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I will be extremely grateful if someone could please answer this basic question.

How can one plot a 3D (translation, scale, amplitude) plot from the Continuous wavelet transform (CWT) coefficients?

The CWT coefficient is a M X N matrix. Which of the axis corresponds to the translation, scale and Magnitude.

Thanks for your help.

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2 Answers 2

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It suffices to use the translation and scale as $(X,Y)$ axes, and build some elevation map from the absolute values of the CWT (or the phase, the real or imaginary parts). A simple example in Matlab is:

load mtlb
scal = abs(cwt(mtlb,'bump',Fs));
mesh(scal)
axis tight

CWT wavelet 3D plot as a surface

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The output may depend on what package/language you are using to compute the cwt. If you are using matlab's "cwt", the documentation indicates that "If x is real-valued, wt is an Na-by-N matrix, where Na is the number of scales, and N is the number of samples in x."

In other words, the the first dimension corresponds to scale and the second dimension corresponds to sample number (time, usually).

The documentation provides a simple example in matlab which automatically plots the results:

load mtlb cwt(mtlb,"bump",Fs)

documentation in Matlab: https://www.mathworks.com/help/wavelet/ref/cwt.html#responsive_offcanvas

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