AUX User`s Manual version 1.0 I. Introduction II. Basic
Contents
1. tone 600 500 am noise 1000 8 db 20 am noise 1000 8 0 01 20 dB Amplitude Modulation rms Compute the rms value in dB Syntax rms signal Arguments signal any valid signal dur Get the duration of signal in ms Syntax dur signal rand Generates a double precision random number Syntax rand max_val Note Double precision random number between 0 and max_val with a uniform distribution irand Generates an integer random number Syntax irand max_val Note Integer random number between 1 and max_val with a uniform distribution randperm Generates a randomly permuted array from 1 to val Syntax randperm val Note An integer array from 1 to val and its order is randomly permuted is generated Page 9 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park tbegin Get the beginning time in ms first time point where the signal is non null tend Get the ending time in ms last time point where the signal is non null mean Get the mean value of signal max min Get the maximum or minimum value of the signal Syntax tbegin signal tend signal mean signal min signal max signal Also the following functions are available for numerical calculation sin Sine cos Cosine log Natural log log10 10 base log abs Absolute value exp Exponential A a b a raised by b sqrt Sqrt root mod Modulo VI2. MATLAB style can be avoided or at least the repeated use of MATLAB style expressions can be avoided by using user defined functions Here are a few MATLAB style expressions or conventions supported in AUX that might be useful Page 4 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park i ii iii iv v To define an empty vector do this V gt Don t be confused this with null signal We just need this definition to initialize an empty vector for subsequent accumulation For example V then later V V something else in a loop or something A vector can be defined in brackets e g V 0 20 40 60 80 A vector can be defined by the colon operator e g V 0 10 1000 The colon operator works a little differently from in MATLAB if there is only one colon You figure the difference from the examples below 1 5 isequalto 1 2 3 4 5 In AUX 5 1 isequalto 5 4 3 2 1 In MATLAB 5 1 isequalto empty In other words if you need to define a vector 5 4 3 2 1 in AUX you may specify it as 5 1 1 as you do in MATLAB but in addition you may do 5 1 to make it simpler gt you will enjoy this simplification As in MATLAB indexing is one based Example 6 If x is defined as a sequence with the step of 10 from 0 to 1000 x 0 10 1000 then x 1 2 9 indicates the following vector 0 20 40 60 80 Example 7 Continuing from examples 2 and 3 A 22050 1 is identical to A
3. User defined function Users may make their own functions if you don t like the functions that are provided you can override them It needs to be saved with the extension of aux and accessible by the program It has the following format similar to MATLAB function outputl output2 function_name inputl input2 Main body of the function that prepares and specifies output variables as results Similar to MATLAB the function keyword declared in the top of the file is visible to the program If there are more functions defined in the middle of the file using the same function keyword these are only accessible within the file i e local functions Page 10 of 10 Date March 2010
4. think about the actual implementation of the sound as the digitized samples in the digital domain rather you consider it as an abstract entity sound with certain properties i e frequency duration etc The presumption is that the issues of implementation are all taken care of by the program that uses AUX library not by the user Therefore in this AUX document the sampling rate is not considered or discussed at all in realistic applications the application should provide some mechanisms to adjust or set the sampling rate to meet the demand in hand so that the user can set the sampling rate properly for example if a 15000 Hz tone is to be created the sampling should be greater than 3000 Hz or if the programmer wants to fix the sampling rate at one value and does not want to allow the user to change at least it should notify the user if it exceeds the Nyquist rate However in MATLAB language you construct all the digitized samples from scratch and in doing so you need to explicitly specify how digitization should occur by supplying the sampling rate every time you define a signal It should also be noted that MATLAB style expressions are supported in AUX to define or construct vectors true arrays of values not actual sounds To summarize the definition of signal in AUX is high level while the definition of signal in MATLAB style is low level It is user s choice to use which option is proper for them For the most part
5. tonal glide Syntax tone freq duration initial_phase 0 Arguments freq frequency in Hz a two element vector of frequencies for a tone gilde duration duration in msec initial_phase between 0 for 0 and 1 for 27 Examples tone 226 400 a 226 Hz tone from 0 to 400 ms tone 226 400 5 226 Hz tone of 400 ms 180 degrees out of phase tone 250 500 400 a tone glide from 250 Hz to 500 Hz noise Generate a white noise signal Syntax noise duration Arguments duration duration in msec fm Generate a frequency modulated tone signal Syntax fm freql freq2 mod_rate duration init_phase 0 Arguments freql freq2 the boundary frequencies in Hz mod_rate how many times the frequency will swing between freql and freq2 must be a positive value duration duration in msec init_phase The initial modulation phase between 0 and 1 0 means it begins with freq and 1 means it begins with freq2 xamples fm 500 700 4 2000 a 2 second FM tone between 500 and 700 Hz at 4 Hz silence Generate a silence signal dc Generate a dc signal gnoise Generate a gaussian noise signal Notes The same format as noise it takes only one argument the duration in ms wave Read a wav file Syntax wave wave_name Arguments wave_name name of wave file Use double quotation marks or a string variable If path is not included current folder the same directory as the psycon exe will be searched The exten
6. vector lengths is not necessary but only consideration of time in millisecond But even easier the ramp function is provided in the AUX library to apply a raised cosine square function to a signal for a specified ramping duration And even further if the user needs a different type of envelope smoothing such as a different windowing or different times for onset and offset etc then a user defined function can be prepared and used for repeated uses In other words the user does not need to Page 3 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park write the codes in Example 5 over and over again Finally many MATLAB style expressions are also valid in AUX language This feature was added first to help seasoned MATLAB users transition to AUX easily and second to define and represent any signals or processing that can be done in MATLAB As of now not all MATLAB expressions are supported in AUX probably all of them will not ever because it is not necessary to bring the restrictions in MATLAB to AUX Plus if you specify a sound from scratch as a vector you will need to consider all the low level stuff such as the sampling rate sample count etc See the following two expressions that both produce the same sound in AUX tone 440 1000 sin 2 3 141592 440 1 fs 1 fs 1 The first expression is in the original AUX style and the second is MATLAB style Do you see the difference In AUX you don t
7. voice with doubled pitch and half of the duration 2 5 Stereo signal A B gt A stereo signal A on the left channel B on the right channel A and B need not have the same duration nor they may have entirely unrelated time arrangement 2 6 Null signal or null portion A null signal is defined as a signal that is not defined And null portion is the time portion that the signal is not defined As such arithmetic operations of a null signal or operations during the null portion have no effect Note that null signal is different from a signal with zero value For example in the signal defined as tone 1000 100 gt gt 500 the signal is not defined from 0 to 500 ms The concept of null signal is useful to apply arithmetic operations only for partial portion of a signal Example 5 For ramping damping of a signal envelope smoothing vector should be multiplied at the onset and offset With the concept of null signal this can be easily done as follows windowl tone 25 10 tone 25 10 cosine square function for increasing arc for 10 ms window2 windowl 10 0 gt gt 490 mirror image in time for offset window windowl window2 defined during the onset and offset portions null otherwise Finally smoothing occurs only during onset and offset smoothed_signal window original_signal 2 7 Further basics The above example illustrates why AUX is easier than in MATLAB because management of indices or
8. 1000 0 in example 3 presuming that the sample size of A is 22050 vi vii viii Cell arrays can be defined in the same ways in MATLAB using braces A string variable can be defined either double or single quotation marks e g str c soundfiles test wav wave str String variables have the same rules and conventions as in MATLAB such as concatenating or accessing by indices 2 8 Other conventions full scale order of operations In AUX we shall use 1 as the full scale And functions tone and noise produce the sound at the full scale at the amplitude of 1 In the current form AUX does not check whether the expression leads to clipping Therefore it is the user s responsibility to avoid clipping e g tone 440 300 tone 880 300 produces clipping A proper scaling is necessary such as 0 5 tone 440 300 0 5 tone 880 300 Page 5 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park The following is AUX operators in the order of precedence highest to lowest The precedence is pretty much standard except for a few AUX native operators which are placed between multiplication division and addition subtraction Their associativity indicates in what order operators of equal precedence in an expression are applied Personally we wouldn t memorize this because we think we should use parentheses whenever in doubt But we are including this information to remind you tha
9. AUX User s Manual version 1 0 Authors BJ Kwon JH Park I Introduction AUX stands for AUditory syntaX used to define arbitrary sound signals and operations processing of auditory signals It is semi mathematical i e signal components can be added subtracted multiplied or divided Unlike MATLAB two signals with different lengths can be added or multiplied without worrying about the indices or vector lengths even the operation between a signal and a scalar is possible Users only need to be familiar with conventions in such operations Il Basic format of signals and operators 2 1 Terminology Vector An array of values Signal Same as the vector but connoting a sound signal AUX itself doesn t differentiate a signal from vector but the different use of these words might be helpful for this document Conceptual difference you conceptualize a vector as an array of values with a certain length in sample counts whereas you conceptualize a sound as a sound with a duration in seconds By definition all signals in AUX specifications are time bound therefore a duration or sample count is determined when you define a signal Scalar A constant value a special form of vector Variable A variable can be used to denote or define a vector or signal and use it later Below A and B are signals a and b are scalars For arithmetic operations regardless of the duration of the signals the operation
10. Bstop 40 hpf signal freq order 8 kind 1 dBpass 5 dBstop 40 bpf signal freql freq2 order 8 kind 1 dBpass 5 dBstop 40 bsf signal freql freq2 order 8 kind 1 dBpass 5 dBstop 40 Arguments order Filter order Default 8 kind 1 for Butterworth default 2 for Chebyshev and 3 for Elliptic dBpass Passband ripple in dB default 0 5 dB dBstop Stopband attenutation in dB default 40 dB Examples lpf noise 1000 2000 Lowpass noise with a cutoff frequency of 2000 Hz 8th order Butterworth hpf noise 1000 3000 6 2 Highpass noise with a cut of 3000 Hz 6th order Chebyshev bpf noise 1000 1900 2000 6 3 1 80 bandpass noise between 1900 and 2000 Hz 6th order Elliptic with 1dB ripple and 60 dB attenuation note Be sure to check the HR filter s stability Note that some filtering specs such as very narrow bandpass filtering will be difficult to obtain stable filter coefficient filt Filter the signal with the specified coefficients Syntax filt signal num_array den_array filt signal mat_file matlab_filter_variable Arguments num_array den_array Numerator or denominator coefficient arrays Must use a bracket or tag see how to use tag mat_file The matlab file mat that contains the variable specified in the 3rd argument Must use double quotation marks This could include a path Default extension is mat mat lab_filter_variable The ma
11. ds Examplel tone 1000 100 is a 1000 Hz tone with 100 ms tone 1000 100 gt gt 500 is the same tone but begins at 500 ms instead of 0 2 2 RMS scaling operator A a gt Scale the signal A at a dB rms re 0 dB full scale of the sound card A B a7 Scale the signal A at a dB rms re 0 dB full scale of the sound card Example2 Let A be a waveform read from a wave file A wave bob wav Then A 20 specifies the signal rescaled to make its rms 20 dB re the full scale A wave masker 5 specifies that the signal be adjusted its scale to its rms 5 dB above that of another signal masker wav 2 3 Extraction operator A a b gt Extract a time portion between a and b millisecond from signal A If b lt a the extracted signal is time reversed Example 3 From the signal A defined in Example 2 A 300 500 is the extracted portion of the waveform from 300 to 500 ms Suppose that A has a duration of 1000 ms then A 1000 0 isa time reversal version of signal A Page 2 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park 2 4 Playback adjustment operator The operator changes the playback rate the signal i e modulating the pitch of voice and making the duration faster or slower accordingly Example 4 Continuing from example 5 A 2 is the signal of the voice with the half of the pitch with doubled duration and A 5 or A 1 2 is the signal of the
12. is applied as long as each operand is valid and available For example note that we haven t discussed how a signal can be defined in AUX signals here are defined in verbal expressions A a 500 Hz tone from 300 ms til 600ms B white noise from 500 ms til 1000ms Then A B is a 500 Hz tone from 300 ms til 500 ms the same tone plus noise from 500 ms till 600 ms then noise from 600 ms til 1000 ms The same principle applies to multiplication For the operations between a scalar and a signal essentially the scalar operand applies through the Page 1 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park entire duration of the signal From signal A defined above 0 2 Ais the signal A multiplied scaled by 0 2 for the entire duration of the signal 0 2 A is the signal A plus a dc shift with the DC amplitude of 0 2 The above explanation appears more complicated than it actually is And this kind of convention allows flexible application of arithmetic operations particularly with the concept of null signal see below If you are unsure now please keep reading this By the end of section 2 you will have a clear idea about the fundamental framework of AUX Also in the examples below functions are used without explanations just keep reading it those will be covered in section 3 2 2 Time shift operator gt gt A gt gt a Shift the signal A in time forward by a millisecon
13. sion wav can be omitted Examples wave c soundData specialnoise Read the signal from specialnoise wav in the specified directory file Read from text ascii file the values will be read into an array delimited by a space CR LF or tab character Syntax file file_name Page 7 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park Arguments file name name of text file Use double quotation marks or a string variable If path is not included current folder the same directory as the psycon exe will be searched The extension txt can be omitted IV Signal modification functions am Amplitude Modulate the signal Syntax am signal mod_rate mod_depth 1 init_phase 0 Arguments mod_rate AM modulation rate in Hz mod_depth Modulation depth between 0 no mod and 1 full mod If skipped full modulation is assumed init_phase The initial modulation phase between 0 and 1 Examples am noise 1000 8 0 5 AM of a white noise at 8 Hz with a depth of 0 5 Ipf IIR filtering Lowpass highpass bandpass and bandstop filtering respectively Ipf hpf and hpf require at least 2 arguments signal and edge frequency and bpf and bsf bpf require at least 3 arguments signal and two edge frequencies The rest arguments bsf are optional and available for tweaking detailed filter settings Syntax lpf signal freq order 8 kind 1 dBpass 5 d
14. t there is a priority of operation when there are no parentheses i e don t presume that the signal you defined is unambiguous to everyone specifically the developers of AUX Description Associativity Parentheses sub expression function call vector indexing Braces array subscript Unary plus minus sign right to left Logical peeaHon right to left Multiplication division left to right Time shift left to right Playback speed RMS left to right Addition subtraction left to right Range left to right Relational less than less than or equal to left to right Relational greater than greater than or equal to Relational is equal to is not equal to eben TOEA AND Comma separate expressions left to right Example 8 tone 1000 100 gt gt 500 20 is tone 1000 100 gt gt 500 20 and is an ugly super duper clipped signal You should write it as tone 1000 100 gt gt 500 20 if that s what you meant But tone 1000 100 gt gt 500 2 is tone 1000 100 gt gt 500 2 so you should write it as tone 1000 100 gt gt 500 2 if that s what you meant 2 9 Programming support for looping The following syntaxes for control looping are supported the same way as in MATLAB for end Page 6 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park while end if elseif else end Ill Signal construction functions tone Generate a tone signal or
15. tlab variable of filter coefficient generated by sptool Must use double quotation marks Examples filt noise 1000 2 0 2 001 1 2 02 Filter the white noise with these coefficient arrays 2nd order IIR Page 8 of 10 Date March 2010 AUX User s Manual version 1 0 Authors BJ Kwon JH Park filt noise 1000 filters 1p1500 Filter the noise with the coefficients available in matlab variable 1p1500 stored in filters mat filtfilt Anti causal zero delay filter the signal with the specified coefficients Syntax filtfilt signal num array den_array filtfilt signal mat_file matlab_filter_variable ramp Make the beginning and ending points smooth to avoid spectrum splatter Syntax ramp signal ramping time Arguments ramping_time The time in ms for ramping up at the beginning and down at the end Examples ramp tone 1500 500 10 Make the tone with 10 ms beginning and ending ramping Note This uses the cosine square function for smoothing V Computation functions or functions retrieving properties of a signal If you want to use a dB factor for scaling the following db function comes in handy db Calculate the actual factor from a dB value Syntax db db_value Arguments db_value the scale factor of the specified value in dB Examples The following expressions are the same db 6 tone 300 500 0 5 tone 300 500 tone 300 db 6 500
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