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Signal Processing

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Maple's SignalProcessing package offers tools for FFTs, DFTs, wavelet analysis, IIR and FIR filters, signal generation, spectrograms and more.

 

Example - Identifying Signal Frequencies from a Spectrogram and Periodogram

 

> 

withSignalProcessing:

 

Here, we will identify the frequencies of an artificially generated signal. The signal will be a sum of two sinusoids with frequencies of 12 Hz and 24 Hz.

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N≔210:samplingRate≔100:signal≔VectorN,i↦sin12.⋅2⋅π⋅isamplingRate+1.5⁢sin24.⋅2⋅π⋅isamplingRate,datatype=float8:


Plot the spectrogram and periodogram

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Spectrogramsignal,samplerate=samplingRate,size=1000,200

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Periodogramsignal,samplerate=samplingRate,size=1000,200


The spectrogram and power spectrum correctly identifies the two frequencies used to generate the original data.

 

Example - Filtering Audio

 

First import the audio

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file≔cat⁡kernelopts⁡datadir,//audio//MapleSimMono11025.wav

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originalSpeech≔AudioTools:-Read⁡file

originalSpeech≔?

(1)

 

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samplingRate≔attributesoriginalSpeech1

samplingRate≔11025

(2)
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Spectrogram⁡originalSpeech,size=1000,200,reduceplot=1

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Periodogram⁡originalSpeech,size=1000,200,reduceplot=4

 

Now let's apply a Butterworth filter to the audio. Define the critical frequency, generate the filter taps, and apply the filter.

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fc≔800

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taps≔GenerateButterworthTaps9,fcsamplingRate,filtertype=lowpass;filteredSpeech≔InfiniteImpulseResponseFilter⁡originalSpeech,taps

Then generate the spectrogram and periodogram

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Spectrogram⁡filteredSpeech,samplerate=samplingRate,size=1000,200,reduceplot=1

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Periodogram⁡filteredSpeech,samplerate=samplingRate,size=1000,200

 

You can also export the filtered audio

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#A≔AudioTools:-CreatefilteredSpeech,rate=11025;#AudioTools:-WriteIIRtest.wav,A

> 

 

 

 

Applications

Identifying Periodicity of Sunspots

Signal Denoising

FIR and IIR Filters

Apply Filters to Audio

Spectrogram Examples