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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: 3,892
Registered: 12/7/04
Re: time and frequency marginals in the wavelet scalogram and energy
Posted: Dec 11, 2013 3:23 PM
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On Thursday, December 12, 2013 4:18:06 AM UTC+13, palmar wrote:
> TideMan <mulgor@gmail.com> wrote in message <df595ab3-3e34-425e-bf0d-9029db106673@googlegroups.com>...
>

> > 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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> > >
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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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> > >
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> > >
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> > > I have done a double integral of the scalogram and the result doesnt 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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> > >
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> > >
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> > >
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> > > integral(integral(P(f,t))= sum(norm(s(t)).^2)
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> > >
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> > >
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> > >
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> > > P(f,t)= scalogram and s(t) signal
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> > >
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> > >
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> > >
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> > > Time marginal:
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> > >
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> > > integral(P(f,t)df=|s(t)|.^2
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> > >
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> > > Frequency marginal
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> > >
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> > > integral(P(f,t)dt=|S(w)|.^2
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> > >
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> > > Any ideas?
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> > >
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> > > Thanks
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> >
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> > BTW
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> > Why do you use:
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> > integral(integral(P(f,t))= sum(norm(s(t)).^2)
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> > and not
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> > integral(integral(P(f,t))= var(s)
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> > which is Parseval's Law.
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>
>
> Many many thanks TideMan
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>
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> Regarding the above you are right. Point taken.
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>
>
> the nice link you sent with the ever important Torrece´s paper is very good but I can´t find in there any mentiion to the marginals calcultaion.
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>
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> There is a matlab function in http://tftb.nongnu.org/ that does the marginals, incidentally only for the Cohen Class time-frequency representations, not scalograms I gather.
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>
>
> Still looking!!


I'm afraid I don't know what you mean by "marginals", but one way to reconstitute the signal into a set of time series for each level of frequency (scale)is with this snippet of code:

scale=scale(:); % Make sure it's a column vector
denom=scale*ones(1,nt);
ywrecon=real(wave)./sqrt(denom);
ywrecon=ywrecon*sqrt(dt)*dj*factor;

where the variables are those in T&C's wavelet.m and factor is from Table 2 of their paper (dependent upon the mother wavelet).
Once you have this matrix, ywrecon(nt,nf), i.e. a time series for each frequency interval, you can do:
var(ywrecon)
to get the frequency spectrum, or
sum(var(ywrecon))
to get the total energy, or
sum(ywrecon,2)
to get s(t).






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