dlcwt

Deep learning continuous wavelet transform

Since R2022b

Syntax

cfs = dlcwt(x,psifvec,filteridx)

cfs = dlcwt(x,psifvec,filteridx,DataFormat=fmt)

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™.

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

Examples

Deep Learning Continuous Wavelet Transform of ECG Signal

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

Deep Learning Continuous Wavelet Transform of Multisignal

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            183110  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)")

Input Arguments

x — Input data

dlarray object | numeric array

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

psifvec — CWT filter bank

array

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

filteridx — Bookkeeping matrix

matrix

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

fmt — Input data format

character vector | string scalar

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

cfs — Continuous wavelet transform

formatted dlarray object | unformatted dlarray object

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

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2022b