12 14 Signal Processing Toolset I 10 two channel perfect reconstruction filter banks 10 1 to 10 11 biorthogonal filter banks 10 4 to 10 9 orthogonal filter banks 10 9 to 10 11 relationship with wavelet transform 10 2 to 10 3 two channel filter bank figure 10 1 2D Analysis Filter Bank for I16 VI 12 7 to 12 8 2D Analysis Filter Bank VI 12 5 to 12 6 2D Gabor Expansion VI 4 6 to 4 7 2D signal processing 10 11 to 10 13 2D STFT VI 4 4 to 4 5 2D Synthesis Filter Bank for I16 VI 12 9 2D Synthesis Filter Bank VI 12 8 V VirtualBench DSA 31 1 to 31 13 acquiring and measuring signals 31 7 to 31 10 Acquisitions tab of DSA Settings dialog box figure 31 8 Hardware tab of DSA Settings dialog box figure 31 7 Triggering tab of DSA Settings dialog box figure 31 9 Computations panel 31 5 to 31 6 of Harmonics for THD control 31 6 AC Estimate indicator 31 6 Channel Select ring controls 31 6 DC Estimate indicator 31 6 Harmonic Frequencies and Amplitudes indicator 31 6 illustration 31 5 Power Estimate indicator 31 6 THD Noise indicator 31 6 THD indicator 31 6 front panel 31 1 to 31 5 Channel Select control 31 2 National Instruments Corporation Display 1 Display 2 controls 31 3 Display Settings 31 2 Function control 31 2 illustration 31 1 Legend control 31 3 Log Linear Mode c
208. m configuration to answer your questions as quickly as possible National Instruments has technical assistance through electronic fax and telephone systems to quickly provide the information you need Our electronic services include a bulletin board service an FTP site a fax on demand system and e mail support If you have a hardware or software problem first try the electronic support systems If the information available on these systems does not answer your questions we offer fax and telephone support through our technical support centers which are staffed by applications engineers Electronic Services Bulletin Board Support National Instruments has BBS and FTP sites dedicated for 24 hour support with a collection of files and documents to answer most common customer questions From these sites you can also download the latest instrument drivers updates and example programs For recorded instructions on how to use the bulletin board and FTP services and for BBS automated information call 512 795 6990 You can access these services at United States 512 794 5422 Up to 14 400 baud 8 data bits stop bit no parity United Kingdom 01635 551422 Up to 9 600 baud 8 data bits stop bit no parity France 01 48 65 15 59 Up to 9 600 baud 8 data bits 1 stop bit no parity FTP Support To access our FTP site log on to our Internet host ftp natinst com as anonymous and use your Internet address such as joesmith anywhere co
209. m online analysis Figure 5 5 illustrates the front panel of the Online Analyzer The bottom plot displays the time waveform The top plot displays the corresponding STFT spectrogram The following sections describe how to manipulate controls and read indicators on the Online Analyzer panel Online Analyzer File Edit Operate Project Windows Help STFT Spectrogram Data Acquire Settings device channel samp freq 2000 Hz input limita window scan backlog i Hanning o of points window length in memory al 256 3 p suce uu US Genius 1 Acquire Jui Data Stop Stop AETE D Figure 5 5 Online STFT Spectrogram Analyzer Panel Setting NI DAQ D ata Acquire Settings To properly preform online analysis the Online Analyzer needs to know the device number channel number and input limits Choose a sampling frequency samp freq based on the application The maximum samp freq depends on the DAQ card and the computer you use scan backlog refer to Figure 5 5 indicates whether samp freq is adequate If the scan backlog value keeps increasing reduce samp freq For more information input limita samp freq sa Hz HESS on DAQ settings consult your NI DAQ manual National Instruments Corporation 5 7 Signal Processing Toolset Chapter 5 Joint Time Frequency Analysis Applications window Hanning window length 256 py Capture Data Stop of
210. mage from the analysis filter bank I15 High Low contains the third subimage from the analysis filter bank I6 High High contains the fourth subimage from the analysis filter bank Output is the reconstructed X image of the signal error Refer to Chapter 14 Wavelet Error Codes for a description of the error m r3 r3 m LL LL National Instruments Corporation 12 9 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference Decimation Filter VI This VI performs a decimation filter decimate factor Initial condition mI vii id Ee enor final condition h n decimate factor indicates the data reduction rate in the y i array Only every Mth point of the output from filter G is kept in the y i array DBL initial condition contains the initial condition of the x i DBL x i contains the input signal DBL final condition contains the final condition of the x i h n contains the filter coefficients rmm es EC e Li f p DEL yli contains the output array z P error Refer to Chapter 14 Wavelet Error Codes for a description of the error This VI performs the following operation X Gz YM Y That is Ng y 2 rct ao d 9 0 1 ceil L n 1 M Signal Processing Toolset 12 10 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference where n 1s the size of X G are the h n n is
211. mat Precision and Mapping Mode of the y axis With Format you select notation for the axis Some options are Octal Decimal and Hexadecimal Precision controls the number of digits after the decimal Mapping Mode controls whether the data is displayed using a linear or logarithmic scale e Pan Mode changes the display to pan mode so you can scroll the data on the display by clicking on and dragging on the display Use the following Main Control Bar buttons to acquire data and information w Run starts or stops continuous data acquisition If you enabled averaging you can stop data acquisition by clicking on the Run button to clear the averaging buffers Use the Pause button to stop data acquisition without clearing the averaging buffers Single acquires a single frame of data um EN Pause pauses the acquisition in progress If you enabled averaging stopping data acquisition using the Pause button retains the averaging buffers Using the Run button to stop data acquisition clears the averaging buffers Trigger Timeout turns yellow when a trigger does not occur within a ingol the time period the trigger timeout specifies in the Trigger Configuration dialog box Signal Processing Toolset 31 4 National Instruments Corporation Chapter 31 VirtualBench DSA Use the Measurement Displays to show measurements reference waveforms and markers for marker measurements e The Status Display indicator shows imp
212. mber of columns of C m n It must be a power of two C m n is the Gabor coefficient error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions ma Lr z e ua National Instruments Corporation 4 3 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS Gabor Expansion Represents a signal s i as the weighted sum of the frequency modulated function h i comple C oom dM Esp ermar signal length complex determines if the reconstructed signal is a complex value coe C m n is the Gabor coefficient h i is the synthesis window function function h i must be evenly divisible by dM signal length controls the length of the reconstructed signal dM is the Gabor time sampling interval The length of the synthesis yli is the reconstructed time waveform error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions 2D STFT Computes the Gabor coefficients of a 2D signal Gabor expansion liIk Sed cpm po pm ny analysis 1 analysis z Signal Processing Toolset 4 4 National Instruments Corporation Chapter 4 Joint Time Frequency Analysis VIs x i k is a 2D signal eus analysis 1 is the cluster for the analysis window function of the row analysis 1 dM1 15 N12 DBL r1 i is the analysis function for the row of x i k
213. mping factor gives an array of exponential damping factors frequency gives an array of frequencies Matrix Pencil Method Applies the matrix pencil method to estimate parameters of exponentially damped sinusoids The parameters include amplitudes phases damping factors and frequencies Compared to Prony s method this method in general is faster and less sensitive to noise DEL I 3 B F F Signal Processing Toolset hose amp n amplitude AH order phase H of complex sinusoids damping Factor sampling frequency frequency positive frequency 7 Peer ere rere rrr rr rrr F x n is the time waveform AR order determines the order of the auto regressive model which has to be bigger than or equal to the number of complex sinusoids For a good frequency estimation a higher order is recommended Usually AR order is at least two times larger than the number of complex sinusoids of complex sinusoids determines the number of sinusoids Notice that a real sinusoid generates two complex sinusoids The parameter of of complex sinusoids is crucial and directly affects the accuracy of the resulting estimation However you can apply the MDL vi to estimate this parameter if you are not sure how many sinusoids exist sampling frequency controls the sampling frequency The default value is 1 Hz positive frequency When it is true the VI provides only amplitudes phases and frequencies associated with the positive f
214. mples to 25 only model based spectra are able to tell the difference between two frequencies For FFT based spectra you cannot distinguish two different frequencies no matter what kind of windows you apply If you change the noise intensity you can see that the performance of the PCAR method is much less sensitive to the noise than the covariance method You also can vary the set of phase amplitude and damping factor to see how the estimation results change In general the matrix pencil method is more accurate and computationally efficient than Prony s method 18 6 National Instruments Corporation super Resolution Spectral Analysis References This chapter lists reference material that contains more information on the theory and algorithms implemented in the Super Resolution Spectral Analysis toolkit Hua Y and T K Sarkar Matrix Pencil Method for Estimating Parameters of Exponentially Damped Undamped Sinusoids in Noise IEEE Transaction on Acoustic Speech and Signal Processing vol 38 5 1990 814 824 Kay S M Modern Spectral Estimation Englewood Cliffs N J Prentice Hall 1987 Kolmogorov A N Interpolation and Extrapolation von Stationaren Zufalligen Folgen Bull Acad Sci USSR Ser Math vol 5 1941 3 14 Marple Jr S L Digital Spectral Analysis with Applications Englewood Cliffs N J Prentice Hall 1987 Wold H Stationary Time Series Uppsala Sweden Almqvist and
215. mpling frequency nose estimation positive frequency x n is the time waveform rma DEL LL AR order determines the order of the auto regressive model which has to be bigger than or equal to the number of complex sinusoids For a good frequency estimation a higher order is recommended Usually AR order is at least two times larger than the number of complex sinusoids of complex sinusoids determines the number of sinusoids Notice that a real sinusoid generates two complex sinusoids The parameter of of complex sinusoids is crucial and directly affects the accuracy of the resulting estimation However you can apply the MDL vi to estimate this parameter if you are not sure how many sinusoids exist sampling frequency controls the sampling frequency The default value is 1 Hz positive frequency When it is true the VI provides only amplitudes phases and frequencies associated with the positive frequency components 1E XY Graph gives parameters for the plot of the power spectrum AT Graph O nmm Ax 0 00 yf x0 indicates the lower bound of the frequency range which is fixed at f 2 where f denotes the sampling frequency Ax indicates the frequency increment Signal Processing Toolset 17 4 National Instruments Corporation Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs DEL y n indicates the estimated power spectrum in the log scale The number of freque
216. n the application by selecting Start Programs National Instruments Signal Processing Toolset Third Octave Analyzer or by launching LabVIEW and opening the Third Octave Analyzer vi found in octave 11b The analyzer opens a Setup panel as shown in Figure 25 1 National Instruments Corporation 25 1 Signal Processing Toolset Chapter 25 Operating the Third Octave Analyzer p gt Setup yi Setup device sampling rate data blocks to average Jo 425 BKHz eli Channel Window Type Average Type Weighting x Ch 20 Hanning linear na weighting ChB 1 Hanning linear no weighting x Che 22 Hanning linear no weighting x ChD 23 Hanning linear no weighting FFT size Internal Data Averaging eae ho averaging Figure 25 1 Third Octave Analyzer Setup Dialog Box The following paragraphs describe the Setup front panel parameters and buttons that you can customize for your application device device assigns an identification number to your device In Windows you assign this number to your device when you run the NI DAQ Configuration Utility sampling rate sampling rate designates the rate at which your device samples The 25 6KHz Third Octave Analyzer offers three sampling rates 12 8 kHz 25 6 kHz and 51 2 kHz The corresponding data frequency ranges analyzed are 5 Hz 5 kHz 10 Hz 10 kHz and 20 Hz 20 kHz data blocks to average ata blo
217. nal In signal processing you often want to represent certain attributes of the signal explicitly Figure 2 1 Basis Functions Used for Fourier Transform Although the Fourier transform has been widely recognized in many disciplines it possesses certain disadvantages that prevent its use in many important applications Figures 2 2 and 2 3 depict two common signals seismic and ECG electrocardiogram Unlike the sinusoid functions used as the basis of the Fourier transform that extend over the entire time domain refer to Figure 2 1 the seismic signal lives only for a very short period and the ECG signal basically consists of isolated bursts Using the Fourier series to represent those signals you need an infinite number of sinusoid functions that can cancel each other to achieve the near zero points Therefore the classical Fourier series cannot economically represent these applications seismic Figure 2 2 Seismic Signal Signal Processing Toolset 2 2 National Instruments Corporation Chapter 2 The Need for Joint Time Frequency Analysis Figure 2 3 ECG Signal As mentioned earlier another important application of the Fourier transform is spectral analysis Figure 2 4 illustrates a word hood spoken by a 5 year old boy The bottom plot depicts the time waveform The upper right plot depicts the conventional power spectrum The conventional power spectrum shows that the word hood
218. nal determines whether the signal to process is an analytical signal DEL xli is the time waveform Signal Processing Toolset 4 10 National Instruments Corporation DBL Chapter 4 Joint Time Frequency Analysis VIS parameter controls the resolution and crossterm interference parameter must be greater than zero Decreasing parameter suppresses the crossterm interference in the resulting spectrogram Unfortunately decreasing parameter also reduces the resolution of rows determines the maximum number of rows of the spectrogram pli k of frequency bins determines the number of columns of the spectrogram p illk by ELAR IB SUC 4 4 2 number of columns of frequency bins must be a power of two plil k is the Choi Williams distribution error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions Cone Shaped Distribution Computes the cone shaped kernel distribution TF DEL Analytical Signal 7 T t e BH Pus H of rows AM icd H of frequency bins Analytical Signal determines whether to process the analytical signal x i is the time waveform parameter controls the resolution and crossterm interference parameter must be greater than zero Decreasing parameter suppresses the crossterm interference in the resulting spectrogram Unfortunately decreasing parameter also reduces the resolution of rows
219. nal Controls for Arbitrary FIR Design Panel 20 29 Analysis of Filter Desron Panel zi Oi a tolecerbiawd gies 20 31 Maende Fy CS OMS scciaces dt hondh da sande a eode iue d odi d dusUe 20 32 Phase Response utat oo a e dtlauetia tiv Iba TU Ie unes 20 32 Tapuke RESPONS C Loss ved las a sisson es tenant Deseo a snewiees 20 33 Ste RESPON E ducas eom ada actor esu qct odes Obi md fuat fus Ebert cud d Ut rud ia 20 33 Z Plane Ploto sui S geo ticae a ec eae Ue te Ub CE unt UD ecu 20 33 HC Tor AR FEIE i eoe tita eti eite LE eaa eit OL ht ds 20 34 iS Nro oat al CU ei a te 20 34 IDA Oran Filter Pane lass esie pP oou Rn Li epi aa 20 35 Switching DISDIaVS Sotto ees a eei uon M o pd ton a hne 20 36 Cascaded Tiler Seg 685r qivitebh un eDreams tec ups ores e cod 21 12 Direct Fonn SUA CUTE seats aces es PU pont tad ca a eb teceepteediniastiiads 21 13 Direct Form IL Stu Cre unde UR UR UU A a 21 13 Third Octave Analyzer Setup Dialog BOX cccccccccesseeceeeeeeeeeeeeeeees 25 2 Internal Data Averaging Dialog Box serere 25 5 Four Channel Third Octave Analyzer Panel ssssss 25 6 One Channel Third Octave Analyzer Panel with Reference Signal 25 8 xvi National Instruments Corporation Contents Figure 26 1 Multistage Third Octave Analyzer Design Using FFT 26 4 Figure 26 2 Internal Data Averaging Procedure sssseeeee 26 5 Fig
220. nal Instruments Corporation 5 3 Signal Processing Toolset Chapter 5 Joint Time Frequency Analysis Applications window length window war zh 27E 0 coefficients sid 100 150 200 S00 350 392 gt high frequency gt high frequency Figure 5 3 Subimage Frequency Contents Signal Processing Toolset 5 4 National Instruments Corporation Chapter 5 Joint Time Frequency Analysis Applications Figure 5 4 illustrates the 2D STFT VI used for the image analysis plotted in Figure 5 2 In this example the row analysis window r1 i and column analysis function r2 i are the same Moreover N1 N2 4 and dM1 dM2 2 In other words the oversampling rate is 2 The relationship between the analysis windows and the resulting subimage is determined as follows e The ratio of the number of rows between the original image and the new image is equal to the oversampling rate N1 dM1 In this example 2 e The number of vertical subimages is equal to N1 e The ratio of the number of columns between the original image and the new image is equal to the oversampling rate N2 dM32 In this example 2 e The number of horizontal subimages is equal to N2 e The total number of subimages is equal to the product of the number of vertical subimages and the number of horizontal subimages In this example 16 National Instruments Corporation 5 5 Signal Processing Toolset Chapter 5 Joint Time Frequency Analysis
221. nalysis filter and H denotes a synthesis filter The subscript 0 denotes a lowpass filter and I denotes a highpass filter National Instruments Corporation In orthogonal filter banks Po z can be either maximum flat or positive equiripple f Mastlat Equinipple In biorthogonal filter banks Po z can be maximum flat general equiripple or positive equiripple y Masfla General Equinpple Postive Equinpple The maximum flat filter differs from the Butterworth filter and has the following form P z z 2 The parameter p is controlled by the zero pairs at 7 control Q z is a 2p 2 order polynomial which you can uniquely determine if p is decided Therefore the total number of coefficients of Po z is 4p 1 The equiripple is further divided into the general equiripple and positive equiripple filters However you can select only general equiripple filters for biorthogonal filter banks Although both are halfband filters the sum of the normalized passband and stopband frequencies equals 0 5 the Fourier transform of the positive equiripple filter po n is always real and non negative There are 11 7 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit two parameters associated with equiripple filters the of taps and normalized passband frequency as illustrated in Figure 11 7 Design Panel 4 File Edit Operate Project Windows Help Menu w O
222. namic link libraries for Windows users Chapter 25 Operating the Third Octave Analyzer describes the Third Octave Analyzer application and explains the program features Chapter 26 Third Octave Analysis Design describes the design specifications and algorithms of the Third Octave Analysis toolkit Chapter 27 Third Octave Filters VI describes the Third Octave Filters VI and its parameters Chapter 28 Building Windows Applications for Third Octave Analysis describes how to build a third octave analysis application under Windows 95 NT Chapter 29 Third Octave References lists reference material that contains more information on the theory and algorithms implemented in the Third Octave Analysis toolkit Chapter 30 Third Octave Error Codes lists the error codes returned by the Third Octave Filters VI and the C function ThirdOctave Analyzer XXi Signal Processing Toolset About This Manual Part VI VirtualBench DSA e Chapter 31 VirtualBench DSA explains the VirtualBench DSA features and how to acquire and measure signals with the DSA e Appendix A Customer Communication contains forms you can use to request help from National Instruments or to comment on our products and manuals e The Glossary contains an alphabetical list and description of terms used in this manual including abbreviations acronyms metric prefixes mnemonics and symbols e The ndex contains an alphabetical list of key terms and topics in th
223. nclude Magnitude vs Frequency plot y axis passband response stopband attenuation and tracking cursor magnitude The frequency and magnitude indicators display the location of the tracking transparent square cursor This cursor is locked to the frequency response H f so moving this cursor updates the frequency and magnitude digital displays with data points from H f You can enter the complete filter specifications using the text entry portion of the design panel as shown in Figure 20 9 passband resp pp 2600 Dn passband freq stopband atten stopband freq 3000 O00 z aj 2 5 kil 5 Bn p type alb andpass design Elliptic sampling rate Figure 20 9 Text Entry Portion of Design Panel The passband response is the minimum gain in the passband The horizontal blue cursor line represents this response in the Magnitude vs Frequency plot 20 12 National Instruments Corporation Chapter 20 Digital Filter Design Application In the passband the filter gain is guaranteed to be at least as high as the specified passband response Gp IH f Gp The first passband frequency defines one frequency edge of the passband The first vertical blue cursor line represents this frequency in the Magnitude vs Frequency plot The second passband frequency defines the second frequency edge of the passband The second vertical blue cursor line represents this frequency in the Magnitude vs Fre
224. nctions refers to the sets of periodic sinusoidal functions with fundamental frequencies that are all multiples of a single positive frequency 27 T You accomplish the comparison process with the following correlation or inner product operation 27k a a poem Ara T where a is the Fourier coefficient and denotes a complex conjugate The magnitude of a indicates the degree of similarity between the signal s t and the elementary function exp j27kt T If this quantity is large it indicates a high degree of correlation between s t and exp j27kt T If this quantity is almost 0 it indicates a low degree of correlation between s t and exp j27kt T Therefore you can consider a as the measure of similarity between the signal s t and each complex sinusoidal function exp j27ki T Because exp j27kt T represents a distinct frequency 27k T a frequency tick mark the Fourier coefficient a indicates the amount of signal present at the frequency 27k T In Figure 9 1 s f consists of two truncated sine waveforms The inner product of such truncated signal and pure sine waveforms which extends from minus infinity to plus infinity never vanishes In other words a is not zero for all k However the dominant a with the largest magnitude 9 2 National Instruments Corporation Chapter 9 Wavelet Analysis corresponds to 1 Hz and 2 Hz elementary functions This indicates that the primary components of s t are 1 Hz and 2 Hz si
225. ncy points is fixed at 2 048 The peak value is normalized to O db amplitude gives an array of amplitudes DEL DEL phase gives an array of phases DEL frequency gives an array of frequencies DBL noise estimation indicates the covariance of the Gaussian white noise Prony s Method Applies the Prony s method to estimate the parameters of exponentially damped sinusoids The parameters include amplitudes phases damping factors and frequencies positive frequency xn amplitude of complex sinusoids phase sampling frequency damping factor frequency TE positive frequency When it is true the VI provides only amplitudes phases and frequencies associated with the positive frequency components DEL x n is the time waveform of complex sinusoids determines the number of sinusoids Notice that a real sinusoid generates two complex sinusoids The parameter of of complex sinusoids is crucial and directly affects the accuracy of the resulting estimation However you can apply the MDL vi to estimate this parameter if you are not sure how many sinusoids exist Ll sampling frequency controls the sampling frequency The default value is 1 Hz i DBL amplitude gives an array of amplitudes National Instruments Corporation 17 5 Signal Processing Toolset Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs DBL DBL DBL phase gives an array of phases da
226. nd you load a specification file saved in the Classical FIR Design panel the DFD application prompts you to open the Classical FIR Design panel to resume work on the loaded filter specifications Saving Filter Coefficients Select DFD Menu Save Coeff to save your filter coefficients to a file The DFD application first prompts you for the format of the coefficient file You can select text format or log format Select text format to view or print the coefficient file or to use the coefficients in other non LabVIEW filtering applications Select log format for LabVIEW only filtering applications However LabVIEW filtering utilities read both text formatted and log formatted coefficient files After you select the format of the coefficient file the DFD application prompts you for the name of the filter coefficient file to save Name your coefficient files appropriately for a given filter design For example if you save bandpass IIR filter coefficients name the file bpiir txt or bpiir log depending on the coefficient file type National Instruments Corporation 20 5 Signal Processing Toolset Chapter 20 Signal Processing Toolset Digital Filter Design Application Analyzing Filter Designs To analyze your filter design choose DFD Menu Analysis The DFD application loads and runs the Analysis of Filter Design panel From this analysis panel you can view the filter magnitude response phase response impulse response step resp
227. nel See Digital Filter Design DFD application Analysis2DArraySize function 12 20 to 12 21 AnalysisFilterBank function 12 22 to 12 23 AnalysisFilterBank2D function 12 24 to 12 28 AR auto regressive model 16 1 to 16 3 coefficients and power spectra 16 3 to 16 4 damped sinusoids and 16 4 to 16 5 description 16 1 to 16 3 principle component auto regressive method 16 6 to 16 7 selecting upper bound AR order 18 3 National Instruments Corporation Arbitrary FIR Design panel See Digital Filter Design DFD application ARMA auto regressive and moving average model 16 1 to 16 3 ARMA filters See IIR filters auto regressive AR model See AR auto regressive model biorthogonal filter banks 10 4 to 10 9 B spline filter banks 10 7 to 10 8 halfband filter figure 10 6 maximum flat filter 10 6 to 10 7 Zeros distribution for maximum flat filter figure 10 7 bulletin board support A 1 C cascade form IIR filtering 21 2 to 21 3 Choi Williams distribution CWD Choi Williams distribution VI 4 10 to 4 11 description 3 9 Offline Joint Time Frequency Analyzer application 5 14 three tone test signal figure 3 9 Classical FIR Filter Design panel See Digital Filter Design DFD application Classical IIR Filter Design panel See Digital Filter Design DFD application Cohen s class description 3 8 to 3 9 historical background 2 6 Cohen s Class VI 4 10 Computations panel VirtualBench DSA 31 5 to 3
228. ng example application included with the Super Resolution Spectral Analysis toolkit This example software is designed to help you learn about model based analysis Chapter 19 Super Resolution Spectral Analysis References lists reference material that contains more information on the theory and algorithms implemented in the Super Resolution Spectral Analysis toolkit XX National Instruments Corporation About This Manual Part IV Digital Filter Design Toolkit Chapter 20 Digital Filter Design Application describes the DFD application you use to design infinite impulse response IIR and finite impulse response FIR digital filters Chapter 21 ZIR and FIR Implementation describes the filter implementation equations for IIR and FIR filtering and the format of the IIR and FIR filter coefficient files Chapter 22 Using Your Coefficient Designs with DFD Utilities describes the DFD utilities you use for filtering applications Chapter 23 DFD References lists reference material that contains more information on the theory and algorithms implemented in the DFD toolkit Part V Third Octave Analysis Toolkit National Instruments Corporation Chapter 24 Overview of the Third Octave Analysis Toolkit explains how you can use this program The Third Octave Analysis toolkit can act as a stand alone application or as an add on toolkit for LabVIEW The toolkit also provides the instrument driver for LabWindows CVI users and dy
229. nl long nh long nsize 8 Computes the sizes of four output arrays for AnalysisFilterBank2D Call this function to compute the sizes for four arrays before calling AnalysisFilterBank2D Parameters Input long integer The size of lowpass filter in the analysis filter bank long integer The size of highpass filter in the analysis filter bank Signal Processing Toolset 12 20 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference Output long integer array The array contains all the size information of four output arrays in AnalysisFilterBank2D The array size of nsize must be 8 Assume the four arrays are low_low low_high high_low and high_high then nsize 0 the number of rows of array low low nsize 1 the number of columns of array low low nsize 2 the number of rows of array low high nsize 3 the number of columns of array low high nsize 4 the number of rows of array high low nsize 5 the number of columns of array high low nsize 6 the number of rows of array high high nsize 7 the number of columns of array high high Return Value a 3 Deep a aa Poe A to Chapter 14 Wavelet Error Codes for a description of the error National Instruments Corporation 12 21 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference AnalysisFilterBank long status AnalysisFilterBank double x long nx FilterBankPtr AnalysisFilters long padtype
230. nsform to reconstruct the original signal The resulting signal has less noise interference if the threshold is set properly Refer to Donoho 1995 for more information about wavelet transform based denoising Although Figure 9 10 uses only 25 percent of the data the reconstruction preserves all important features contained in the original image The left image is transformed into the wavelet basis with 75 percent of the wavelet components set to zero those of smallest magnitude The right image is reconstructed from the remaining 25 percent wavelet components Original Image Reconstruction Figure 9 10 Denoise Performance Issues Although wavelet analysis possesses many attractive features its numerical implementation is not as straightforward as its counterparts such as conventional Fourier transform and short time Fourier transform The difficulty arises from the following two aspects e In order to reconstruct the original signal the selection of the mother wavelet w t is not arbitrary Although any function can be used in Equation 9 2 you sometimes cannot restore the original signal based on the resulting wavelet coefficients W n W t is a valid or qualified National Instruments Corporation 9 13 Signal Processing Toolset Chapter 9 Wavelet Analysis wavelet only if you can reconstruct the original signal from its corresponding wavelet coefficients The selection of the qualified wavelet is subject to certain r
231. nt or the discontinuity of the first derivative is at k 500 The remaining plots are wavelet coefficients with National Instruments Corporation 9 9 Signal Processing Toolset Chapter 9 Wavelet Analysis different scale factors m As the scale factor increases you can pinpoint the location of the discontinuity Discontinuity on 400 EDD 800 1000 Large Scale m Medial Scale m Small Scale m Figure 9 7 Detection of Discontinuity Using wavelet analysis to detect the discontinuity or break point of a signal has helped to successfully repair scratches in old phonographs The procedure works by taking the wavelet transform on the signal smoothing unwanted spikes and inverting the transform to reconstruct the original signal minus the noise In 1889 an agent of Thomas Edison used a wax cylinder to record Johannes Brahms performing his Hungarian Dance No 1 in G minor The recording was so poor that it was hard to discern the melody By using wavelet transform researchers improved the sound quality enough to distinguish the melody Signal Processing Toolset 9 10 National Instruments Corporation Chapter 9 Wavelet Analysis Multiscale Analysis Using wavelet analysis you also can look at a signal from different scales commonly called multiscale analysis Wavelet transform based multiscale analysis helps you better understand the signal and provides a useful tool for selectively discarding undesired components
232. nu 20 11 to 20 12 filter order indicator 20 14 frequency and magnitude indicators 20 12 to 20 13 linear dB button 20 12 sampling rate control 20 13 type control 20 13 using 20 9 to 20 11 Index filter specification transfers table 20 7 loading filter specifications 20 5 returning to Main Menu 20 7 saving filter coefficients 20 5 saving filter specifications 20 4 to 20 5 simulated DAQ and filter testing 20 6 suggested specification filename extensions table 20 5 transferring filter designs 20 6 to 20 7 graph cursors 20 9 Main Menu panel 20 2 to 20 3 directly loading filter specification files 20 3 editing preferences 20 3 opening filter design panels 20 3 quitting application 20 3 overview 20 1 to 20 2 panning and zooming options 20 7 to 20 8 Pole Zero Placement filter design panel 20 19 to 20 24 add pole button 20 21 add zero button 20 21 controls and displays 20 21 to 20 24 common controls and features 20 4 to 20 9 DAQ and Filter panel 20 35 to 20 36 coordinates control 20 22 to 20 24 delete selected button 20 21 DAQ Setup button 20 36 DFD Menu 20 36 Filter Design control 20 36 illustration 20 35 on off switch 20 36 sampling rate indicator 20 36 DFD Menu 20 4 to 20 7 analyzing filter designs 20 6 DAQ and filter real world testing 20 6 National Instruments Corporation l 3 DFD Menu 20 21 gain control 20 24 illustration 20 20 sampling rate control
233. nx sizeof double LELIXOJ 4 free y0 free y1 goto errend tmp double malloc nx sizeof double if tmp free y0 free yl free x0 goto errend Compute the output from synthesis lowpass filter err InterpolationFilter y0 ny0 synptr gt Lowpass synptr gt nl 2 x0 nx if err free tmp return err Compute the output from synthesis highpass filter errernterpoldtionPilter yl nyl Synpbr Hrglhpass synptr nh 2 bmp rnx if err free tmp return err Compute the output from the synthesis filter bank for 1t 0si lt nxen f 30L1 tmp LL errend free x FreeCoeffWFBD anaptr FreeCoetfWEBD Synptr Signal Processing Toolset 12 36 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference ReadCoeffWFBD long status ReadCoeffWFBD char coeffPath FilterBankPtr AnalysisFilter FilterBankPtr SynthesisFilter Reads the analysis and synthesis filter bank coefficients from a text file You must call AllocCoeffWFBD to allocate filter bank structures for both analysis filter banks and synthesis filter banks The text file is created by using WFBD exe Parameters Input coeffPath The path of the text file to read Output AnalysisFilter FilterBankPtr The structure that holds the analysis filter bank coefficients If this pointer is set to NULL the function does not read the analysis filter bank coeffici
234. o known as the Gabor spectrogram Scientists at National Instruments developed In 1970 Gabor 1900 1979 was awarded the Nobel Prize in Physics for his discovery of the principles of holography 2 Wigner s pioneering application of group theory to an atomic nucleus established a method for discovering and applying the principles of symmetry to the behavior of physical phenomena In 1963 he was awarded the Nobel Prize in Physics Signal Processing Toolset 2 6 National Instruments Corporation Chapter 2 The Need for Joint Time Frequency Analysis the Gabor spectrogram in the early 1990s Based on the conventional Gabor expansion and the WVD the adaptive representation based spectrogram the adaptive spectrogram also was introduced by scientists at National Instruments Unlike the linear JTFA method the quadratic JTFA method is not unique This toolkit contains the following quadratic algorithms e adaptive spectrogram e Cohen s class Choi Williams distribution cone shaped distribution STFT spectrogram WVD e Gabor spectrogram Which method should you use Often the choice is application dependent Through these methods you can process the signals that the conventional Fourier transform cannot handle National Instruments Corporation 2 Signal Processing Toolset Joint Time Frequency Analysis Algorithms This chapter describes the algorithms the joint time frequency analysis JTFA VIs use
235. o perform computations The Power Estimate indicator shows the calculated power estimate in Vrms and dB V The power estimate is the sum of the total power in the frequency bins between and including the start and end frequency inclusive For dB V 1 Vrms 0 dB The AC Estimate and DC Estimate indicators show the calculated AC signal level in Vrms and dB and the calculated DC signal level in Volts Use the of Harmonics for THD control to set the number of harmonics to detect for total harmonic distortion THD and harmonic computation The computations are independent of the panel displays There is no relation between the harmonic markers on the display and the number of harmonics computed here The Harmonic Frequencies and Amplitudes indicator displays the frequencies and amplitudes for the selected channels e Hz displays the frequency of the harmonic e Vrms displays the amplitude in Vrms of the harmonic e dB displays the amplitude in dB V of the harmonic For dB V 1 Vrms 0 dB The THD Total Harmonic Distortion indicator displays fundamental amplitude harmonic amplitudes fundamental amplitude The THD Noise indicator shows the THD plus noise calculation in percentage and dB For best results use the 7 term Blackman Harris window when measuring THD Noise THD Noise also measures the Signal to Noise Ratio when the input signal is a pure tone single frequency sinusoid Signal Processing
236. o regressive PCAR method Compared to the covariance method the PCAR is less sensitive to noise but needs more computing time n AR coefficients AR order pear sels H of complex sinusoids DEL x n is the time waveform AR order determines the order of the auto regressive model which has to be bigger than or equal to the number of complex sinusoids For a good frequency estimation a higher order is recommended Usually AR order is at least two times larger than the number of complex sinusoids LII of complex sinusoids determines the number of sinusoids Notice that a real sinusoid generates two complex sinusoids The parameter of of complex sinusoids is crucial and directly affects the accuracy of the resulting estimation However you can apply the MDL vi to estimate this parameter if you are not sure how many sinusoids exist AR coefficients gives an array of auto regressive model coefficients m E D tne roots gives an array of polynomial roots that are complex numbers in general National Instruments Corporation 17 3 Signal Processing Toolset Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs PCAR Power Spectrum Computes the PCAR method based power spectrum Compared to the covariance based spectrum estimator this algorithm is less sensitive to noise but needs more computing time AT Graph amp n amplitude AH order phase H of complex sinusoids frequency sa
237. o test the signal are time shifted frequency modulated single window functions all with some envelope Because this modulation does not change the time or frequency resolutions Qian and Chen 1996 the time and frequency resolutions of the elementary functions employed in STFT are constant Figure 9 4 illustrates the sampling grid for the STFT frequency i time Figure 9 4 Short Time Fourier Transform Sampling Grid For wavelet transform increasing the scale parameter m reduces the width of the wavelets The time resolution of the wavelets improves and the frequency resolution becomes worse as m becomes larger Because of this wavelet analysis has good time resolution at high frequencies and good frequency resolution at low frequencies National Instruments Corporation 9 7 Signal Processing Toolset Chapter 9 Wavelet Analysis Figure 9 5 illustrates the sampling grid for wavelet transform Suppose that the center frequency and bandwidth of the mother wavelet w t are Wo and Aj respectively The center frequency and bandwidth of y 2 t are 2 p and 2 A Although the time and frequency resolutions change at different scales m the ratio between bandwidth and center frequency remains constant Therefore wavelet analysis is also called constant Q analysis where Q center frequency bandwidth frequency l S 2 0 D D V gt O D JE 3 2009 9 o 8 e m 5 Wo D Q time Figure
238. o the Wigner Ville distribution as the order increases If the order is low the type of analysis window influences the Gabor spectrogram although the effect is not as large as that on the STFT Select your Gabor spectrogram analysis window based on the window information obtained in step 1 4 Increase the order until the crossterm interference becomes obvious For most applications an order of three to five should be adequate 5 Reduce the data block length and increase the freq zoom to examine detailed features Can I Measure a Signal s Energy in the Joint Time Frequency Domain Point to Point This question addresses a fundamental issue in the joint time frequency analysis area Except for a few special cases the answer is no As far as scientists are aware no algorithm can meaningfully measure a signal s energy point to point in the joint time frequency domain Roughly speaking the result P t w of all quadratic JTFA algorithms indicates a certain type of weighted average energy near the point f f Some algorithms take an average over a larger area such as the STFT spectrogram In this case the time frequency resolution is poor but it is always greater than or equal to zero Some methods cause heavy weights on a small number of points such as the high order Gabor spectrogram which yields better time frequency resolution In this case some points might approach negativity which is not acceptable for certain applications
239. oefficients Show Wavelets invokes the Wavelets and Filters panel Use this panel to display the mother wavelet scaling functions and the filter coefficients Save Design saves the design information in a binary file Load Design loads a saved design information file 11 9 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit e Save Filter Coefficients saves the designed analysis filter coefficients and synthesis filter coefficients in a text file e Show Filter Coefficients displays a table that lists the designed analysis and synthesis filter coefficients 1D Data Test You can use the 1D Test panel shown in Figure 11 8 to test the designed wavelet and filter bank for 1D data To access the panel in LabVIEW open 1D Test in Examples 11b in the Examples Signal Processing Toolset Wavelet and Filter Bank Designer directory in your LabVIEW directory If you are not using LabVIEW the Wavelet Application dialog box appears when you launch the Wavelet and Filter Bank Design toolkit Use the pull down menu in this dialog box to select and open 1D Test Extension Type I 1D Test symmetric Display l l l l l l 11 250 500 750 1000 1250 1500 1738 d path 2 01 0 100 200 300 400 500 EDO 700 800 858 t Palo l l l l l l l l l 100 200 300 400 500 B00 700 00 S33 Figure 11 8 1D Test Pane
240. ogram with a Wideband Hanning Window for the Three Tone Test Signal Signal Processing Toolset 3 4 National Instruments Corporation Chapter 3 Joint Time Frequency Analysis Algorithms Wigner Ville Distribution and Pseudo Wigner Ville Distribution For a signal s i the Wigner Ville distribution is L 2 WVDI k Y Rl m e 77 m L 2 where the function R i m is the instantaneous correlation given by R i m z i m z i m The WVD can also be computed by L 2 WVDU k V Ri men m L 2 where Rfi m Zli m Z i 2 m Z k denotes the Fourier transform of z 7 The Wigner Ville distribution is simple and fast It has the best joint time frequency resolution of all known quadratic JTFA algorithms However if the analyzed signal contains more than one component the WVD method suffers from crossterm interference Figure 3 3 depicts the WVD of the three tone test signal Three real signal terms are centered at 0 03 sec 400 Hz 0 09 sec 100 Hz and 0 09 sec 400 Hz Three crossterms exist labeled as 1 2 and 3 in Figure 3 3 Autoterms at 0 03 sec 400 Hz and 0 09 sec 400 Hz which have different time centers cause crossterm 1 Autoterms at 0 09 sec 100 Hz and 0 09 sec 400 Hz which have different frequency centers cause crossterm 3 Autoterms at 0 03 sec 400 Hz and 0 09 sec 100 Hz create crossterm 2 The crossterm reflects the correlation between a pair of corresponding autoterms al
241. only with half of the z plane Once you select z the program automatically includes its complex conjugate z Signal Processing Toolset 11 2 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Figure 11 2 Non Negative Equiripple Halfband Filter For both orthogonal and biorthogonal wavelets and filter banks you can use either maximum flat or equiripple filters for the product of lowpass filters Po z The maximum flat filters have good frequency attenuation but wider transition band Because the filter has the form Py tz Q you can impose as many zeros at T as you like On the other hand the halfband equiripple filters can have only a pair of zeros at m which gives the equiripple type filters slower convergence rates However it is easier to balance the frequency attenuation and transition band for an equiripple filter For a given transition band the attenuation is proportional to the filter order of Po z The larger the order the better the attenuation National Instruments Corporation 11 3 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Once you determine Po z you must factorize it into the lowpass filters Go z and H z The combination of zeros is not unique Table 11 1 summarizes some important filter combinations Figures 11 3 through 11 5 plot the zeros distribution Table 11 1 Filter Comparison Real com
242. onse and pole zero plot You also can view and print full screen plots of each response From the full screen views you can save the analysis results to a text file DAQ and Filter Real World Testing If you have a National Instruments DAQ device you can test the present filter design on real world signals by choosing DFD Menu DAQ and Filter The DFD application loads and runs the DAQ and Filter panel From this panel you can configure your DAQ device and then acquire real signals The acquired data passes through the currently designed filter and the DFD application plots the input and output waveforms and spectrums Simulated DAQ and Filter Testing You also can test your filter designs using a built in simulated function generator Choose DFD Menu DAQ and Filter and configure the DAQ source to simulated DAQ You then can click the Function Generator button on the DAQ and Filter panel to view and edit settings that include signal type frequency amplitude and noise level Transferring Filter Designs You can transfer some filter design specifications from one design panel to another For example you can configure your passband and stopband requirements while you design an FIR filter and find the IIR filter that meets your design specifications Not all design panels can share specifications Table 20 2 shows the transfers you can perform and the corresponding DFD Menu options 20 6 National Instruments Corporation Chapter 2
243. ontrol 31 2 Magnitude Unit control 31 2 Magnitude Phase Mode control 31 2 Main Control Bar buttons 31 4 Marker button 31 3 Marker Display indicator 31 5 Markers control 31 2 Measurement Displays 31 5 Palette controls 31 3 to 31 4 Pause button 31 4 Phase Unit control 31 2 Run button 31 4 Single button 31 4 Status Display indicator 31 5 Trigger Timeout indicator 31 4 launching 31 1 overview 1 3 waveforms 31 10 to 31 13 generating reports for use in other applications 31 12 to 31 13 loading reference waveforms 31 10 to 31 11 precise measurements using markers 31 10 saving reference waveforms 3 11 to 31 12 Visual Basic Third Octave Analysis applications 28 4 W waveforms in VirtualBench DSA 31 10 to 31 13 generating reports for use in other applications 31 12 to 31 13 National Instruments Corporation l 11 Index loading reference waveforms 31 10 to 31 11 precise measurements using markers 31 10 saving reference waveforms 31 11 to 31 12 wavelet analysis 9 1 to 9 14 applications of 9 9 to 9 13 denoise 9 13 detrend 9 12 discontinuity detection 9 9 to 9 10 multiscale analysis 9 11 compared with Fourier analysis 9 7 to 9 9 compared with Fourier transform comparison of transform processes figure 9 9 short time Fourier transform sampling grid figure 9 7 wavelet transform sampling grid figure 9 8 comparison of FFT JTFA wavelets and model based methods table 15
244. ortant information about the window type and averaging used and the state of the source output as shown in Figure 31 2 Figure 31 2 VirtualBench DSA Status Display e The Marker Display indicator shows the location of the m1 and m2 markers as shown in Figure 31 3 The Marker Display also shows the difference between the m1 and m2 markers HHFUIITEEHIENCERHUIENEUTENEUEDOTENU EDIT Figure 31 3 VirtualBench DSA Marker Display Computations Panel Features This section explains the features of the Windows Computations panel shown in Figure 31 4 With the Computations panel you can make several different computations on one or two channels while simultaneously acquiring data in the Measurements panel To select the channels to make computations on click one or both of the Channel Select controls at the top of the panel E Computations File Help Channels Power Eshmate EXEEZXE views 2 AC Estimate ERET BEDS EEM Start Freg Hz DC Estimate End Freq Hz Es Vols 000 00 b HHamonics ioe THO M Hamanie Fiege and Ampls Channel B Powe Estimate BE o EE C Start Freq Hz ow DC E stimaba End Freq Hz EE vos Mon I Haemornics ice THO M Hamonic Freq s ard Amps Figure 31 4 Computations Panel National Instruments Corporation 31 5 Signal Processing Toolset Chapter 31 VirtualBench DSA Use the Channel Select ring controls to select the channel or reference waveform on which t
245. oves that point from the selection list linear intere The interpolation control selects the type of interpolation the DFD application uses to generate the desired response from the array of frequency magnitude points Choose linear interp to create flat filters lowpass highpass bandpass and bandstop Choose spline interp to create smoothly varying filters Click the ins button to insert a frequency magnitude point between the selected point and the next point If the selected point is the last point in the frequency magnitude array the DFD application inserts the new point between the last two points of the array The DFD application inserts new points halfway along the line connecting the two outer points Click the del button to delete the selected frequency magnitude points The DFD application deletes all selected points The selected points indicator displays the selected frequency magnitude points as shown in Figure 20 21 You can select points on the Arbitrary Magnitude Response graph by clicking the point You also can select points directly from the frequency magnitude array by clicking the circle to the right of each point as shown in Figure 20 22 selected points Figure 20 21 Selected Points Indicator National Instruments Corporation 20 27 Signal Processing Toolset Chapter 20 Digital Filter Design Application filter order lb ripple 1 3708E Signal Processing Toolset Figure 20 22 displays the a
246. pa pi Mem uos rua dir anat anda weaned cane dedseubeu Lov ben epe ud 20 4 Example Or Graph Paletiet csse ese od us vada Irvine b dea atate pious 20 7 Zoom Tool Pop Up MGBU aia tpe t ota ead tds n west Tees ora hanes 20 8 Example of Two Cursors on a Graph sse 20 9 Classical TTR Dest om Pane lendsi na eu aptos esa UOS EA UR D DE 20 9 Mapnitude ys PEeQUEDE Vossius e tC HO EE PARA ELE atr eates crwiod v id quus 20 11 Text Entry Portion of Design Panel sene 20 12 Classical FIR Design Panels corp e Ear recen ERE t bd 20 14 Frequency Response Magnitude sincsen a 20 17 Text Based IntetlaCe inset Pu in a diu eb be meo pac inet ids 20 18 Pole Zero Placement Filter Design Panel eeesese 20 20 Z Plane Plotor Filt r Poles and Zeros ioien Here t ler visit ease 20 21 Array of Zeros in Rectangular Coordinates ssseeseeeessseee 20 22 Array of Poles in Rectangular Coordinates cccccccccceeceeeeeeeeeeeeeees 20 23 Array of Zeros and Poles in Polar Coordinates 20 23 Ma snitudevsErequerney ids edo ubi a Haero tas eel Acca ee 20 24 Arpitrary FIR Design P riel cci es a E a Eu Ee 20 25 Desired and Actual Magnitude Response eeeeeeeeeesseee 20 26 Selected Points Indicator des uei eub Lp ed ode totu aae assetto d ure 20 27 Array of Frequency Magnitude Points seeeee 20 28 Additio
247. ples Among these samples 93 05 percent are from the low low subimage 12 147 coefficients 6 23 percent are from the low high subimage 814 coefficients and 0 85 percent are from the high low subimage 111 coefficients None are from the high high subimage Remaining Data displays your choice for the percentage of the largest data from the four subimages which is used for the reconstruction Signal Processing Toolset 11 14 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit extension determines the padding method for the data You have the following choices zero padding adds zeros at the beginning and end of the original data symmetric extension symmetrically adds the input data at the beginning and end of the original data In both cases you can add the number of points at the beginning and the end of the original data with the following formula aA NON 2 2 where N is the number of coefficients of Po z N is the number of coefficients of filter Go z and N is the number of coefficients of filter Ho z 1 Data reads a 2D spreadsheet text file or standard image file such as a tif or bmp file Be sure to choose the correct data type when reading the data file Wavelets and Filters As illustrated in Figure 11 12 the Wavelets and Filters panel displays the mother wavelet and scaling functions and the filter coefficients Go z G4 z Ho z and H z
248. plex conjugate easy to implement 11 2 symmetrical Minimum Phase z lt 1 for all i on or important for control systems inside of unit circle all zeros have to be on or inside of the unit circle Linear Phase must contain both z and desirable for image processing its reciprocal 1 z the pair of reciprocals must be in the same filter Orthogonal cannot have z and its analysis and synthesis have the reciprocal 1 z same performance SEQUI convenient for bit allocation and z and its reciprocal quantization error control have to be in the not linear phase separated filters contradictory to linear even length N odd phase Signal Processing Toolset 11 4 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Figure 11 3 Minimum Phase Filter joe 150 LE 1 00 075 0 50 0 25 41107 200 150 100 050 O00 o50 1 00 Figure 11 4 Linear Phase Filter 2 00 ilem 1 50 25s 1 00 Dea 0 50 0 25 amp 10 i 2 00 150 1 00 0 50 Figure 11 5 Orthogonal Filter i Note The conditions for linear phase and orthogonality are contradictory In general you cannot achieve linear phase and orthogonality simultaneously National Instruments Corporation 11 5 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Design Panel If you use LabVIEW with the WFBD toolkit you design your wavel
249. processing You can use the Third Octave Analysis toolkit to analyze stationary acoustic and audio signals Because the frequency contents and average properties of a stationary signal do not vary with time the spectrum of the signal also does not change over time For example the speech waveform of a conversation or the noise from a vehicle roughly can be regarded as a stationary signal over a short time interval You should not use the Third Octave Analysis toolkit with transient signals The Third Octave Analysis toolkit meets the conditions for Order 3 Type 3 D one third octave filters as defined in the ANSI S1 11 1986 standard Table 24 1 shows the filter band center frequencies in hertz as defined by this standard You can see in this table that the center frequency increases at a logarithmic rate For a given filter in the filter bank the bandwidth of the filter is determined by 2 9 21 1 fm where fm is the designated center frequency Because fm increases logarithmically the bandwidth also increases logarithmically Table 24 1 Filter Bands for ANSI 1 11 ANSI A weighting dB Band Center Frequency Factor to mimic Number Hz 1 3 Octave human hearing Data is out of the dynamic range of the analyzer Signal Processing Toolset 24 2 National Instruments Corporation Chapter 24 Overview of the Third Octave Analysis Toolkit Table 24 1 Filter Bands for ANSI 1 11 Continued A weighting dB Center Frequency
250. pt for order l where must be odd But even order terms are arbitrary You can summarize these observations by the following formula 0 n odd and n 1 poln 2 4 2 pm 10 8 arbitrary n even This reduces the design of two channel PR filter banks to two steps 1 Design a filter Po z that satisfies Equation 10 8 2 Factorize Po z into Go z and Ho z Then use Equation 10 3 to compute G z and H z National Instruments Corporation 10 5 Signal Processing Toolset Chapter 10 Digital Filter Banks The following two types of filters are frequently used for Po z e anequiripple halfband filter Vaidyanathan and Nguyen 1987 e amaximum flat filter In the first filter the halfband refers to a filter in which O T where and denote the passband and stopband frequencies respectively as in Figure 10 4 Figure 10 4 Halfband Filter The second filter is the maximum flat filter with a form according to the following formula Py z Q o 10 9 which has 2p zeros at z 1 or 7 If you limit the order of the polynomial Q z to 2p 2 then Q z is unique i s Note The maximum flat filter here differs from the Butterworth filter The low frequency asymptote of the Butterworth filter is a constant The maximum flat filter is not In all cases the product of lowpass filter Po z is a type I filter poln pglN n N even where N denotes the filter order Consequently the number of coe
251. pter 3 Joint Time Frequency Analysis Algorithms current data gauss3 tut gauss3 t t but data length sec 1286 1 spectrum is 4 0E 2 3 0E 2 2 0E 2 1 0E 2 0 0E 0 2 0E 0 1 0E 0 000E 0 sec 2 15E 2 Hz 0 0E 0 1 0E 0 1 7E 0 i i i sec 0 0E 0 2 UE 2 4 0E 2 6 0E 2 B 0E 2 1 0E 1 1 3E 1 Exe siot contral Figure 3 4 Pseudo Wigner Ville Distribution with Gaussian Window w m for the Three Tone Test Signal In the second method you assign weights to the instantaneous correlation R i m in the frequency domain L 2 WVDlik s Him 9t yug uen 3 4 m L 2 This weighting function effectively suppresses crossterms that correspond to a pair of autoterms with different frequencies such as crossterms 2 and 3 in Figure 3 3 Figure 3 5 illustrates the PWVD with the Gaussian window function H m Compared with the WVD in Figure 3 3 the PWVD successfully eliminates crossterms 2 and 3 National Instruments Corporation 3 7 Signal Processing Toolset Chapter 3 Joint Time Frequency Analysis Algorithms Cohen s Class Signal Processing Toolset current data gauss3 tut gauss3 t t but data length sec 1 28E 1 spectrum Tp 4 0E 2 3 0E 2 2 0E 2 1 0E 2 D OE 0 2 0E 0 1 0E 0 000E 0 sec 2 15E 2 Hz 0 0E 0 1 0E 0 1 7E 0 I I I I I I sec D E 0 20E 2 406 2 amp E2 80E 2 10E4 aes EM control s Figure 3 5 Pseudo Wigner
252. quency plot The stopband attenuation is the minimum attenuation in the stopband The horizontal red cursor line represents this attenuation in the Magnitude vs Frequency plot In the stopband the filter gain is guaranteed to be no higher than the specified stopband attenuation Gs IH f lt Gs The first stopband frequency defines one frequency edge of the stopband The first vertical red cursor line represents this frequency in the Magnitude vs Frequency plot The second stopband frequency defines the second frequency edge of the stopband The second vertical red cursor line represents this frequency in the Magnitude vs Frequency plot The sampling rate control specifies the sampling rate in samples per second hertz The type control specifies one of four classical filter types according to the following values e lowpass e highpass e bandpass e bandstop National Instruments Corporation 20 13 Signal Processing Toolset Chapter 20 Digital Filter Design Application filter order The design control specifies one of four classical filter design algorithms according to the following values e Butterworth e Chebyshev e Inverse Chebyshev e Elliptic The filter order indicator displays the estimated filter order of the classical IIR filter The DFD application automatically estimates the filter order as the lowest possible order that meets or exceeds the desired filter specifications The message window displ
253. r 24 1 See also Third Octave Analyzer Offline Joint Time Frequency Analyzer 5 8 to 5 15 adaptive spectrogram 5 13 to 5 14 applying pre emphasis filter 5 11 changing spectrogram display 5 9 Choi Williams distribution 5 14 cone shaped distribution 5 15 frequency zooming 5 11 Gabor spectrogram 5 13 illustration 5 9 inputting data 5 10 Pseudo Wigner Ville distribution 5 14 saving results 5 10 selecting JTFA method 5 12 Signal Processing Toolset Index setting time parameters 5 12 STFT spectrogram 5 12 switching between conventional power and instantaneous spectrum 5 10 to 5 11 1D data test Wavelet and Filter Bank Design toolkit 11 10 to 11 13 Online STFT Spectrogram Analyzer 5 7 to 5 8 orthogonal filter banks 10 9 to 10 11 P PCAR Method VI 17 3 PCAR Power Spectrum VI 17 4 to 17 5 Pole Zero Placement filter design panel See Digital Filter Design DFD application power spectra and model coefficients 16 3 to 16 4 pre emphasis filter Offline Joint Time Frequency Analyzer application 5 11 principle component auto regressive method 16 6 to 16 7 Prony s method 16 7 Prony s Method VI 17 5 to 17 6 Pseudo Wigner Ville distribution description 3 6 to 3 8 with Gaussian window for three tone test signal figure 3 7 Offline Joint Time Frequency Analyzer application 5 14 PWVD VI 4 13 three tone test signal figure 3 8 Q quadratic JTFA algorithms 3 3 to 3 13 adaptive spectrogram 3 1
254. r 12 WFBD Toolkit Function Reference a iene integer E TTE UE UNIONE size of lowpass filter in the synthesis filter bank nh long integer The size of highpass filter in the synthesis filter bank Output rows wows a integer PilsiondsesiheDeduU D row size of the 2D output array for SynthesisFilterBank2D cols long integer The column size of the 2D output array for SynthesisFilterBank2D Return Value status integer Refer to Chapter 14 Wavelet Error Codes for a description of the error National Instruments Corporation 12 39 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference SynthesisFilterBank long status SynthesisFilterBank double yO long nyO double yl long nyl FilterBankPtr SynthesisFilters double x long nx Computes the output of a 2 channel synthesis filter bank It performs the same operation as in the 2 Channel Synthesis Filter Bank VI Refer to the description for that VI for more information 2xny0 nl 1 2xnyl nh 1 Parameters E EN Nme ame Tye Description double precision The input data array for the synthesis array lowpass filter double precision The input data array for the synthesis array oo a filter SynthesisFilters FilterBankPtr The structure that holds the oa NN filter bank coefficients nx long integer The array size of x It must be 2xny0 nl 1 2xXnyl nh 1 The values of ny0 ny1 nl and nh must meet the above condition
255. r banks contains the following three steps 1 Determine the type of wavelet and filter banks orthogonal or biorthogonal 2 Select the type of filters based on the product P z of the two lowpass filters Go z and H z 3 Factorize Po z into Go z and H z National Instruments Corporation 11 1 Signal Processing Toolset Chapter 11 Using the Wavelet and Filter Bank Design Toolkit Step 1 Step 2 Step 3 Product of Lowpass Factorization Po z Go z Ho z B spline _1k Go z z me ar h Q z Maximum Flat Linear Phase 1 z 5 90 G z has to contain both zero z and its reciprocal 1 z Arbitrary l Linear Phase PANOJN Go z has to contain both General i Equiripple zero z and its reciprocal 1 z Arbitrary Linear Phase a G z has to contain both Positive l l Equiripple zero z and its reciprocal 1 z Arbitrary Minimum Phase Daubechies Maximum Flat Go z contains all zeros z l lt 1 1 2p 1 Arbitrar Orthogonal eee Ns d Zz gt Go z Minimum Phase 1 z gt Ho z Positive G z contains all zeros Iz lt 1 Equiripple Arbitrar P e 20 y Figure 11 1 Design Procedure for Wavelets and Filter Banks Because all filters in the WFBD toolkit act as real valued finite impulse response FIR filters the zeros of Po z Go z and Ho z are symmetrical in the z plane This implies that for any zero z there always exists z if z is complex refer to Figure 11 2 You need to deal
256. r best results however there are several things to consider For example the signal has to be a certain type of time series For example it should be able to be generated by the recursive difference equation P x n a x n k w n 15 3 k 1 where w n denotes the error Moreover you need to select the order of the model correctly Otherwise you might obtain an incorrect spectrum or parameter estimate Figure 15 9 is the plot of super resolution power spectra for the sum of two sinusoids in Figure 15 3 computed by the same model based methods as that in Figure 15 5 Covanance FCAR zl aj 40 40 AO F I I i I I l 60 l I I I I l 0 5 0 4 0 2 0 0 0 2 0 4 0 5 0 5 0 4 0 2 0 0 0 2 O4 0 5 Signal Processing Toolset Figure 15 9 Super Resolution Power Spectra with Order 10 for Sum Of Two Sinusoids 15 6 National Instruments Corporation Chapter 15 Introduction to Model Based Frequency Analysis Instead of choosing order four here the order is artificially increased to 10 Consequently in addition to the four real components several spurious peaks appear that do not actually exist Blindly applying model based techniques does not lead to a good estimation The good estimation relies on a proper selection of the signal model as well as the model order The rest of this section of the manual deals with this central topic One reason for using a few samp
257. rd Octave Analysis Toolkit Scientists and engineers in the fields of acoustics and vibration use the Third Octave Analysis toolkit to determine the spectral energy contained in a specific set of third octave bands With the Third Octave Analysis toolkit you can measure sound vibration and noise signals quickly and easily Third octave analysis applications include vibration tests of machines architectural acoustics power measurements and appliance testing The Third Octave Analysis toolkit conforms to ANSI Standard S1 11 1986 and features an easy to use graphical user interface for third octave analysis and data acquisition You can choose from one to four input channels each with its own windowing weighting and averaging capabilities You can compare the results of third octave analysis on the signal from each channel to those of a reference signal you have analyzed previously VirtualBench DSA Use the VirtualBench DSA Dynamic Signal Analyzer to acquire signals and measure the power spectrum harmonic content amplitude spectrum cross power spectrum frequency response coherence and impulse response You also can use the VirtualBench DSA as a low frequency oscilloscope to view signals separately in the time and frequency domains simultaneously With the VirtualBench DSA you gain the functionality of simultaneously analyzing signals on two channels VirtualBench DSA also provides markers for measuring the total harmonic distort
258. re much less sensitive to noise than that of the covariance method Prony s Method This method estimates the parameters of damped sinusoids First apply the covariance method to compute the AR coefficients aj Then find the complex roots z of the polynomial in Equation 16 14 The phase of z indicates the frequency and the amplitude is the damping factor Finally insert z into Equation 16 13 to solve Cj The amplitude and phase of the National Instruments Corporation 16 7 Signal Processing Toolset Chapter 16 Model Based Frequency Analysis Algorithms sinusoid component z are equal to the amplitude and phase of C respectively Matrix Pencil Method This is a modified Prony s method that is faster and less sensitive to noise than Prony s method However the derivation is more involved Refer to Hua and Sarkar 1990 for more information Minimum Description Length This algorithm determines the number of sinusoids n by min NIno 3nlnN where 6 is an estimation of the noise variance and N is the number of data samples The optimal value n can be used as the AR order p for the covariance method or the number of complex sinusoids L for PCAR and matrix pencil methods Signal Processing Toolset 16 8 National Instruments Corporation Super Resolution Spectral Analysis and Parameter Estimation Vis This chapter describes VIs used to perform super resolution and parameter estimation Each algorithm includ
259. record might be a result of a genuine lack of data as in the seismic patterns of an erupting volcano or a result of an artificially imposed restriction necessary to ensure that the spectral characteristics of a signal do not change over the duration of the data record as in speech processing When the data record is small scientists often think that the frequency resolution of FFT based power spectra is not adequate For example reduce the number of data samples to 15 Figure 15 3 shows the 15 sample data record The resulting FFT based power spectra are 15 2 National Instruments Corporation Chapter 15 Introduction to Model Based Frequency Analysis plotted in Figure 15 4 In this case neither one yields the frequency resolution high enough to resolve those two close sinusoids sum af two sinusoids Figure 15 3 Two Sinusoids with 15 Samples Covariance Rectangular Window Hamming Window 10 10 20 2l 30 30 40 40 5 i i i l 307 l i i l l 0 5 0 4 0 0 0 2 0 4 0 5 0 5 0 4 0 2 0 0 1 2 0 4 0 5 o 2A A far 95 1 Figure 15 4 FFI Based Power Spectra Based on 15 Samples An alternative is the model based method By employing model based analysis techniques you can achieve super resolution spectra Once you assume a suitable signal model and determine its coefficients you are presumably able to predict the missing data based on the given finite da
260. red cursor line represents this attenuation in the Magnitude vs Frequency plot In the stopband the filter gain is guaranteed to be no higher than the specified stopband attenuation Gs IH f lt Gs The first stopband frequency defines one frequency edge of the stopband The first vertical red cursor line represents this frequency in the Magnitude vs Frequency plot 20 18 National Instruments Corporation Chapter 20 Digital Filter Design Application The second stopband frequency defines the second frequency edge of the stopband The second vertical red cursor line represents this frequency in the Magnitude vs Frequency plot The sampling rate control specifies the sampling rate in samples per second hertz The type control specifies one of four classical filter types according to the following values e lowpass e highpass e bandpass e bandstop The filter order indicator displays the estimated filter order of the classical Ier order FIR filter The DFD application automatically estimates the filter order as the lowest possible order that meets or exceeds the desired filter specifications ere eer The minimize filter order button controls whether the DFD application minimizes the estimated filter order If this button 1s OFF the DFD application uses a fast formula to estimate the filter order to meet or exceed the desired filter specifications If this button is ON the DFD application iteratively adjusts the f
261. rent import libraries under wind11 1ib subdirectory of your installation directory For examples of how to call these functions check the directory CVI Support examples subdirectory of your installation directory WFBD Instrument Driver The Wavelet and Filter Bank Design toolkit provides an instrument driver wfbd fp for LabWindows CVI developers using the Windows 95 NT platform You can find this file in the CVI Support instr subdirectory of your installation directory The following are the function prototypes in the instrument driver typedef struct double Lowpass pointer to lowpass filter coefiierents long nl number of coefficients in Lowpass double Highpass pointer to the lowpass filter coefficients long nh number of coefficients in Lowpass IEilterBankStruct FilterBankPtr National Instruments Corporation 12 17 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference long status AnalysisFilterBank double x long nx FilterBankPtr AnalysisFilters long padtype double yol long ny0 double vin Long ny1 long status SynthesisFilterBank double yO long nyO double yll long nyl FilterBankPtr SynthesisFilters double x long nx long status DecimationFilter double x long nx double coef long ncoer double Init long ni double tirnmadk gt dong unb long deciact double y long ny long status InterpolationFilter double x long nx
262. requenc pling freq Cy 15 2 number of FFT points There 1s no such limitation for the model based methods Therefore the model based methods are much more accurate than that of the FFT based techniques The number of samples in Equation 15 1 and the number of FFT points in Equation 15 2 might not be equal For a given num ber of data samples you always are able to increase the number of FFT points simply by zero padding Increasing the number of FFT points reduces the frequency increment but does not improve the ability of resolving two close sinusoids National Instruments Corporation 15 5 Signal Processing Toolset Chapter 15 Introduction to Model Based Frequency Analysis Besides the super resolution power spectra model based analyses are also fundamental in many other signal processing applications such as e linear prediction for example linear predict code e signal synthesis e data compression for example speech compression e system identification Although the focus of this section of the manual is on frequency analysis the main engines signal model estimation provided in this software easily can be tailored for many other applications such as those listed in the previous paragraph Applying Model Based Method Properly As mentioned in the preceding section using model based methods can achieve super resolution power spectra with a limited number of data samples or estimate the parameters of damped sinusoids Fo
263. requency components noise indicates the Gaussian white noise covariance 17 6 National Instruments Corporation Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs DEL amplitude gives an array of amplitudes phase gives an array of phases m E E mf m P damping factor gives an array of exponential damping factors DEL frequency gives an array of frequencies Minimum Description Length Estimates the order of the AR model When PCAR or matrix pencil methods are used the output of this VI also can be used to estimate the number of sinusoids For PCAR or matrix pencil methods the order of the AR model is usually set at least two times larger than the number of sinusoids n l largest order optimal AR order DBL x n is the time waveform largest order determines the upper bound of AR orders A larger upper bound gives more choices for the optimal AR order The upper bound cannot be bigger than the number of samples x n Moreover the bigger the upper bound the longer the computing time p LII optimal AR order gives the estimated order of the AR model National Instruments Corporation 17 7 Signal Processing Toolset Applying Super Resolution Spectral Analysis and Parameter Estimation This chapter describes a comprehensive testing example application included with the Super Resolution Spectral Analysis toolkit This example software is designed to help you
264. rmonic Refer to the Making 31 2 National Instruments Corporation Chapter 31 VirtualBench DSA Precise Measurements Using Markers section in this chapter for more information The Display 1 Display 2 controls change the marker positions and display attributes of the respective displays Tal QPF MEEME National Instruments Corporation Use the Marker button to precisely control the position of markers 1 and 2 m1 and m2 You can select either marker by clicking the middle button The marker that appears on the middle button is the marker you can move with the left and right arrow buttons Refer to the Making Precise Measurements Using Markers section in this chapter for more information about markers Use the Legend control to display the trace attributes of each channel Pop up on a trace in the legend to see a menu of the following trace attributes e Common Plots configures a plot for a preset combination of point line and fill styles in one step A variety of preset options exist e Point Style Line Style and Line Width contains different display styles you can choose to distinguish your traces Your printer might not be able to print hairlines e Bar Plots options are vertical bars horizontal bars or no bars at all e Fill Baseline sets which baseline to fill Zero fills from the trace to a baseline generated at zero Infinity fills from the trace to the positive edge of the graph Infinity fills from t
265. ror m z z E i P t The VI performs the following operation Gl z Yo YI X GOz B W2 Y0 If you define input as x i and outputs as y0 and yl then Theo y0 5 GC i l nol yl A dons Bla i i where n 0 l nyo 1l m 0 1 ny 1 n o is the length of output yO nyo ceil n n 1 2 ny is the length of output y1 n ceil n ngo 1 2 n is the size of input array x i Nog 1s the size of GO Ng is the size of G7 GO 1s the analysis lowpass filter coefficients G is the analysis highpass filter coefficients XI is the input signal x i plus the initial condition Xi and final condition Xf which is decided by the selection of extension Signal Processing Toolset 12 2 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference If extension is zero padding zeros are added at the beginning and the end of x i Figure 12 1 shows how the VI constructs X in this case All the elements in Xi and Xf are zeros and the lengths of Xi and Xf are 2 Nog tNgy n ES dE That is 0 Osnsn 1 Xd ees n Sen big P 0 n tn SnsS2n n 1 X1 Xi X Xt Figure 12 1 Zero Padding If you select symmetric extension for your extension input x i is extended symmetrically at the first point at the beginning and the last point at the end according to the following equation Xs Ln Osnsn 1 xl Xn n n Snsn n 1 Xn n n n
266. rray of frequency magnitude points the DFD application uses to construct the desired filter magnitude response The DFD application forms the desired filter response by interpolating between these points frequency magnitude 20 0000 0000 O 271 428 21 0000 O 1142 85 21 0000 O Figure 20 22 Array of Frequency Magnitude Points The frequency of each point is in hertz and the magnitude is in linear or decibel units of gain depending on the setting of the button in the upper left corner of the Arbitrary Magnitude Response graph You can select points in this array by clicking in the circle to the right of each point You then can delete the selected points by clicking the del button You can move selected points by clicking the desired direction diamonds in the cursor movement control in the lower right corner of the Arbitrary Magnitude Response graph The filter order control specifies the total number of coefficients in the digital FIR filter The ripple indicator displays the largest absolute error linear between the desired and actual filter responses The message window displays errors that occurred during the FIR design procedure 20 28 National Instruments Corporation Chapter 20 Digital Filter Design Application Select the locked frequencies checkbox as shown in Figure 20 23 to lock the present frequency values of the frequency magnitude points If you select this checkbox you can alter only the magni
267. rs zio quos ete Edna de rente lusso Lors tls iets 21 11 CascadesPorm UR EAMECEHTEY iai oae bo ee EE PEE E tet ra itor 21 12 Pinte Impulse Response Filters coii odore boy ott e E ebd e pecie luat pibe iui eene 21 14 Format of the Pilter Coethicient Text Files etr or Etre Vel ta eiua 21 14 LEIR Coetticient brle FOrDlat sooo des guttis pute toni E Dv en ddas 21 14 TR Coebhicient FileFormat 5o correre REEL eh ters PR PP SR ee exe otc ta 21 16 Chapter 22 Using Your Coefficient Designs with DFD Utilities Tab VIBW DFO U DNUS oo etteiechum inb aeo eo pues eid Vt M Tta eeodi Poco Pico S 22 1 Read DFD dro RIS SEU LU TM 22 2 DED EE UTEM T ec o 22 3 LabWandows C Vi HG Six sites or etat o er UE ORE fap ROI re Do eoe Fen eb rea A 22 4 The DPDnstr tuent DE Ver sirota o tario Da Das b uU te e Podio Pu besar us 22 4 Using the DFD Instrument Driver 2 n EHE EratrD DE I On v eru treo eia 22 4 PINTO CC OCT big MT 22 5 Read Braves dB el usciti cttm E cunc dae t etapa iet 22 6 L tecC OCT DEDI eei Seed coa e pice vanaiin sata M Ocsccuse edam o oM d et eto m One nain 22 7 rer FD m EE 22 8 Windows DEL DED U GNIS 2 5 2 5 0d oe EEUU DEei Rb emtpbatbbxd coU nesopd codes O aaa 22 0 National Instruments Corporation Xi Signal Processing Toolset Contents Chapter 23 DFD References Part V Third Octave Analysis Toolkit Chapter 24 Overview of the Third Octave Analysis Toolkit D seription oftan Octave Amalyzet zoe e dom eodd e Ur IAM Oisea
268. rthogonal w I I I 0 6 0 8 1 0 Hoftaps passband 77 fom 4 19 0304 me Boe Sp Than 0 Must Be 4p 1 p 2 3 Figure 11 7 Equiripple Filter The of taps control displays the number of coefficients of Po z Because Po z is a type I FIR filter the length of Po z must be 4p 1 where p 2 3 The passband control displays the normalized cutoff frequency of Po z which must be less than 0 5 3 Factorize Po z into Go z and H z The plot in the lower half of the Design Panel in Figure 11 6 displays the zeros distribution of Po z Because all the zeros are symmetrical with respect to x axis only the upper half of the plane is displayed The selection of Go z and H z is to group different zeros The blue circle represents the zeros in Go z and the red cross represents the zeros in Ho z To select a zero place the cursor on the zero that you want to choose and click the left mouse button This switches the zeros from Go z to H z and vice versa All the zeros go to either Go z or Ho z The plot in the upper half of the panel displays the frequency response of filters Go z and G z G z is the sign alternated version of Hoz Therefore G z must be a highpass filter if Ho z is a lowpass filter If two zeros are too close to choose use the Zoom Tool palette located in the lower right corner of the Design Panel to zoom in on the zeros until you can identify the zero
269. s Title Signal Processing Toolset Reference Manual Edition Date January 1999 Part Number 322142A 01 Please comment on the completeness clarity and organization of the manual If you find errors in the manual please record the page numbers and describe the errors Thank you for your help Name Title Company Address E Mail Address Phone ___ Fax Mail to Technical Publications Fax to Technical Publications National Instruments Corporation National Instruments Corporation 6504 Bridge Point Parkway 512 794 5678 Austin Texas 78730 5039 Glossary Numbers Symbols Percent oo Infinity T Pi 1D One dimensional 2D Two dimensional A A D Analog digital alias term An image term in the frequency domain alternating flip For a periodic sequence g n with a period N the sequence 1 g N n is considered as alternating flip of g n analysis filter bank A filter bank that converts a signal from time domain into wavelet domain ANSI American National Standards Institute ANSI S1 11 1986 Specifications for octave band and fractional octave band analog and digital filters array Ordered indexed set of data elements of the same type ASCII American Standard Code for Information Interchange National Instruments Corporation G 1 Signal Processing Toolset Glossary basis biorthogonal filter bank block diagram Boolean controls and indicators Butterworth filter C
270. s For maximum flat filters there are Signal Processing Toolset 11 8 National Instruments Corporation Chapter 11 Using the Wavelet and Filter Bank Design Toolkit multiple zeros at z 0 Use the zeros at x control to determine how many zeros at z 0 go to Go z For the given Po z you have the following four choices for Go z and Ho z e Linear Phase Any zero and its reciprocal must belong to the same filter e Minimum Phase G z contains all the zeros inside the unit circle When P z is maximum flat and Go z is minimum phase the resulting wavelets are traditionally named Daubechies wavelets e B Spline Only available when the filter is biorthogonal and maximum flat In this case epo 1 2p k Go z 1 z A z 1 z Q z where k is decided by the zeros at x control p is decided by the zeros at T control as mentioned earlier e Arbitrary No specific constraints Once you decide the type of Go z and Ho z the program automatically computes the constraints For example once you select a zero its reciprocal automatically is included if you choose Go z for linear phase All possible design combinations provided by this panel are summarized in Figure 11 1 The Design Panel also provides other utilities You can access these utilities from the Menu control National Instruments Corporation wf Menu Show Wavelets Save Design Load Design Save Filter Coefficients Show Filter C
271. s linear and quadratic Chapter 4 Joint Time Frequency Analysis VIs describes the JTFA VIs Chapter 5 Joint Time Frequency Analysis Applications introduces some JTFA applications Because JTFA is relatively new it is less known among practicing engineers and scientists unlike the well known Fourier analysis The examples in this chapter reveal only the potential of JTFA The power of JTFA has not been fully explored These examples can help you learn and apply JTFA to your applications Chapter 6 Frequently Asked Questions addresses some questions JTFA users frequently ask Chapter 7 JTFA References lists reference material that contains more information on the theory and algorithms implemented in the JTFA toolkit Chapter 8 JTFA Error Codes lists the error codes the JTFA VIs return Part Il Wavelet and Filter Bank Design Toolkit National Instruments Corporation Chapter 9 Wavelet Analysis describes the history of wavelet analysis compares Fourier transform and wavelet analysis and describes some applications of wavelet analysis X X Signal Processing Toolset About This Manual Chapter 10 Digital Filter Banks describes the design of two channel perfect reconstruction filter banks and defines the types of filter banks used with wavelet analysis Chapter 11 Using the Wavelet and Filter Bank Design Toolkit describes the architecture of the Wavelet and Filter Bank Design WFBD toolkit lists the design
272. s wideband mediumband and narrowband If you adjusted the window length using the STFT method use that value to determine which analysis window you should select for the Gabor spectrogram as shown in Table 5 1 Table 5 1 Guidelines for Choosing Analysis Window STFT Spectrogram Analysis Window Window Length for Gabor Spectrogram Adaptive Spectrogram method If you can consider a signal as the sum of linear chirp functions with adaptive different Gaussian envelopes use the adaptive spectrogram to achieve the residual best time frequency resolution 9 0E 2 H of terms of terms determines the number of linear chirp functions used to approximate the analyzed signal The more elementary the linear chirp functions the more accurate the approximation and the smaller the BH 5 residual Unfortunately the more elementary functions you specify the longer the computation time Usually you should start with a small number National Instruments Corporation 5 13 Signal Processing Toolset Chapter 5 Joint Time Frequency Analysis Applications method method m PFEP x choiwiliams analytic paramet 1 00 Signal Processing Toolset of terms Increase of terms until residual is satisfactory The residual is computed as Y Isin aln l Y lsin residual where a n denotes the approximation If the approximation is equal to the original signal s n residual reduces to zero Pseudo Wign
273. s clicked Click the DAQ Setup button to change the data acquisition settings such as the device number number of samples to acquire triggering parameters or sampling rate You also can set the source to either DAQ Device or Simulated DAQ If you configure the source to Simulated DAQ a built in simulated function generator provides signals to the DAQ and Filter panel From the DAQ and Filter panel click the Function Generator button to view and edit settings including signal type frequency amplitude and noise level To change the view of a response plot use the ring control above the plot Select either Time Waveform or Spectrum for the input acquired signal or the filtered signal Figure 20 33 shows an example of switching displays for the spectrum of both the input and filtered signals Input Spectrum Output 2 Spectrum 1 0E 2 1 0E2 DES UE Sie 3 E UEST TORS 1 0E 6 0 00 2000 00 3984 3 0 00 2000 00 39843 Figure 20 33 Switching Displays The actual sampling rate appears in an indicator at the lower left side of the DAQ and Filter panel 20 36 National Instruments Corporation IIR and FIR Implementation This chapter describes the filter implementation equations for IIR and FIR filtering and the format of the IIR and FIR filter coefficient files Infinite Impulse Response Filters Infinite impulse response IIR filters are digital filters with impulse responses that theoretically c
274. seeseens 10 7 Figure 10 0 B Spline Filter Bank enisi ERES INE e e RENE RH RS CE EuuU RM UU o Fl erent es 10 7 LPieure I0 7 Dual B Spline Filter Bank rec rte eoe rr acai a bor da 10 8 Figure 10 8 Third Order Daubechies Filter Banks and Wavelets 10 11 Lieure T09 2D Sio nal BEOCOSSIDIE is cas ierat io rr pat PR aede SOS beUo URS pad 10 12 Figure 10 10 2D Image Decomposition seeeeeeeneennnnennnnnnnnnn nennen nnne 10 13 Signal Processing Toolset XIV National Instruments Corporation Figure 11 1 Figure 11 2 Figure 11 3 Figure 11 4 Figure 11 5 Figure 11 6 Figure 11 7 Figure 11 8 Figure 11 9 Figure 11 10 Figure 11 11 Figure 11 12 Figure 11 13 Figure 11 14 Figure 11 15 Figure 12 1 Figure 12 2 Figure 12 3 Figure 12 4 Figure 12 5 Figure 15 1 Figure 15 2 Figure 15 3 Figure 15 4 Figure 15 5 Figure 15 6 Figure 15 7 Figure 15 8 Figure 15 9 Figure 17 1 Figure 18 1 Figure 18 2 Figure 18 3 Figure 18 4 Figure 18 5 Figure 18 6 Contents Design Procedure for Wavelets and Filter Banks 11 2 Non Negative Equiripple Halfband Filter ssssessese 11 3 Minimum Phase Pater zai a UR ius oc akoa tu Von ER nenne E TU UNAM 11 5 I 3n6at Phase BEIGE sad mec tb n R EL PRbIREE plc tobetd nva mucus FoU URSUS 11 5 Orthogonal Faliek o gained ta Nat pA EE VP EDH Rd EE 11 5 Deseni Pane
275. select Time Waveform in the Function selector of the Display Settings control Set the mode to magnitude the units to vrms and the scale to linear Select Markers Off in the Markers section Use the left or right arrow buttons to change the display indicator to Display 2 in the Display Settings control on the front panel Set the Channel Selector to the same channel you used in step 4 9 Onthe front panel select Pwr Spectrum in the Function selector of the Display Settings control Set the mode to magnitude the units to vrms and the scale to dB 10 Click on the Single button VirtualBench DSA displays a single frame of data The Time Waveform is on Display 1 and the Power Spectrum is on Display 2 If no data is visible click on the y axis Autoscale National Instruments Corporation 31 9 Signal Processing Toolset Chapter 31 VirtualBench DSA button the button with the y and up down arrows in the Palette control Check your signal connections if data is still not visible 11 Click on Run VirtualBench DSA continuously acquires and displays frames of data 12 Click on Run again to stop acquisition Working with Waveforms This section explains how to make precise measurements using markers and shows you how to load save and clear waveforms It also describes how to generate reports with other applications Making Precise Measurements Using Markers VirtualBench DSA provides dual or harmonic markers that you can us
276. sign DFD application 20 1 to 20 36 Analysis of Filter Design panel 20 30 to 20 35 analysis displays 20 32 to 20 35 Design Analyzed control 20 31 DFD Menu 20 31 H z for FIR Filters display 20 34 to 20 35 H z for IIR Filters display 20 34 illustration 20 31 Impulse Response display 20 33 Magnitude Response display 20 32 Phase Response display 20 32 Step Response display 20 33 Z Plane Plot display 20 33 Arbitrary FIR Design panel 20 25 to 20 30 points control 20 27 del button 20 27 DFD Menu 20 26 filter order control 20 28 illustration 20 25 import from file checkbox 20 30 ins button 20 27 interpolation control 20 27 linear dB button 20 26 locked frequencies checkbox 20 29 message window 20 28 multiple select button 20 27 ripple indicator 20 28 sampling rate control 20 30 selected points indicator 20 27 to 20 28 National Instruments Corporation sort by frequency checkbox 20 29 uniform spacing checkbox 20 29 Classical FIR Filter Design panel 20 14 to 20 19 controls and displays 20 16 to 20 19 DFD Menu 20 16 to 20 17 filter order indicator 20 19 frequency and magnitude indicators 20 17 to 20 19 linear d B button 20 17 message window 20 19 minimize filter order button 20 19 sampling rate control 20 19 type control 20 19 using 20 14 to 20 16 Classical IIR Filter Design panel 20 9 to 20 14 controls and displays 20 11 to 20 14 design control 20 14 DFD Me
277. sign 1 0E 0 1 0 Classical IR EpE4 LAM Controli ae 0 0E 0 T E eel n off 1 0E OEE i 0 00 0 01 0 00 0 01 0 02 DAG Setup AREE ies a IT sampling rate W S dd m lj sd em 8000 00 Figure 20 32 DAQ and Filter Panel If you select DFD Menu DAQ and Filter from a filter design panel the DAQ and Filter panel uses that particular set of filter coefficients when filtering the acquired signals You also can use any of the four filter designs from the Filter Design ring control The DAQ and Filter panel uses the filter parameters from the selected design specifications National Instruments Corporation 20 35 Signal Processing Toolset Chapter 20 Digital Filter Design Application DFD Menu Ww Filter Design Classical IR Mon Acquire of Once sampling rate 8000 00 Signal Processing Toolset Use the DFD Menu to load and test filter designs from previous work open the Analysis of Filter Design panel go to the selected filter design panel or return to the Main Menu panel Use the Filter Design control to designate the filter design to use in filtering the acquired signal From the DFD Menu select Go to Design to load and run the corresponding filter design panel Use the on off switch to control whether you want the DFD to acquire blocks continuously or on demand Set the switch to on to continuously acquire blocks of data Set the switch to off to acquire when the Acquire Once button i
278. signal Processing Toolset Reference Manual Sinstruments January 1999 Edition Part Number 322142A 01 Internet Support E mail support natinst com FTP Site ftp natinst com Web Address http www natinst com Bulletin Board Support BBS United States 512 794 5422 BBS United Kingdom 01635 551422 BBS France 01 48 65 15 59 Fax on Demand Support 512 418 1111 Telephone Support USA Tel 512 795 8248 Fax 512 794 5678 International Offices Australia 03 9879 5166 Austria 0662 45 79 90 0 Belgium 02 757 00 20 Brazil 011 288 3336 Canada Ontario 905 785 0085 Canada Qu bec 514 694 8521 Denmark 45 76 26 00 Finland 09 725 725 11 France 01 48 14 24 24 Germany 089 741 31 30 Hong Kong 2645 3186 Israel 03 6120092 Italy 02 413091 Japan 03 5472 2970 Korea 02 596 7456 Mexico 5 520 2635 Netherlands 0348 433466 Norway 32 84 84 00 Singapore 2265886 Spain 91 640 0085 Sweden 08 730 49 70 Switzerland 056 200 51 51 Taiwan 02 377 1200 United Kingdom 01635 523545 National Instruments Corporate Headquarters 6504 Bridge Point Parkway Austin Texas 78730 5039 USA Tel 512 794 0100 Copyright 1993 1998 National Instruments Corporation All rights reserved Important Information Warranty Copyright Trademarks The media on which you receive National Instruments software are warranted not to fail to execute programming instructions due to defects in materials and workmanship for a period of 90 days from d
279. sion the elementary functions h i mAM e 7 are time shifted and frequency modulated versions of the single prototype function A i Refer to Equation 3 1 To better match the analyzed signal the adaptive representation was developed to decompose the signal s i as a sum of weighted linear adaptive chirp modulated Gaussian functions D 1 s i A h Li 3 2 k 0 where the linear chirp modulated Gaussian function h i is defined by i i 2 h il on 7 apl Oy 2nrti i 2n 4 which has four tuple parameters 0 ir fe By Therefore the adaptive representation is more flexible than the elementary function used in the Gabor expansion The parameter D in Equation 3 2 denotes the total number of elementary functions used by h i A is the weight of each individual h 7 as computed by the adaptive transform Scientists at National Instruments and Mallat and Zhang 1993 independently developed the adaptive representation also known as the matching pursuit The adaptive methods in this toolkit were implemented with the adaptive oriented orthogonal projective decomposition algorithm The source code for this algorithm was developed by Professor Qinye Yin and Zhifang Ni at Xi an Jiaotong University China Yin 1997 Signal Processing Toolset 3 2 National Instruments Corporation Chapter 3 Joint Time Frequency Analysis Algorithms Quadratic JTFA Algorithms The quadratic JTFA algorithms include the following
280. sis Filter Bank VI Synthesis Filter Bank Low Low Low High High Law High High Synthesis Filter Bank contains the synthesis filters coefficients DBL Lowpass contains the lowpass synthesis filter coefficients DBL Highpass contains the highpass synthesis filter coefficients Low_Low contains the first subimage from the analysis filter bank Low_High contains the second subimage from the analysis filter bank High_Low contains the third subimage from the analysis filter bank High_High contains the fourth subimage from the analysis filter bank y m n is the reconstructed X image of the signal error Refer to Chapter 14 Wavelet Error Codes for a description of the error BEBE Signal Processing Toolset 12 8 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference 2D Synthesis Filter Bank for 116 VI This VI computes the 2D output of a synthesis filter bank It reconstructs the four subimages into the original image if the four images are the outputs from the same 2D Analysis Filter Bank VI Synthesis Filter Coefficients Low Low Law High High _Low High High Synthesis Filter Coefficients contains the synthesis filters coefficients 116 Lowpass contains the lowpass synthesis filter coefficients 116 Highpass contains the highpass synthesis filter coefficients 116 Low_Low contains the first subimage from the analysis filter bank 116 Low_High contains the second subi
281. ssian function o in Equation 4 2 If the Normalized Gaussian Window Function VI is used for the STFT or Gabor expansion the variance is os the number of frequency bins x dM 2T In this case the MSE of the dual function is minimum as computed by the Fast DualVI and the Normalized Gaussian Window Function VI The resulting representation is known as the orthogonal like Gabor expansion DEL yli is the resulting normalized Gaussian window function error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions Signal Processing Toolset 4 6 National Instruments Corporation Chapter 4 Joint Time Frequency Analysis VIS Adaptive Spectrogram Computes the adaptive representation based spectrogram COR rma LI DBL B B w i H of Terms pti adapt residual spect H af rows P error H of frequency bins x i is the time waveform either a real valued or analytical signal of Terms determines the maximum number of elementary functions used for the adaptive representation The more elementary functions the more accurate the presentation Unfortunately computation time increases as the number of elementary functions increases of rows determines the maximum number of rows of the spectrogram pli k of frequency bins determines the number of columns of the spectrogram pliJ k by number of frequency bins 1 4 3 number of columns
282. sub images perfect reconstruction determines if the results can be reconstructed 116 x m n contains 2D input image data Analysis Filter Coefficients contains the analysis filter bank coefficients 116 Lowpass contains the lowpass analysis filter coefficients 116 Highpass contains the highpass analysis filter coefficients extension decides the initial condition and final condition extension has two options 0 zero padding changes all the initial conditions and final conditions to zeros 1 symmetric extension extends signal X symmetrically as the initial condition and final condition Refer to the Analysis Filter Bank VI for more information about how to add data in these two cases 116 Low_Low contains the output of the first subimage from the analysis filter bank 116 Low_High contains the output of the second subimage from the analysis filter bank 116 High_Low contains the output of the third subimage from the analysis filter bank National Instruments Corporation 12 7 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference 116 High_High contains the output of the fourth subimage from the analysis filter bank error Refer to Chapter 14 Wavelet Error Codes for a description of the 2D Synthesis Filter Bank VI This VI computes the 2D output of a synthesis filter bank It reconstructs the four subimages into the original image if the four images are the outputs from the same 2D Analy
283. t Chapter 1 Signal Processing Toolset Overview distribution the short time Fourier transform the cone shaped distribution and the adaptive spectrogram Wavelet and Filter Bank Design Toolkit The Wavelet and Filter Bank Design toolkit provides an intuitive and interactive interface for designing wavelet transforms and filter banks You can use wavelets for feature extraction and data compression By interactively selecting a wavelet prototype equiripple or maxflat and different finite impulse response combinations you easily can find the best wavelet or filter bank for your application As you design the wavelets you can apply them to 1D and 2D signals images and immediately see the effect of the design on your signal The Wavelet and Filter Bank Design toolkit is extremely powerful for signals that have short time duration and wide frequency bandwidth Super Resolution Spectral Analysis Toolkit Several applications use a model based signal analysis method when the number of data samples is limited The Super Resolution Spectral Analysis toolkit contains a standalone application you can use to test algorithms such as covariance the Prony s method the principle component auto regression and the matrix pencil method for model based analysis Some of these methods have previously not been commercially available Besides directly using the built in test panel you also can use VIs to construct your own applications in LabVIEW
284. t the order should be AR coefficients gives an array of auto regressive model coefficients roots gives an array of polynomial roots that are complex numbers in general noise estimation indicates the covariance of the Gaussian white noise Covariance Power Spectrum Computes the covariance method based power spectrum DBL Signal Processing Toolset AH order sampling frequency x n is the time waveform AR order determines the order of the auto regressive model The selection of the AR order is crucial and directly affects the accuracy of the estimation However you can apply the MDL vi to estimate the AR order if you are not sure what the order should be sampling frequency controls the sampling frequency The default value is 1 Hz XY Graph gives parameters for the plot of the power spectrum AT Graph x0 indicates the lower bound of the frequency range which is fixed at f 2 where f denotes the sampling frequency Ax indicates the frequency increment 17 2 National Instruments Corporation Chapter 17 Super Resolution Spectral Analysis and Parameter Estimation VIs DEL y n indicates the estimated power spectrum in the log scale The number of frequency points is fixed at 2 048 The peak value is normalized to O db noise estimation indicates the Gaussian white noise covariance F PCAR Method Computes the AR coefficients and the corresponding roots by the principle components aut
285. ta set When you use the model based method it is as if you have an infinite number of data samples Thus you can substantially improve the frequency resolution Figure 15 5 depicts two model based super resolution power spectra for the sinusoids in Figure 15 3 04 05 a 4 1 2 0 04 05 Figure 15 5 Super Resolution Power Spectra Based on 15 Samples National Instruments Corporation 15 3 Signal Processing Toolset Chapter 15 Introduction to Model Based Frequency Analysis Signal Processing Toolset Although the FFT based methods need at least 50 samples the model based super resolution power spectra detect two sinusoids satisfactorily with only 15 samples Another important application of model based methods is to estimate the parameters of damped sinusoids such as the amplitude phase damping factor and frequency You can compute the signal frequency and phase by applying the FFT if the number of data samples is large enough However there is no clue about the signal damping behavior In nature the signal amplitude often changes with time gradually decreasing or increasing until blowing out The damping behavior is an important aspect of the signal that indicates whether the corresponding system is stable Figure 15 6 depicts a sum of two damped sinusoids in which the sampling frequency is Hz sum of two damped sinusoids Figure 15 6 Damped Sinusoids Table 15 1 lists
286. tal Filter Design Application Impulse Response The Impulse Response of a digital filter is the output of the filter when the input is a unit sample sequence 1 0 0 The input before the unity sample is also zero Figure 20 27 illustrates the impulse response of the selected filter design Figure 20 27 Impulse Response Step Response The Step Response of a digital filter is the output of the filter when the input is a unit step sequence 1 1 1 The input samples before the step sequence are defined as zero Figure 20 28 illustrates the step response of the designed filter Figure 20 28 Step Response Z Plane Plot Figure 20 29 illustrates the z plane plot of the filter poles and zeros Each pole is represented by a red x Each zero 1s represented by a blue o 1 0 3 l 0 05 OO 05 1 Figure 20 29 Z Plane Plot National Instruments Corporation 20 33 Signal Processing Toolset Chapter 20 Signal Processing Toolset Digital Filter Design Application H z for IIR Filters H z is the z transform of the designed digital filter as shown in Figure 20 30 Miz 0 01515 0 015152 2 Drz 1 0 380152 1 0 875412 2 Figure 20 30 H for IIR Filters For an IIR filter H z can be represented by a product of fractions of second order z polynomials N T N AZ A z lro where N z is the numerator for stage k D z is the denominator for stage k N is the number of s
287. ter is maintained using the DFD filter coefficient structure The number of output samples equals the number of input samples n Parameters Input inputArray double array Input array of unfiltered samples long integer Number of elements in input array filter Coefficients FilterPtr Pointer to filter coefficient structure Output outputArray double array Output array of filtered samples that must be at least as large as inputA rray Return Value err long integer Error code Signal Processing Toolset 22 6 National Instruments Corporation Chapter 22 Using Your Coefficient Designs with DFD Utilities Windows DLL DFD Utilities This section contains descriptions of the DFD utilities you can use from within your Windows 95 NT applications to read DFD filter coefficient files and to filter your data using the coefficients When you install the DFD toolkit a 32 bit DLL named DFD32 DLL is installed for Windows 95 NT users This DLL is located in the Libraries subdirectory of your installation directory along with the header file D dutils h The DFD DLL and header file have the following function prototypes FilterPtr AllocCoeffDFD void long ReadCoeffDFD char coeffPath FilterPtr filterCoefficients double samplingrate long FreeCoeffDFD FilterPtr filterCoefficients long FilterDFD double inputArray long n FilterPtr filterCoerricients double outputArrayll Refer to the descriptions for each fun
288. text or characters that you should enter from the keyboard sections of code programming examples and syntax examples This font is also used for the proper names of disk drives paths directories programs subprograms subroutines device names functions operations variables filenames and extensions and for statements and comments taken from programs monospace italic Italic text in this font denotes that you must enter the appropriate words or values in the place of these items Related Documentation The following documents contain information that you might find helpful as you read this manual e G Programming Reference Manual e LabVIEW Online Reference e LabVIEW User Manual e LabWindows CVI User Manual Customer Communication National Instruments wants to receive your comments on our products and manuals We are interested in the applications you develop with our products and we want to help if you have problems with them To make it easy for you to contact us this manual contains comment and configuration forms for you to complete These forms are in Appendix A Customer Communication at the end of this manual National Instruments Corporation xxiii Signal Processing Toolset signal Processing Toolset Overview This chapter provides an overview of the Signal Processing Toolset components system requirements and installation instructions For more information about each component refer to the correspondin
289. the WVD A lower order Gabor spectrogram has less crossterm interference but lower resolution A higher order Gabor spectrogram has better resolution but more crossterms Moreover the higher the order the longer the computation time For best results choose an order of three to five The Gabor spectrogram has better resolution than the STFT spectrogram and much less crossterm interference than the cone shaped Choi Williams or Wigner Ville distributions National Instruments Corporation 3 11 Signal Processing Toolset Chapter 3 Joint Time Frequency Analysis Algorithms Figure 3 8 illustrates the fourth order Gabor spectrogram for the three tone test signal It possesses high time frequency resolution and does not have the crossterm interference that appears in the cone shaped Choi Williams or Wigner Ville distributions The computational speed of the fourth order Gabor spectrogram is slower than the STFT spectrogram and WVD but faster than the CWD or cone shaped distribution current data gauss3 tt gauss3 tst but data length sec 1 28E 1 m2 spectrum ey 4 0E 2 3 0E 2 2 0E 2 1 0E 2 0 0E 0 2 0E 0 1 0E 0 000E 0 sec TET 3 01E z2 Hz OE 0 1 0E 0 7E 0 l man sec D DOE 0 2 UE 2 4 0E 2 6 0E 2 B UE 2 1 0E 1 1 3E 1 Eu control Figure 3 8 Gabor Spectrogram Order Four for the Three Tone Test Signal Scientists at National Instruments developed the Gabor spectrogram method w
290. the corresponding parameters and Figure 15 7 plots the resulting FFT based power spectra Applying FFT based methods provides no way to tell the complete information about the two damped sinusoids Table 15 1 Damped Sinusoids signll signll 010 10 15 4 National Instruments Corporation Chapter 15 Introduction to Model Based Frequency Analysis Rectangular Window Hamming Window 5 10 10 2D 15 30 20 i i i m m 4l i i i 0 5 0 4 4 2 nn 0 2 n4 nh 45 0 4 0 2 0 0 0 2 n4 0 5 Figure 15 7 FFI Based Power Spectra for Damped Sinusoids Figure 15 8 illustrates the estimated result by a model based algorithm the matrix pencil algorithm Notice that a real signal produces two imaginary symmetrical complex sinusoids The lower left of Figure 15 8 indicates that there are a total of four complex sinusoids for the samples shown in Figure 15 6 Figure 15 8 also lists the parameters of the components with positive frequencies that match Table 15 1 perfectly The amplitude of the complex sinusoids is half that of the corresponding real sinusoid Estimated Parameters amplitude phase damping frequency 0 50 010 4 20 0 11 4 complex sinusoids Matris Pencil Figure 15 8 Parameter Estimation by Matrix Pencil Method The precision of the FFT based methods is accurate only at frequencies that are integer multiples of the frequency increment sampling f
291. the data block The two types of possible averages are linear or exponential averaging The analyzer defaults to linear averaging If data blocks to average is Q then S Kk is the instantaneous power output of data block p and the averaged power output after the number of Q data blocks 1s So K The following formula defines the linear averaging also called true or additive averaging p 900 5 Y 00 p 0 The following is the formula for exponential averaging also referred to as discount or RC averaging Sk 17 a K aS K where a and 0 a l Weighting Weighting designates the weighting types The human sense of hearing no weighting responds differently to different frequencies and does not perceive sound 7 equally Choosing A Weighting tells the analyzers to mimic human hearing responses to acoustical signals Refer to Table 24 1 Filter Bands for ANSI S1 11 in Chapter 24 Overview of the Third Octave Analysis Toolkit for a list of default A Weighting values incorporated in the analyzer You also can choose no weighting and custom weighting When you choose custom weighting you must read your weighting file This file is a spreadsheet file with two columns where the first column is 31 center frequencies and the second column is 31 corresponding weighting values An example of a weighting file is aweight dat in the TestData subdirectory Make sure the weighting value corresponds National Instr
292. the designed digital filter Signal Processing Toolset 20 16 National Instruments Corporation Chapter 20 Digital Filter Design Application Magnitude vs Frequency e g4 25 00 50 00 TEDOS 94 24 Hz l l l l 0 00 1000 00 2000 00 300000 4000 00 es 3 A frequency magnitude j v3 mj 2750 00 13 304 Figure 20 11 Frequency Response Magnitude The magnitude y axis is in linear or decibel units depending on how you set the button in the upper left corner of the graph The frequency x axis is in hertz The full scale ranges from 0 0 to Nyquist half the sampling rate By moving the blue cursor lines or crosshairs you control the passband response horizontal lines and the passband frequencies vertical lines By moving the red cursor lines you control the stopband attenuation horizontal lines and the stopband frequencies vertical lines These cursors represent the filter design specifications for the selected classical FIR filter In the passband the filter has a gain greater than or equal to the specified passband response In the stopband the filter has a gain less than or equal to the specified stopband attenuation Use the linear dB button to control the display units linear or dB of all magnitude and gain controls and displays These controls and displays include Magnitude vs Frequency plot y axis passband response stopband attenuation and tracking cursor magnitude a The frequ
293. the noise reduced time waveform x n compute the Gabor expansion of the signal s Gabor coefficients obtained in step 2 4 Repeat steps 1 through 3 The number of iterations depends on the original SNR The lower the SNR the more iterations Signal Processing Toolset 5 2 National Instruments Corporation Chapter 5 Joint Time Frequency Analysis Applications gt Denoise Gabor Edit Operate Project Windows Help Gabor coefficients of iterations power spectrum 0 5 hn BEN li l TL h i I SIME db3 O37 FAE 2 OE 59EH noise control hi I _ reconstruction amp 100 125 150 175 200 225 Figure 5 1 Gabor Expansion Based Denoise In this example there are three iterations The resulting SNR is 10 52 db The bottom plot depicts the time waveform based on the prominent Gabor coefficients selected from the joint time frequency domain Notice an improvement of approximately 11 db an impossible improvement using traditional techniques Scientists at National Instruments and Hughes Aircraft jointly developed this iterative denoise method Image Analysis By applying the 2D STFT method you can decompose a 2D image into several subimages as shown in Figure 5 2 Figure 5 3 describes the corresponding frequency contents of each subimage If you adjust the analysis window functions you can have each subimage represent only the information in which you are interested Natio
294. the size of G Y is the y i array M is the decimate factor XI is initial condition plus x i plus final condition according to the following formula Xl i 0 1 n 1 xl Xin i nN Ry 1 n n 1 2 Sieh hh utn t na l where Xi is the array of initial condition n is the size of Xi xf is the array of final condition ngs the size of Xf The operation is illustrated in Figure 12 3 The VI performs a regular finite impulse response filtering or convolution followed by a decimation factor of M The first plot in Figure 12 3 shows the signal of X7 National Instruments Corporation 12 11 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference tr xi EX xt ER n 1 Yo Nu first point n 1 Vn iBo 1 n 1 sub n o2 n 1 YL m last point L Figure 12 3 Filtering Operation In Figure 12 3 Y is the decimation version of Y Yn Yun where n 0 1 L 1 M L is the length of X7 where L nyi n ny For the two channel PR filter banks the requirement for n and n y is Ny Ny Ng N 1 2 I where Ney is the length of the analysis lowpass filter Ng is the length of the analysis highpass filter Signal Processing Toolset 12 12 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference If n and n meet the above condition using the Decimation Filter VI and the Interpolation Filter VIs produces a perfect reconstructed signal with no d
295. the size of output arrays err Analysis2DArraySize rows cols anaptr nl anaptr nh nsize if err goto errend Allocate memory for the output arrays ll double malloc nsize 0 nsaize l sizeotf double if ll goto erreng lh double malloc nsize 2 nsize 3 sizeof double TEECLELB 4 Pree Ci 3 goto erreng hl double malloc nsize 4 nsize 5 sizeof double if hl 4 rtreethli s free 1h goto errend National Instruments Corporation 12 45 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference hh double malloc nsize 6 nsize 7 sizeof double cin gs ps a Ge ae free 11 free 1h free hl goto errend err AnalysisFilterBank2D x rows cols anaptr 0 1ll lh hl hh nsize if err free 11 free lh hl free hh goto erreng free Compute the size of 2D output from the synthesis filter bank 7 Synthesis2DArraySize nsize synptr nl synptr nh amp xOrows amp x0cols Allocate 2D output for the synthesis filter bank x0 double malloc xOrows xOcols sizeof double if hh free 11 free 1h free hl free hh goto errend erresSynthesisPFrilterBank2D ll lh hl hh nsrze synptr x0 x rows x0cols free ll free lh free hl free hh free x0 errend free x FreeCoeffWFBD anaptr FreeCoeffWFBD synptr Signal Processing Toolset 12 46 National
296. the unit circle along and above the x axis You can move each zero blue o anywhere along and above the x axis Figure 20 14 Z Plane Plot of Filter Poles and Zeros dalate Click the delete selected button to delete the selected pole or zero Click poles and zeros to select them Click the add pole button to add a pole to the z plane The new pole is located at the origin Click the add zero button to add a zero to the z plane The new zero is located at the origin National Instruments Corporation 20 21 Signal Processing Toolset Chapter 20 Digital Filter Design Application 2 rectangular coordinates Signal Processing Toolset The coordinates control specifies how the DFD application displays the poles and zeros either in rectangular or polar coordinates Figure 20 15 shows the array of zeros in rectangular coordinates The complex value of each zero represents its rectangular position on the z plane The integer 3 in the upper left box is the index of the displayed zero By changing this index value you can display a particular zero of the array of zeros When you select a particular zero in the z plane plot the DFD application sets the index value of the array to the selected zero value 0 3309 0 9437 i reallp uc order Ot Fil Figure 20 15 Array of Zeros in Rectangular Coordinates If you select the real checkbox the zero becomes purely real and is limited to real axis movement When you
297. thod The covariance method only minimizes the error between x n and x n for p amp n N that is N p points even though there are N samples of x n The PCAR method formulates the linear system as RES X Xb where a denotes the data vector T x a lai ay alee a xy and x denote the right side vectors of the forward prediction in Equation 16 5 and backward prediction in Equation 16 10 respectively You also can write this as Xf _ T N J xtp xlp 1 x N 1 x 0 x 1 x N p 1 Xb Signal Processing Toolset 16 6 National Instruments Corporation Chapter 16 Model Based Frequency Analysis Algorithms Similarly the matrices Xf and Xb are the left side matrices of the forward prediction in Equation 16 5 and backward prediction in Equation 16 10 respectively x p 1 x p 2 x 0 x p x p 1 Got Xel x N 2 x N 1 xIN p 1 X x 1 x 2 X p x 2 x 3 X p 1 Consequently the linear system in Equation 16 15 uses forward and backward prediction information In this manner you obtain extra data points and average more errors Moreover you solve for the coefficients by gt l Fok a i X 16 16 where xe bj ai ge E 16 17 X denote the L largest eigenvalues of the matrix X v are L corresponding eigenvectors The parameter L represents the number of complex sinusoids Because you use only L principle components in Equation 16 16 the results obtained by PCAR a
298. time and frequency resolution You can use the resulting window length as a reference for the Gabor spectrogram Refer to the following Gabor Spectrogram section for more information If you cannot achieve satisfactory resolution with the STFT spectrogram try the Gabor spectrogram or one of the other methods explained later in this chapter 5 12 National Instruments Corporation Chapter 5 Joint Time Frequency Analysis Applications Gabor Spectrogram methad If the time frequency resolution of the STFT spectrogram is not Gabor satisfactory try the Gabor spectrogram next This method requires more analysis window computation time than the STFT spectrogram but the Gabor spectrogram mediumband has better time frequency resolution order To process the Gabor spectrogram you need to set the order and analysis window parameters order controls the resolution and crossterm interference The higher the order the better the time frequency resolution As the order goes to infinity the Gabor spectrogram converges to the Wigner Ville distribution Notice that as the order increases crossterms become more obvious Furthermore computation time is proportional to the order selected Set order from three to five to achieve the best compromise between resolution and crossterm interference In general the Gabor spectrogram is less sensitive to window length than the STFT spectrogram Hence there are only three analysis window selection
299. tion Mother Wavelets 4 00 2 00 0 00 2 00 4 00 4 00 l l l l 5 00 00 10 20 30 40 50 60 70 0 0 1 0 h fn hi n 1 00 m 0 75 0 50 0 50 0 25 0 00 E EEE ENE NE E E E E 0 00 I 3 sce 050 0 75 Figure 10 7 Dual B Spline Filter Bank You must remember that two channel PR filter banks do not necessarily correspond to the wavelet transform The wavelet transformations are special cases of two channel PR filter banks The conditions of two channel PR filter banks are more moderate than those for the wavelet transform Finally the analysis filter banks and synthesis filter banks presented in this section are orthogonal to each other y sil Ahn 0 k 10 10 and ysin 2kWjn 0 i l Vk Signal Processing Toolset 10 8 National Instruments Corporation Chapter 10 Digital Filter Banks The filters banks that satisfy Equation 10 10 are traditionally called biorthogonal filter bank In addition to Equation 10 10 if the analysis filter banks also satisfy the following equations y sii 2k gla 800 10 11 and y sl 2k g n 0 iz Vk the resulting filter banks are called orthogonal filter bank Orthogonal filter banks are special cases of biorthogonal filter banks Orthogonal Filter Banks As shown in the preceding section once you determine Po z the product of two lowpass filters you must factorize Po z into Go z and H
300. tion Triggering Markers Frame sizes gt 1024 require 32 MB RAM Frame Size Averaging Type 1024 Ot Sample Fate Hz t of averages 1 ez Uh Window Type Lines 512 Mene Uniform OF Cancel Figure 31 6 Acquisition Tab of DSA Settings Dialog Box g Set the Frame Size control to 1024 for VirtualBench DSA to analyze data in blocks of 1024 points h Select a Sample Rate that is at least twice the maximum frequency that you are trying to measure i Select the Averaging Type as Off and Window Type as None Uniform j Click on the Triggering tab in the DSA Settings dialog box shown in Figure 31 7 Signal Processing Toolset 31 8 National Instruments Corporation Chapter 31 VirtualBench DSA bl DSA Settings Hardware Acquisition Triggering Markers Trigger Type Trigger Channel Slope Mone fe Rising E i Falling Pretrigger Samples Level v D t Trigger Timeout sec Hysteresis V 1 00 0 00 DK Cancel Figure 31 7 Triggering Tab of DSA Settings Dialog Box k Set the Trigger Type to None This setting puts the acquisition in free run mode l Click on OK 3 Use the left or right arrow buttons to change the display indicator to Display 1 in the Display Settings control on the front panel 4 Select Channel A or B depending on where you connected your signal in the channel selector of the display settings control 5 Onthe front panel
301. tion Series ooi etos rebat oo ire baa REOR Ee Ve E RERO EROS 4 15 Chapter 5 Joint Time Frequency Analysis Applications Lincar Als Orth Examples ctu otbuia qaad eto ta Seat dta Oa OUR bU A OR esI SE LINESRO uas 5 DENOI C eaasa 5 WGC Analysis tacite eu LUC MI EDI SUN I IQ MEDALS DE 5 3 Time Dependent Spectrum Analysis Examples cccccccssccsssssessesseeeesseeeeseesseeeeseees 5 6 Online STFT Spectrogram Analyzer eeeeeeeeeeeeeeeeeeeeeee ene 5 7 setine NI DUAO oes at uustit deti o Mna E 5 7 Signal Processing Toolset vi National Instruments Corporation Contents Setting the Analysis WindOwW ccccccccccccccceeeeeeeeeeeeceeeaeeeeseeaaaanaaaaes 5 8 JACQUIFIDO TQUE Gies tetutes ten nha o pa e Ec tcd Render cc a on TR T e Mess 5 8 SEL qug B oi eec MuR Te OP 5 8 Offline Joint Time Frequency Analyzer cccccccccececceceeeecccecceseceesseneseeeess 5 8 Changing Spectrogram Display ccccccsssessssesseeeesseeeesseeeseeeeeeees 5 9 Putin BEIC S 5 10 SAVNE RESUS e sitis ida es a e bh IRE NO EN A Re beE CE 5 10 Switching Between Conventional Power and Instantaneous Spectrum ccccccccccccccccceccceceeceeeeeeeeeeeeeeeeeeeees 5 10 PREQUENCY ZOOMING cse RU cscansiiseacierncinleanel A 5 11 Applying the Pre Emphasis Filter senes 5 11 Seno Pinte Parameters lt 5 icin opo add fxev m e o ER eaae M Eo RE RRUS 5 12 Selecting The ITFA Method 6
302. to modify the same filter design that the DFD application Classical IR is analyzing the application recomputes all filter responses National Instruments Corporation 20 31 Signal Processing Toolset Chapter 20 Signal Processing Toolset Digital Filter Design Application Analysis Displays Each of the five filter plots has a zoom box in the upper right corner Click in this box to display a full screen version of the plot In the full screen versions of these plots you can change the units from linear to decibel Magnitude Response from radians to degrees Phase Response or from seconds to samples Impulse and Step Responses From each full screen view you can save the response data to text files Magnitude Response The Magnitude Response is the magnitude of the filter response H f as frequency varies from zero to half the sampling rate Figure 20 25 illustrates the magnitude response of the selected filter design Magnitude Response El 1 0 5 p p Jie 00 1000 0 2000 0 3000 0 4000 0 Figure 20 25 Magnitude Response Phase Response The Phase Response is the phase of the filter response H f as frequency varies from zero to the sampling rate Figure 20 26 illustrates the phase response of the selected filter design eons Phase Response U 0 3 E I I I I 0 0 1000 0 2000 0 3000 0 4000 0 Figure 20 26 Phase Response 20 32 National Instruments Corporation Chapter 20 Digi
303. trademarks of National Instruments Corporation Product names referenced in this document are trademarks or trade names of their respective companies WARNING REGARDING MEDICAL AND CLINICAL USE OF NATIONAL INSTRUMENTS PRODUCTS National Instruments products are not designed with components and testing intended to ensure a level of reliability suitable for use in treatment and diagnosis of humans Applications of National Instruments products involving medical or clinical treatment can create a potential for accidental injury caused by product failure or by errors on the part of the user or application designer Any use or application of National Instruments products for or involving medical or clinical treatment must be performed by properly trained and qualified medical personnel and all traditional medical safeguards equipment and procedures that are appropriate in the particular situation to prevent serious injury or death should always continue to be used when National Instruments products are being used National Instruments products are NOT intended to be a substitute for any form of established process procedure or equipment used to monitor or safeguard human health and safety in medical or clinical treatment Contents About This Manual Organization of This Manual Part I Joint Time Frequency Analysis Toolkit Part II Wavelet and Filter Bank Design Toolkit Part III Super Resolution Spectral Analysis Toolkit Part IV Digital F
304. ts software product Version Configuration The problem is List any error messages The following steps reproduce the problem Signal Processing Toolset Hardware and Software Configuration Form Record the settings and revisions of your hardware and software on the line to the right of each item Complete a new copy of this form each time you revise your software or hardware configuration and use this form as a reference for your current configuration Completing this form accurately before contacting National Instruments for technical support helps our applications engineers answer your questions more efficiently National Instruments Products Hardware revision Interrupt level of hardware DMA channels of hardware Base I O address of hardware Programming choice National Instruments software Other boards in system Base I O address of other boards DMA channels of other boards Interrupt level of other boards Other Products Computer make and model Microprocessor Clock frequency or speed Type of video board installed Operating system version Operating system mode Programming language Programming language version Other boards in system Base I O address of other boards DMA channels of other boards Interrupt level of other boards Documentation Comment Form National Instruments encourages you to comment on the documentation supplied with our products This information helps us provide quality products to meet your need
305. ts to compute the octave outputs in the 21 highest frequency bands No data is thrown away This option results in a slower execution time so you should select it when the signal is not completely stationary e custom averaging allows you to choose other internal averaging settings The no averaging and complete averaging are the two extreme cases of the Internal Data Averaging When you choose custom averaging an edit button appears to the right of the Internal Data Averaging control When you click the Edit button the Set Internal Averaging dialog box appears as shown in Figure 25 2 Signal Processing Toolset 25 4 National Instruments Corporation Chapter 25 Operating the Third Octave Analyzer gt Set Internal Average ft vi Please read the manual to understand the meaning of this parameter before changing it Internal Average Times E N OF L ancel Figure 25 2 Internal Data Averaging Dialog Box Internal Average Times indicates the number of blocks of data to average in the higher frequency bands The first number in the control should be in the range of 1 150 The second number should be in the range of 1 15 The lower bound on both controls 1 corresponds to no averaging and the upper bound 150 for the first control and 15 for the second control is complete averaging Any number in between these two numbers is partial averaging The more the averaging the slower the execution time Refer to the nt
306. tude or y value of the frequency magnitude points lacked frequencies O sort by frequency uniform spacing Ll import from file Figure 20 23 Additional Controls for Arbitrary FIR Design Panel Select the uniform spacing checkbox to space the frequency values of the frequency magnitude points The DFD application spaces the frequency magnitude points uniformly from 0 0 to half the sampling rate inclusive Select the sort by frequency checkbox to sort the frequency magnitude points in both the response graph and the array according to ascending frequency The value of each frequency magnitude point remains unchanged Only the order of the points can change National Instruments Corporation 20 29 Signal Processing Toolset Chapter 20 Digital Filter Design Application zj sampling rate 5 U00 00 Select the import from file checkbox to import frequency magnitude points from a text file The imported file format consists of the following tab delimited columns Ist line sampling rate dB linear setting 0 for linear 1 for dB 2nd line frequency 1 magnitude 1 3rd line frequency 2 magnitude 2 4th line frequency 3 magnitude 3 last line last frequency last magnitude For example a file with five frequency magnitude points appears as 8000 0 1 0 0 00 30 1000 0 40 0 2000 0 2 0 0 3000 0 00 4000 0 60 30 The sampling rate control specifies the sampling rate in samples per second hertz Analysis of Filter
307. u can compute the mother wavelet function y t by highpass t as shown in Figure 10 2 e The outputs of each of the highpass filters are approximations of the wavelet transform You can accomplish wavelet transform with a tree of two channel PR filter banks The selection of a desirable mother wavelet becomes the design of two channel PR filter banks Figure 10 3 illustrates the relationship of filter banks and wavelet transform coefficients frequency filter banks time Figure 10 3 Filter Bank and Wavelet Transform Coefficients The following sections describe the design fundamentals for two types of two channel PR filter banks biorthogonal and orthogonal In most equations only results are given without justifications You can find mathematical treatments in the related references listed in Chapter 13 Wavelet References National Instruments Corporation 10 3 Signal Processing Toolset Chapter 10 Digital Filter Banks Biorthogonal Filter Banks Signal Processing Toolset Refer to Figure 10 1 You can define Strang and Nguyen 1995 Vaidyanathan 1993 the output of the low channel as Yo z AH G EGo OX Go z XC7z Similarly you can define the output of the up channel as Yi Hy MG Xe Gi z X z Add them together to obtain TOG H 2 G IXE LH G HL 2 G C XCz 10 1 One term involves X z and the other involves X z For perfect reconstruction the term with X z traditionally c
308. u sU IUIS Dade 24 Introduction to the Third Octave Analysis Toolkit see 24 2 Chapter 25 Operating the Third Octave Analyzer Setting Up the Third Octave Analyzer 2o occa reno bie Poder e nies 25 1 Running the Third Octave Analyzer eese nnne 25 5 Chapter 26 Third Octave Analysis Design Alsorithi Des crip Onc erun A A ue nbn tuere ed UR ue 26 1 Multistase Decimation Lechrlques uius froteus citer than dto deo Lon D Pu D Orla Pbi bed dte duce 26 2 Internal Data Avera Cio asscotescd tovt trad tiom Ped Ta dfe eee ees 26 5 Specifications of the Third Octave Analysis Toolkit eeeeeeeeeseseesssssess 26 6 Chapter 27 Third Octave Filters VI T rrd Octave Filters WE abu bea eph DE to ME des MD coe MM ee 27 1 Chapter 28 Building Windows Applications for Third Octave Analysis Third Octave Analysis Applications in LabWindows CVI seeeeeeeeeees 28 1 Third Octave Analysis Instrument Driver cccccccccccccccceeeeeeeeeeeeeennnneeeees 28 1 Running Third Octave Analysis Applications in LabWindows CVI 28 3 Third Octave Analysis Applications in Windows essen 28 4 Third Octave Analysis Applications in Visual Basic seen 28 4 Chapter 29 Third Octave References Signal Processing Toolset xii National Instruments Corporation Chapter 30 Contents Third Octave Error Codes Chapter 31 Part
309. uments Corporation 25 3 Signal Processing Toolset Chapter 25 Operating the Third Octave Analyzer correctly to the right frequency The analyzer adds the weighting value to the final power value before displaying it View Weighting displays a table that shows all the weighting values at each frequency for each channel FFT size FFT size is the size used to compute fast Fourier transform FFT a512 internally It has two options 512 and 256 Using 512 point FFT gives more accurate results but takes twice the memory and runs slower than using 256 point FFT FFT size defaults to 512 Internal Data Averaging indicates the input data in one block that needs averaging A block of data that is acquired each time is just enough for computing the outputs of the first 10 third octave filters in the lower frequencies but it is more than enough for computing the outputs of the 21 higher frequency bands This parameter controls how to compute the power in the 21 third octave filters in the highest frequencies rene lene Ano There are three Internal Data Averaging parameter options a 4 no averaging no averaging means the analyzer uses only the minimum points of the data to compute the octave outputs in the 21 highest frequency bands and throws all the rest of the data away If your signal is almost stationary use this option complete averaging custom averaging complete averaging means the analyzer uses all the data poin
310. ure 31 1 Front Panel of VirtualBench DSA eeeeseseeeeeeeeeens 31 1 Figure 31 2 VirtualBench DSA Status Display seen 31 5 Figure 31 3 VirtualBench DSA Marker Display eene 31 5 Pigure 34 Computations Panels onn e en Raptor duos RM EDS E E eu D 31 5 Figure 31 5 Hardware Tab of DSA Settings Dialog Box eeee 31 7 Figure 31 6 Acquisition Tab of DSA Settings Dialog Box eeeeeeeeeee 31 8 Figure 31 7 Triggering Tab of DSA Settings Dialog Box eees 31 9 Figure 31 8 Load Reference Waveforms Dialog Box cccceeccccccccceceeceeeeeeeeeeeeeees 31 11 Figure 31 9 Save Reference Waveforms Dialog BOX ccccecccccccceccececeeeeeeeeeeeess 31 12 Figure 31 10 Generate Report Dialog Box ee 31 13 Tables Table 5 1 Guidelines for Choosing Analysis Window sess 5 13 Table 6 1 Quadratic JTFA Algorithms eeeeeeeeeeeeeeeeeeee eene 6 2 Table 8 1 PUP AYR ror COUGOS aie itenom ete sat E Na 8 1 Table Riel Filter COHIDAEISOID uec eee eee er hdi eir E mesa eeu ego ned erst 11 4 Table 14 1 LabVIEW VI and LabWindows CVI Function Error Codes 14 1 Table 15 1 Damped Sinusoids eeseesseeseeseeeeeeeeern nnne 15 4 Table 15 2 FFT JTFA Wavelets and Model Based Methods 15 7 Table 18 1 Default Sinusoid Parameters
311. urier in 1807 During the study of heat propagation and diffusion Fourier found that a series of harmonically related sinusoids was useful in representing the temperature distribution throughout a body Later he claimed that any periodic signal could be represented by such a series and any aperiodic signal could be represented as a weighted integral of sinusoids By the 1820s Fourier s revolutionary claims were proved mathematically by S D Poisson A L Cauchy and P L Dirichlet Since then the Fourier transform has become one of the most important signal analysis methods By applying the Fourier transformation you easily can decompose any signal as a weighted sum of sinusoid functions as shown in Figure 2 1 Consequently you can process either the signal time waveform or its corresponding set of sinusoid functions depending on which form is more convenient In addition to being linear the Fourier transform provides a feasible way of computing the power spectrum for a signal Because the power spectrum usually has a simpler pattern than the time waveform it l Fourier s original paper was never published because of J L Lagrange s vehement objections Lagrange an important mathematician during that time argued that trigonometric series were of very limited use National Instruments Corporation 2 1 Signal Processing Toolset Chapter 2 The Need for Joint Time Frequency Analysis often serves as the fingerprint of the analyzed sig
312. using either text entry or the cursors in the Magnitude vs Frequency graph As you use the mouse to click and drag the cursors the text entries update Likewise as you enter new specifications in the text entries the cursors update The lower passband frequency fp upper passband frequency fp gt and the passband response Gp define the passband specification For the bandpass filter the passband ranges from fp to fp The passband is the region in the frequency domain with a response near 1 0 Gp is the minimum allowable passband gain or filter magnitude response In Figure 20 10 the passband specification is a minimum gain of 5 dB between the frequencies of fp 1900 Hz and fp 2600 Hz The following ranges define the passband lowpass O lt sfsfp highpass IPSIS uu 2 bandpass fpi Sf SSP bandstop OSS SIDS IDI SI S fins 2 where fp is passband frequency 1 fp is passband frequency 2 Samp 18 the sampling rate The stopband frequencies fs and fs and the stopband attenuation Gs define the stopband specification For the bandpass filter the stopband ranges from 0 0 DC to the lower stopband frequency fs and from the upper stopband frequency fs2 to half of the sampling rate Nyquist The stopband is the region in the frequency domain with a response near 0 0 Gs is the minimum acceptable stopband attenuation or filter magnitude response In Figure 20 10 the stopband specification has a minimum attenuat
313. val The length of h i must be evenly divisible by dM of frequency bins controls the number of frequency bins of the resulting STFT and Gabor expansion It must be a power of two The length of h i must be evenly divisible by of frequency bins The ratio of of frequency bins to dM is the oversampling rate For stable reconstruction the oversampling rate must be greater than or equal to one rma LII the number of frequency bins dM oversampling 2 National Instruments Corporation 4 7 Signal Processing Toolset Chapter 4 Joint Time Frequency Analysis VIS DBL r i is the dual function of h i r i and h i constitute a pair of analysis and synthesis functions for the STFT Gabor transform and Gabor expansion considered the inverse Gabor transform error indicates a JTFA VI error Refer to Chapter 8 JTFA Error Codes for a list of JTFA error codes and their descriptions 20083 no solution 20001 rank deficiency Normalized Gaussian Window Function Computes the unit energy Gaussian window function defined by s 2 B i to 4 2g yli o 4 2 which is optimally concentrated in time and frequency domains simultaneously H of samples Pa lil center point Wal gaus Emor of samples determines the length of the normalized Gaussian window function y i center point determines the center point t in Equation 4 2 B E var determines the variance of the normalized Gau
314. ve Filters VI This VI is the main VI the Third Octave Analyzer calls It computes the outputs of 31 third octave filters from the data applied at the Input X DEL DEL block size Input i Band Power sampling rate Center Frequency window tpe Error Average Humber block size determines the FFT size that is used to compute the third octave outputs This parameter has two options 256 or 512 Selecting a size of 512 gives more accurate results but takes more memory and runs slower than selecting a size of 256 The block size parameter defaults to 512 Input X is the input data array The size of this input must be 28680 if block size 256 or 54280 if block size 512 sampling rate is the sampling rate of Input X This parameter determines the frequency range that is being analyzed Assuming sampling rate is fs i fs 12800 fl is the lower bound of the frequency range and fh is the upper bound of the frequency range then fl ix 5 Hz fh ix 5000 Hz For example if fs 25600 Hz then i 2 the frequency range is 10 Hz 10000 Hz The recommended fs should be chosen from 12800 Hz 25600 Hz or 51200 Hz The corresponding frequencies ranges are 5 Hz 5000 Hz 10 Hz 10000 Hz and 20 Hz 20000 Hz The sampling rate parameter defaults to 12800 Hz National Instruments Corporation 2 1 Signal Processing Toolset Chapter 27 Third Octave Filters Vl 132 window type is the type of window that applies to the Input
315. ways sits halfway between two corresponding autoterms and oscillates frequently Although its magnitude can be very large its average usually is limited z i is the analytical or interpolated form of s i See Qian 1996 for more details National Instruments Corporation 3 5 Signal Processing Toolset Chapter 3 Joint Time Frequency Analysis Algorithms B current data gauss3 tst datalength sec 1 28E 1 spectrum zZ O 00E 0 sec 2 15E 2 Hz 7E i i al sec i D DE 0 2 0E 2 4 JE 2 b DE 2 B DE 2 1 0E 1 1 3E 1 EE control gt Figure 3 3 Wigner Ville Distribution for the Three Tone Test Signal To alleviate the crossterm interference you can assign different weights to the instantaneous correlation R i m to suppress the less important parts and enhance the fundamental parts Traditionally two methods exist for applying the weighting function to the instantaneous correlation R i m The first is in the time domain L 2 PWVDli k s V wIm RIi ae E 3 3 m L 2 which is called the Pseudo Wigner Ville distribution PWVD effectively suppresses crossterms that correspond to a pair of autoterms with different time centers such as crossterms 1 and 2 in Figure 3 3 Figure 3 4 illustrates the PWVD with the Gaussian window function w m Compared with the WVD in Figure 3 3 the PWVD successfully eliminates crossterms 1 and 2 Signal Processing Toolset 3 6 National Instruments Corporation Cha
316. wever the signal usually concentrates in a relatively short time period or a narrow frequency band If you convert the noise corrupted signal to the joint time frequency domain you can substantially improve the local or regional Signal to Noise Ratio SNR Figure 2 5 depicts the impulse signal the U S Department of Energy ALEXIS BLACKBEARD satellite received After passing through dispersive media such as the ionosphere the impulse signal becomes the nonlinear chirp signal As shown in Figure 2 5 random noise dominates both the time waveform and the power spectrum Neither indicate the existence of the impulse signal However from the time dependent spectrum you can immediately identify the presence of the chirp type signal that arches across the joint time frequency domain The horizontal lines correspond to radio carrier signals that basically remain unchanged over time Data courtesy of Non Proliferation and International Security Division Los Alamos National Laboratory Signal Processing Toolset 2 4 National Instruments Corporation Chapter 2 The Need for Joint Time Frequency Analysis Hz cumentdata E10176 t data length sec 1 7864 spectum r BE oe AA gt ly mas zm miri riy Egi rig a die Eval ae sec 0 0E 0 206 5 406 5 6065 8DE5 10E4 12E4 146 4 CHEO S A control se Figure 2 5 lonized Impulse Signal Based on the joint time frequency representation you can further mask the des
317. y the number of data samples The relationship of the number of samples and frequency resolution can be quantified by Ape sampling frequency 15 1 number of samples National Instruments Corporation 15 1 Signal Processing Toolset Chapter 15 Signal Processing Toolset Rectangular Window i Hamming Window Introduction to Model Based Frequency Analysis where Af denotes the frequency resolution which characterizes the minimum difference between two sinusoids that can be distinguished Obviously for a given sampling frequency the more the samples the higher the frequency resolution Figure 15 1 illustrates a sum of two sinusoids The frequencies of these two sinusoids are 0 11 Hz and 0 13 Hz respectively To separate those two sinusoids the frequency resolution Af has to be less than or equal to 0 02 Hz Assume that the sampling frequency is 1 Hz Based on Equation 15 1 you need at least 50 samples Figure 15 2 depicts the FFT based power spectra one employs the rectangular window and the other the Hamming window As long as you have enough samples either window is able to separate the two sinusoids sum of two sinusoids 10 15 20 25 30 35 40 45 49 Figure 15 1 50 Samples for a Sum of Two Sinusoids D DANI 5 04 02 oo 02 0405 Figure 15 2 FFI Based Power Spectra Based on 50 Samples In many applications however the number of data samples is limited The shortness of the
318. y for the output of synthesis filter bank x0 double malloc nx sizeof double LELIXOJ 4 free y0 free y1 goto errend err SynthesisFilterBank y0 ny0 yl nyl synptr x0 nx x0 and x should be the same value free x0 errend free xX FreeCoeffWFBD anaptr FreeCoeffWFBD synptr Signal Processing Toolset 12 42 National Instruments Corporation Chapter 12 WFBD Toolkit Function Reference SynthesisFilterBank2D long status SynthesisFilterBank2D void low low void low high vold high low woid high highs long 23nsrzer l FilterBankPtr SynthesisFilters void x long xrows long xcols Computes the output from a synthesis filter bank of a 2D signal Parameters Input low_low double precision The upper left subimage from the analysis 2D array filter bank low_high double precision The upper right subimage from the 2D array analysis filter bank high_low double precision The lower left subimage from the analysis 2D array filter bank high_high double precision The lower right subimage from the 2D array analysis filter bank National Instruments Corporation 12 43 Signal Processing Toolset Chapter 12 WFBD Toolkit Function Reference long integer array SynthesisFilters FilterBankPtr Output Contains the size information for all four input arrays outsize 0 the number of rows of array low low outsize 1 the number of columns of array low low outsize 2

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