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Topic: time and frequency marginals in the wavelet scalogram and energy
Replies: 5   Last Post: Dec 11, 2013 7:24 PM

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 Derek Goring Posts: 3,922 Registered: 12/7/04
Re: time and frequency marginals in the wavelet scalogram and energy
Posted: Dec 10, 2013 9:13 PM

On Wednesday, December 11, 2013 1:54:20 PM UTC+13, palmar wrote:
> Hi there:
>
> I have been looking for some matlab code to compute the time and frequency marginals in the wavelet scalogram.
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>
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> 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.
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>
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> 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.
>
>
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> integral(integral(P(f,t))= sum(norm(s(t)).^2)
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> P(f,t)= scalogram and s(t) signal
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> Time marginal:
>
> integral(P(f,t)df=|s(t)|.^2
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> Frequency marginal
>
> integral(P(f,t)dt=|S(w)|.^2
>
> Any ideas?
>
> Thanks

I assume you're talking about continuous wavelets?
If so, have a look at this site:

There's a paper that explains all this stuff with details of how you must construct the integral depending upon the mother wavelet.
Also, there are Matlab routines.

Date Subject Author
12/10/13 palmar
12/10/13 Derek Goring
12/10/13 Derek Goring
12/11/13 palmar
12/11/13 Derek Goring
12/11/13 palmar