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Continuous Wavelet Analysis of Cusp Signal

This example shows how to perform continuous wavelet analysis of a cusp signal. You can use cwt for analysis using an analytic wavelet and wtmm to isolate and characterized singularities.

Load and plot a cusp signal. Display its definition at the command line.

load cuspamax; 
plot(cuspamax); grid on;

Figure contains an axes. The axes contains an object of type line.

disp(caption)
x = linspace(0,1,1024); y = exp(-128*((x-0.3).^2))-3*(abs(x-0.7).^0.4);

Obtain and view the CWT of the cusp signal. The CWT uses an analytic Morse wavelet with gamma equal to 2 and a time-bandwidth parameter of 2.5. Notice the narrow region in the scalogram converging to the finest scale (highest frequency). This indicates a discontinuity in the signal.

cwt(cuspamax,'WaveletParameters',[2 2.5]);

Figure contains an axes. The axes with title Magnitude Scalogram contains 3 objects of type image, line, area.

Obtain a plot of the wavelet maxima lines using wavelet transform modulus maxima. wtmm returns estimates of the Holder exponents, which characterize isolated singularities in a signal. Notice that the cusp is shown very clearly using wtmm.

wtmm(cuspamax,'ScalingExponent','local');

Figure contains an axes and an object of type uitable. The axes with title Wavelet Transform Maxima Lines contains 7 objects of type image, line.