filterbank

Wavelet time scattering filter banks

Syntax

filters = filterbank(sf)

[filters,f] = filterbank(sf)

[filters,f,filterparams] = filterbank(sf)

[___] = filterbank(sf,order)

Description

filters = filterbank(sf) returns the filter banks used in the computation of the scattering coefficients. filters is a cell array of structure arrays with norder elements, where norder is the number of scattering orders. The first element of filters contains the scaling filter, phift, used in the computation of the 0th-order scattering coefficients. Subsequent elements of filters contain the wavelet filters, psift, and scaling filter, phift, for the corresponding filter banks of the scattering decomposition.

The precision of phift and psift depends on the precision specified in the framework sf.

[filters,f] = filterbank(sf) returns the frequencies corresponding to the DFT bins in the psift and phift fields of filters. If you specify a sampling frequency in the construction of sf, f is measured in hertz. Otherwise, f is measured in cycles/sample.

[filters,f,filterparams] = filterbank(sf) returns the filter parameters for each element of filters. filterparams is a cell array with norder elements. Each element of filterparams is a MATLAB^® table.

[___] = filterbank(sf,order) returns the filter banks used to compute the specified order scattering coefficients. order is an integer between 0 and nfilters inclusive, where nfilters is the number of filter banks in the scattering decomposition inclusive. These input arguments can be used with any of the output syntaxes shown previously.

Examples

Plot Scattering Framework Filter Banks

Create a scattering decomposition framework for a signal sampled at 25 Hz.

sf = waveletScattering('SamplingFrequency',25)

sf = 
  waveletScattering with properties:

          SignalLength: 1024
       InvarianceScale: 20.4800
        QualityFactors: [8 1]
              Boundary: "periodic"
     SamplingFrequency: 25
             Precision: "double"
    OversamplingFactor: 0

Obtain the filter banks, DFT frequency bins, and filter bank parameters.

[filters,f,fparams] = filterbank(sf);

Plot the wavelet filters used in computing the first-order coefficients. Plot the wavelet center frequencies as well.

coefOrder = 1;
wvFilters = filters{coefOrder+1}.psift;
wvcenFrq = fparams{coefOrder+1}.omegapsi;
plot(f,wvFilters)
hold on
cf = plot(wvcenFrq,max(wvFilters),'rx');
grid on
title('Wavelet Filters')
xlabel('Hz')
ylabel('Magnitude')
legend(cf,'Center Frequencies')

Input Arguments

sf — Scattering decomposition framework

waveletScattering object

Scattering decomposition framework, specified as a waveletScattering object.

order — Order of scattering coefficients

positive integer

Order of scattering coefficients, specified as a positive integer between 0 and nfilters inclusive, where nfilters is the number of filter banks in the scattering decomposition sf.

Data Types: double

Output Arguments

filters — Filter banks

cell array

Filter banks using in the computation of the scattering coefficients, returned as a cell array of structure arrays. filters has norder elements, where norder is the number of scattering orders. The first element of filters is a structure with the single field phift. phift contains the scaling filter used in the computation of the 0th-order scattering coefficients. Subsequent elements of filters contain the wavelet filters, psift, and the scaling filter, phift, used for the corresponding filter banks of the scattering decomposition in the structure fields.

The precision of phift and psift depends on the precision specified in the framework sf.

f — Frequencies

real-valued vector

Frequencies corresponding to the DFT bins in the psift and phift fields of filters. If you specify a sampling frequency in the construction of sf, f is measured in hertz. Otherwise, f is measured in cycles/sample.

Data Types: double

filterparams — Filter bank parameters

cell array

Filter bank parameters for each element of filters, returned as a cell array. filterparams has norder elements, where norder is the number of scattering orders.

The first element of filterparams is a MATLAB table with the following variables:

• boundary — The signal extension used in the filters, returned as either 'periodic' or 'reflection'.

• precision — The precision used in the filters, returned as 'double' or 'single'.

• sigmaphi — The time standard deviation of the scaling function, returned as a scalar. If you specify a sampling frequency, sigmaphi is in seconds. Otherwise, sigmaphi is in samples.

• freqsigmaphi — The frequency standard deviation of the scaling function, returned as a scalar. If you specify a sampling frequency, freqsigmaphi is in hertz. Otherwise, freqsigmaphi is in cycles/sample.

• phiftsupport — The frequency support of the scaling function, returned as a scalar. If you specify a sampling frequency, phiftsupport is in hertz. Otherwise, phiftsupport is in cycles/sample.

• phi3dBbw — The 3-dB bandwidth of the scaling function, returned as a scalar.

Subsequent elements of filterparams include additional variables for the wavelet parameters:

• J — The integer number of logarithmically spaced wavelet filters in the scattering filter bank.

• omegapsi — The center frequencies for the wavelet filters in descending order (highest to lowest), returned as a vector. The omegapsi variable includes the center frequencies for any linearly spaced filters.

• freqsigmapsi — The wavelet frequency standard deviations, returned as a vector.

• timesigmapsi — The wavelet time standard deviations, returned as a vector.

• psi3dBbw — The wavelet 3-dB bandwidths, returned as a vector.

• psiftsupport — The wavelet frequency supports, returned as a vector.