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.
N≔210:samplingRate≔100:signal≔VectorN,i↦sin12.⋅2⋅π⋅isamplingRate+1.5sin24.⋅2⋅π⋅isamplingRate,datatype=float8:
Plot the spectrogram and periodogram
Spectrogramsignal,samplerate=samplingRate,size=1000,200
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
file≔catkerneloptsdatadir,//audio//MapleSimMono11025.wav
originalSpeech≔AudioTools:-Readfile
originalSpeech≔?
samplingRate≔attributesoriginalSpeech1
samplingRate≔11025
SpectrogramoriginalSpeech,size=1000,200,reduceplot=1
PeriodogramoriginalSpeech,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.
fc≔800
taps≔GenerateButterworthTaps9,fcsamplingRate,filtertype=lowpass;filteredSpeech≔InfiniteImpulseResponseFilteroriginalSpeech,taps
Then generate the spectrogram and periodogram
SpectrogramfilteredSpeech,samplerate=samplingRate,size=1000,200,reduceplot=1
PeriodogramfilteredSpeech,samplerate=samplingRate,size=1000,200
You can also export the filtered audio
#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
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