This example shows how to oversample a 1-D wavelet scattering transform.

Load an ECG signal sampled at 180 Hz, and create a wavelet scattering framework to process the signal. To perform a critically downsampled wavelet scattering transform, do not change the value of the OversamplingFactor property in sf. Return the number of scattering coefficients for the framework.

load wecg
Fs = 180;
sf = waveletScattering('SignalLength',numel(wecg),'SamplingFrequency',Fs);
ncf = numCoefficients(sf)

ncf = 8

Return the 1-D wavelet scattering transform of wecg, and plot the zeroth-order scattering coefficients. Confirm the number of zeroth-order scattering coefficients is equal to ncf.

s = scatteringTransform(sf,wecg);
display(['Number of zeroth-order scattering coefficients: ',...
  num2str(numel(s{1}.signals{1}))])

Number of zeroth-order scattering coefficients: 8

plot(s{1}.signals{1},'x-')
grid on
axis tight
title('Zeroth-Order Scattering Coefficients')

To oversample the scattering coefficients by a factor of 2, set the OversamplingFactor property of sf equal to 1 (because $${\log }_{2}2=1$$). Return the number of scattering coefficients for the edited framework. Confirm the number of scattering coefficients has doubled.

sf.OversamplingFactor = 1;
ncf = numCoefficients(sf)

ncf = 16

Return the wavelet scattering transform of wecg using the edited framework, and plot the zeroth-order scattering coefficients. Since the number of coefficients in the critically sampled transform is equal to 8, confirm that the number of zeroth-order coefficients in the oversampled transform is equal to 16.

s = scatteringTransform(sf,wecg);
figure
plot(s{1}.signals{1},'x-')
grid on
axis tight
title('Zeroth-Order Scattering Coefficients')