returns the Littlewood-Paley sum for the scattering filter banks in
lpsum = littlewoodPaleySum(
the wavelet time scattering network.
lpsum is an
M-by-L matrix, where M is the
number of elements in the Fourier transform of the scattering filters, and
L is the number of scattering filter banks. The columns of
lpsum are ordered by the position of the filter bank in the
scattering network. For example, the first column of
to the filter bank used for the first-order scattering coefficients.
Since the scattering transform is contractive, the Littlewood-Paley sums will not exceed one.
Plot Littlewood-Paley Sum
Create a wavelet time scattering network with three filter banks for data sampled at 25 Hz.
sf = waveletScattering('QualityFactors',[8 4 1],... 'SamplingFrequency',25)
sf = waveletScattering with properties: SignalLength: 1024 InvarianceScale: 20.4800 QualityFactors: [8 4 1] Boundary: 'periodic' SamplingFrequency: 25 Precision: 'double' OversamplingFactor: 0 OptimizePath: 0
Plot the Littlewood-Paley sums for the second and third filter banks. Note that the sums do not exceed 1. This shows the filters have been normalized so that the scattering transform is contractive.
[lpsum,f] = littlewoodPaleySum(sf); plot(f,lpsum(:,2:3)) grid on legend('Filter Bank 2','Filter Bank 3') xlabel('Hz')
sf — Wavelet time scattering network
Wavelet time scattering network, specified as a
fb — Filter bank index
Filter bank index in the wavelet time scattering network, specified as a positive
integer between 1 and the number of filter banks in
The number of filter banks in
sf is equal to the number of
lpsum — Littlewood-Paley sum
Littlewood-Paley sum for the filter banks in the scattering network
sf, returned as a real-valued matrix.
is an M-by-L matrix, where M is
the number of elements in the Fourier transform of the scattering filters and
L is the number of scattering filter banks. For example, the first
lpsum corresponds to the filter bank used for the
first-order scattering coefficients.
f — Frequencies
Frequencies for the Littlewood-Paley sum, returned as a real-valued vector. If you
specify a sampling frequency in
f is in
hertz. If you do not specify a sampling frequency,
f is in