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dlcwt

Deep learning continuous wavelet transform

    Description

    cfs = dlcwt(x,psifvec,filteridx) returns the deep learning continuous wavelet transform (CWT) of x. psifvec is a real-valued CWT filter bank, and filteridx is a bookkeeping matrix. dlcwt requires Deep Learning Toolbox™.

    example

    cfs = dlcwt(x,psifvec,filteridx,DataFormat=fmt) specifies the data format of x.

    Examples

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    Load the ECG signal. The sampling frequency of the data is 180 hertz. Save the signal as a dlarray in "CBT" format.

    load wecg
    Fs = 180;
    sig = dlarray(reshape(wecg,1,1,[]),"CBT");

    Create a CWT filter bank that is compatible with the signal. Specify periodic boundary conditions.

    fb = cwtfilterbank(SignalLength=length(sig),Boundary="periodic");

    Use the wt object function to obtain the CWT coefficients of wecg. Also obtain the scaling coefficients. Concatenate the coefficients.

    [cfsFB,~,~,scalcfs] = wt(fb,wecg);
    allCFS = [cfsFB ; scalcfs];
    whos allCFS
      Name         Size                Bytes  Class     Attributes
    
      allCFS      82x2048            2686976  double    complex   
    

    Use the cwtfilters2array function to convert the filter bank to a reduced-weight tensor suitable for deep learning. Include the lowpass (scaling) filter in the tensor.

    [psifvec,filteridx] = cwtfilters2array(fb,IncludeLowpass=true);

    Obtain the deep learning CWT of the signal.

    cfsD = dlcwt(sig,psifvec,filteridx);
    dims(cfsD)
    ans = 
    'SCBT'
    

    By default, the output is a dlarray object in "SCBT" format. The spatial dimension corresponds to frequency. Convert the output to a numeric array. Permute the dimensions of the output to correspond with "STCB" format. The result will be a 2-D matrix because there is only one channel and one batch.

    cfs = extractdata(cfsD);
    cfs = permute(cfs,[1 4 2 3]);
    whos cfs
      Name       Size                Bytes  Class     Attributes
    
      cfs       82x2048            2686976  double    complex   
    

    Confirm the CWT and deep learning CWT of the signal are equal.

    max(abs(cfs(:)-allCFS(:)))
    ans = 1.0235e-09
    

    Load the Espiga3 EEG dataset. The data consists of 23 channels of EEG sampled at 200 Hz. There are 995 samples in each channel. Save the multisignal as a dlarray, specifying the dimensions in order. dlarray permutes the array dimensions to the "CBT" shape expected by a deep learning network.

    load Espiga3
    Fs = 200;
    [N,nch] = size(Espiga3);
    x = dlarray(Espiga3,"TCB");
    whos Espiga3 x
      Name           Size                Bytes  Class      Attributes
    
      Espiga3      995x23               183080  double               
      x             23x1x995            183134  dlarray              
    

    Create a CWT filter bank that is compatible with the signal. Specify periodic boundary conditions. Then use the cwtfilters2array function to convert the filter bank to a reduced-weight tensor suitable for deep learning.

    fb = cwtfilterbank(SignalLength=N,Boundary="periodic");
    [psifvec,filteridx] = cwtfilters2array(fb);

    Obtain the deep learning CWT of the multisignal.

    cfsD = dlcwt(x,psifvec,filteridx);
    dims(cfsD)
    ans = 
    'SCBT'
    

    By default, the output is a dlarray object in "SCBT" format. The spatial dimension corresponds to frequency. Convert the output to a numeric array. Permute the dimensions of the output to correspond with "STCB" format. The result will be a 3-D array because there is only one batch.

    cfs = extractdata(cfsD);
    cfs = permute(cfs,[1 4 2 3]);
    whos cfs
      Name       Size                   Bytes  Class     Attributes
    
      cfs       71x995x23            25997360  double    complex   
    

    Obtain the center frequencies from the original filter bank. Display the scalogram of a channel.

    frq = centerFrequencies(fb);
    channel = 4;
    cfsChannel = cfs(:,:,channel);
    tms = (0:N-1)/Fs;
    surface(tms,frq,abs(cfsChannel))
    set(gca,"yscale","log")
    axis tight
    shading flat
    title("Scalogram")
    xlabel("Time (s)")
    ylabel("Frequency (Hz)")

    Figure contains an axes object. The axes object with title Scalogram contains an object of type surface.

    Input Arguments

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    Input data, specified as a real-valued unformatted dlarray object, a formatted dlarray in "CBT" format, or a numeric array. If x is an unformatted dlarray or a numeric array, you must specify the 'DataFormat' as some permutation of "CBT".

    Data Types: single | double

    CWT filter bank, specified as a 1-by-1-by-Nr tensor, where Nr is the number of weights in the reduced-weight CWT filter bank. Use cwtfilters2array to obtain psifvec.

    You can use array2cwtfilters to reconstruct the 2-D CWT filter bank from the outputs of cwtfilters2array.

    Data Types: double

    Bookkeeping matrix, specified as a matrix. The dlcwt function uses filteridx to index into the data x and filter bank psifvec in order to compute the CWT. Use cwtfilters2array to obtain filteridx.

    Data Types: uint32

    Input data format of x, specified as some permutation of "CBT". This argument is invalid if x is a formatted dlarray.

    Each character in this argument must be one of these labels:

    • C — Channel

    • B — Batch

    • T — Time

    The dlcwt function accepts any permutation of "CBT". Each element of the argument labels the matching dimension of x.

    Example: w = dlcwt(x,psifvec,filteridx,DataFormat="BCT") specifies the data format of the unformatted dlarray object as "BCT".

    Data Types: char | string

    Output Arguments

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    Continuous wavelet transform of x, returned as a dlarray object.

    • If x is a formatted dlarray object, cfs is in "SCBT" format. The spatial dimension corresponds to scale, or equivalently the center frequency of the wavelet bandpass filters. The channel, batch, and time dimensions correspond to the channel, batch, and time dimensions of x.

    • If x is an unformatted dlarray object or numeric array, cfs is an unformatted dlarray object. The dimension order in cfs is "SCBT".

    Extended Capabilities

    Version History

    Introduced in R2022b

    See Also

    Functions

    Objects