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cwtfilters2array

Convert CWT filter bank to reduced-weight tensor for deep learning

    Description

    [psifvec,filteridx] = cwtfilters2array(wfb) converts the CWT filter bank wfb to a reduced-weight CWT filter tensor psifvec for deep learning. filteridx is a bookkeeping matrix.

    example

    [psifvec,filteridx] = cwtfilters2array(___,thresh) uses thresh to extract the significant values from each of the CWT filters in wfb. By thresholding, you can significantly reduce the number of learnable parameters in the filter bank.

    [psifvec,filteridx] = cwtfilters2array(___,IncludeLowpass=tf) specifies whether to include the lowpass (scaling) filter in psifvec.

    Examples

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    Create a CWT filter bank appropriate for deep learning. Specify a signal length of 2048 samples. Use the default Morse wavelet.

    len = 2048;
    fb = cwtfilterbank(SignalLength=len,Boundary="periodic");

    Extract the reduced-weight CWT filter tensor from the filter bank. Specify a threshold of 1/4.

    [psifvec,filteridx] = cwtfilters2array(fb,1/4);

    Use the bookkeeping matrix filteridx to plot the filters in psifvec.

    fBins = (0:len-1)/len;
    hold on
    for k=2:size(filteridx,1)
        indX = filteridx(k,1:2);
        indY = filteridx(k,3:4);
        rangeX = indX(1):indX(2);
        rangeY = indY(1):indY(2);
        plot(fBins(rangeX),squeeze(psifvec(rangeY)))
    end
    title("Extracted Filter Tensor")
    xlabel("Normalized Frequency (cycles/sample)")
    ylabel("Magnitude")
    hold off
    ylim([0 2])

    Figure contains an axes object. The axes object with title Extracted Filter Tensor contains 81 objects of type line.

    Input Arguments

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    CWT filter bank, specified as a cwtfilterbank object. wfb must have Boundary="periodic". For more information, see cwtfilterbank.

    Threshold to apply to the CWT filters in wfb, specified as a real scalar. cwtfilters2array uses thresh to extract the significant values from each of the CWT filters in wfb. The filters are normalized so that the peak value for each filter is 2

    • Smaller values of thresh result in more values being retained from the CWT filters and therefore less weight reduction.

    • Larger values of thresh result in more weight reduction and more divergence between the deep learning CWT and transforms computed with the full filter bank.

    • Any threshold less than realmin, the smallest positive normalized floating-point number in double precision, is set to realmin for extracting the filter values.

    Setting thresh to a value which results in no values being retained for any individual filter results in an error.

    Data Types: single | double

    Include lowpass filter, specified as a numeric or logical 1 (true) or 0 (false). Specify true to include the lowpass (scaling) filter in psifvec. The size of filteridx increases to Nfilt+2-by-4, where Nfilt is the number of filters in the CWT filter bank wfb. The meta information for the scaling filter is included in the final row of filteridx.

    Data Types: logical

    Output Arguments

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    Reduced-weight CWT filter tensor, returned as a 1-by-1-by-Nr tensor, where Nr is the number of filter values greater than thresh.

    Data Types: double

    Bookkeeping matrix that describes psifvec, returned as an Nfilt+1-by-4 matrix, where Nfilt is the number of filters in the CWT filter bank wfb.

    • The first row of filteridx is [1 Nf 0 0], where Nf is the number of frequency bins, or equivalently the number of time points in the wavelet filter. Nf is equal to the SignalLength property of wfb.

    • For rows 2 through Nfilt+1, the first two columns of filteridx contain the beginning and ending frequency bins for the corresponding wavelet filters ordered by decreasing center frequency. The third and fourth columns of filteridx contain the beginning and ending indices of the corresponding filter in the reshaped tensor, psifvec.

      Use array2cwtfilters to reconstruct an approximation to the wavelet filter bank from psifvec and filteridx.

    Data Types: uint32

    Version History

    Introduced in R2022b

    See Also

    Functions

    Objects