numFirst2SecondFilterBank

Load the quadratic chirp signal. The signal has 4001 samples. Create a joint time-frequency scattering network appropriate for the signal. Specify a frequency invariance scale of 128 samples.

load quadchirp
len = numel(quadchirp);
jtfn = timeFrequencyScattering(SignalLength=len, ...
    FrequencyInvarianceScale=128);

Use the numFirst2SecondFilterBank object function to obtain the number of first-order time wavelet filter paths going through each second-order time wavelet filter. Find the maximum number of paths going through a second-order time wavelet filter.

numPaths = numFirst2SecondFilterBank(jtfn);
maxPaths = max(numPaths.('Number of First Filter Bank Wavelets'))

maxPaths = 
61

Inspect the size of the frequency invariance scale of the network. Because the desired scale, 128, exceeds the maximum number of paths, 61, the frequency invariance scale is set to maxPaths.

jtfn.FrequencyInvarianceScale

ans = 
61

Obtain as a tensor the JTFS transform of the signal. The format of the tensor is path-by-frequency-by-time. The size of the frequency dimension of the tensor depends on the maximum number of paths and the frequency invariance scale.

smat = scatteringFeatures(jtfn,quadchirp);
size(smat,2)

ans = 
2

ceil(maxPaths/2^floor(log2(jtfn.FrequencyInvarianceScale)))

ans = 
2

Create a second network with a frequency invariance scale of 7 samples.

jtfn2 = timeFrequencyScattering(SignalLength=len, ...
    FrequencyInvarianceScale=7);
jtfn2.FrequencyInvarianceScale

ans = 
7

Use the second network to obtain as a tensor the JTFS of the signal. Confirm the size of the frequency dimension of the tensor is equal to ceil(maxPaths/2^floor(log2(fis))), where fis = jtfn2.FrequencyInvarianceScale.

smat2 = scatteringFeatures(jtfn2,quadchirp);
size(smat2,2)

ans = 
16

ceil(maxPaths/2^floor(log2(jtfn2.FrequencyInvarianceScale)))

ans = 
16