"Richard Owlett" <rowlett@atlascomm.net> wrote in message 
news:1114vvn8gr35ca0@corp.supernews.com...
> Peter K. wrote:
>
>> Richard Owlett wrote:
>>
>>
>>>Can anyone tell me what "Parseval relation" is without resorting to
>>>triple integrals from -infinity to +infinity?
>>
>>
>> The energy of a signal in the frequency domain equals the energy of the
>> same signal in the time domain.

Richard,

Actually Parseval's implies a lot more than what is being stated here.

Parseval's relates the integral of the inner product of two functions in one 
domain to the  integral of the inner product in another domain. Under the 
special case where both functions are made the same, we arrive at Bessel's 
equality which is usually cited as Parseval's relation which is incorrect as 
this is only a special case. Parseval's theorem covers the much more general 
case than simply comparing energies.

inner product (g(t) h*(t) )   =  inner product ( G(w) H*(w) ) * const.

In the case where h(t) = g(t), we have the familiar form due to Bessel.

Clay

They way I think of it is if you take the energy of a signal in the time domain,
and then take the FFT and add up the energy in every bin, you should get the
same answer.

Here's one thing you could do with this:  find the energy in a single bin of an
DFT (say with the Goertzel algorithm).  Then take the energy of the signal in
the time domain over the same window in time.  You can then find out how much of
the total signal is made up of the single bin by comparing them directly--maybe
useful in some types of frequency detectors.  This method is computationally and
coding-wise very efficient since an FFT is not required.

"Richard Owlett" <rowlett@atlascomm.net> wrote in message
news:1114vvn8gr35ca0@corp.supernews.com...
> Peter K. wrote:
>
> > Richard Owlett wrote:
> >
> >
> >>Can anyone tell me what "Parseval relation" is without resorting to
> >>triple integrals from -infinity to +infinity?
> >
> >
> > The energy of a signal in the frequency domain equals the energy of the
> > same signal in the time domain.
> >
> > Ciao,
> >
> > Peter K.
> >
>
> DUH!
>
> Think I asked "wrong" question.
>
> Should I have asked "What does 'Parseval relation' imply?"
>
> Or should I ask "Just how confused am I?"
>

Alberto wrote:
> I have a program that does real time spectral analysis of audio
signals.
> If I interactively change the window used before the FFT, choosing
> between Hamming, Hann, Balckman, etc. etc I can of course see the
> widening or the narrowing of the peaks corresponding to steady
frequencies,
> but I notice also a changing value for the amplitude of the peaks,
> depending on the window used. I compute the values of the peak
amplitudes
> for display using the Parseval relation, but now I would also take
> into consideration a corrective factor depending on which window is
used.
>
> I browsed the Oppenheim & Schafer, but I have found no information
> on this subject. Can anybody be of help ?  Many thanks

I think you migth be comparing apples and oranges here. It is true that
Parseval's relation holds for the raw (unscaled) data. I don't
necessarily agree that it ought to hold for windowed data.

First of all, you don't really need frequency domain data to compute
the energy contained in the signal. The time domain data are sufficient

for that. What you do want with frequency domain data, is to get an
impresion of the "spectral structure" of the data: Is it a broad-band
signal? Narrow-band? Multiple bands? etc.

The periodogram is notorious for haviong a very large variance in its
PSD estimate. So we can't really trust the periodogram when used with
random data. The sole reason for introducing window functions are that
one wantes a more reliable estimate for the "spectral structure" of the

PSD. As you know, time-domain multiplication corresponds to frequency-
domain convolution, so one basically averages nearby spectrum bins when

using windows.

All in all, one could argue that one sacrifices accuracy of the
spectrum
coefficients (an accuracy that was never there, in the first place) and

gains a somewhat better impression of the "spectral structure" of the
data.

Rune

Steve Underwood wrote:
> Richard Owlett wrote:
>
> > Peter K. wrote:
> >
> >> Richard Owlett wrote:
> >>
> >>
> >>> Can anyone tell me what "Parseval relation" is without resorting
to
> >>> triple integrals from -infinity to +infinity?
> >>
> >>
> >>
> >> The energy of a signal in the frequency domain equals the energy
of the
> >> same signal in the time domain.
> >>
> >> Ciao,
> >>
> >> Peter K.
> >>
> >
> > DUH!
> >
> > Think I asked "wrong" question.
> >
> > Should I have asked "What does 'Parseval relation' imply?"
> >
> > Or should I ask "Just how confused am I?"
> >
> It implies Parseval was a good salesman. He managed to get his name
on
> what everyone else would simply call the conservation of energy. :-)
>
> Regards,
> Steve

In maths lingo, Paresval stated that the Fourier Transform preserves
the norm.

Rune

Richard Owlett wrote:

> Peter K. wrote:
>
>> Richard Owlett wrote:
>>
>>
>>> Can anyone tell me what "Parseval relation" is without resorting to
>>> triple integrals from -infinity to +infinity?
>>
>>
>>
>> The energy of a signal in the frequency domain equals the energy of the
>> same signal in the time domain.
>>
>> Ciao,
>>
>> Peter K.
>>
>
> DUH!
>
> Think I asked "wrong" question.
>
> Should I have asked "What does 'Parseval relation' imply?"
>
> Or should I ask "Just how confused am I?"
>
It implies Parseval was a good salesman. He managed to get his name on 
what everyone else would simply call the conservation of energy. :-)

Regards,
Steve

Peter K. wrote:
> What does it imply?
> 
> That energy is conserved?  That you can't create energy by shifting
> domains?
> 
> Apart from statements as generic as these, it doesn't imply much.
> 
> Any other takers?
> 
> Ciao,
> 
> Peter K.

It's intuitively obvious, but it's so useful for proving certain 
non-obvious useful theorems that Its formal proof is important.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

What does it imply?

That energy is conserved?  That you can't create energy by shifting
domains?

Apart from statements as generic as these, it doesn't imply much.

Any other takers?

Ciao,

Peter K.

Peter K. wrote:

> Richard Owlett wrote:
> 
> 
>>Can anyone tell me what "Parseval relation" is without resorting to
>>triple integrals from -infinity to +infinity?
> 
> 
> The energy of a signal in the frequency domain equals the energy of the
> same signal in the time domain.
> 
> Ciao,
> 
> Peter K.
> 

DUH!

Think I asked "wrong" question.

Should I have asked "What does 'Parseval relation' imply?"

Or should I ask "Just how confused am I?"

Richard Owlett wrote:

> Can anyone tell me what "Parseval relation" is without resorting to
> triple integrals from -infinity to +infinity?

The energy of a signal in the frequency domain equals the energy of the
same signal in the time domain.

Ciao,

Peter K.

Can anyone tell me what "Parseval relation" is without resorting to 
triple integrals from -infinity to +infinity?

I don't need to know how to use it. I just wish to be able to read 
comp.dsp ;)