Import Data

Load the electrical consumption signal.

load nelec

Open Wavelet Signal Analyzer and import the signal into the app. By default, a four-level nondecimated wavelet decomposition of the signal appears. The table in the Levels pane indicates that there are 2000 original and retained coefficients at all levels. Plot the relative energies of the decomposition. Most of the energy lies in the approximation coefficients.

Compress Signal

On the Analyzer tab, click Compress. The app applies the same default threshold thr to the coefficients using global hard thresholding. The app sets all coefficients that lie in the interval [–thr, thr] to 0.

Switch to the Decomposition Coefficients pane. Compress the signal. Set 0 to all the detail coefficients. Use all the approximation coefficients to construct the compressed signal.

Generate Script

You have a number of export options available. You can export the original coefficients or generate a script to recreate the decomposition in your workspace. Because you have enabled compression, you can also export the compressed signal or thresholded coefficients, as well as generate a script to recreate the compressed signal in your workspace. To recreate the compressed signal in your workspace, in the Export ▼ menu, select Generate MATLAB Script under Compressed Signal.

An untitled script opens in your editor with the following executable code. You can save the script as is or modify it to apply the same compression to other signals. Run the code.

Note: The app uses time-aligned coefficients only when visualizing the decomposition. The generated script always uses the original coefficients. The state of the Time Align parameter has no impact on the generated script.

% Perform the decomposition using MODWT
numberOfLevels = 4;
wt = modwt(nelec,"sym4",numberOfLevels);

% Compute the energy by level for the decomposition
energyByLevel = 100*sum((wt.^2),2)/sum(wt.^2,"all");

% Thresholds for compressing the imported signal
compressionThresholds = ...
    [464.1 464.1 464.1 464.1 0]';

% Duplicate coefficients for thresholding
wc = wt;

% Apply threshold to coefficients
for idx = 1:numel(compressionThresholds)
    thr = abs(compressionThresholds(idx));
    w = wc(idx,:);
    w = wthresh(w,"h",thr);
    wc(idx,:) = w;
end

% Energy by level for the compressed signal
energyByLevelForCompressed = 100*sum((wc.^2),2)/sum(wc.^2,"all");

% Reconstruct the compressed signal using IMODWT
nelec1_compressed = imodwt(wc,"sym4");

Plot the original signal, nelec, and the compressed signal, nelec1_compressed.

plot(nelec)
hold on
plot(nelec1_compressed,LineWidth=2)
hold off
axis tight
title("Original and Compressed Signals")
legend("Original","Compressed")

Compare the energies by level of the original and thresholded coefficients. Because you set all the wavelet (detail) coefficients to 0, all the energy in the thresholded coefficients is contained in the approximation level.

[energyByLevel energyByLevelForCompressed]

ans = 5×2

    0.0152         0
    0.0124         0
    0.0125         0
    0.0260         0
   99.9338  100.0000