marginals and energy of the scalogram to match the signal

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Paramonte 2013-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/109383-marginals-and-energy-of-the-scalogram-to-match-the-signal

Hi there: I have been looking for some matlab code to compute the time and frequency marginals in the wavelet scalogram.

Moreover I was trying to to verify the so-called total energy condition of the scalogram, basically the energy of the scalogram should match the energy of the signal.

I have done a double integral of the scalogram and the result doesn´t match the energy of the signal, so I should be doing something wrong since the result should be wavelet dependent, and we should take that in account when calculating the energy of the signal.

integral(integral(P(f,t))= sum(norm(s(t)).^2)

P(f,t)= scalogram and s(t) signal

Time marginal: integral(P(f,t)df=|s(t)|.^2 Frequency marginal integral(P(f,t)dt=|S(w)|.^2 Any ideas? Thanks