PSD, CPSD and Coherence for pulse-like signals

Ok, I think I now understand correctly. See, the problem was that none of
my academic books actually contextualized power in this manner, though as
some of you pointed out, you may be interested in the power released by a
detonation, and that is not ( hopefully ) a periodic event! I would
therefore define the power of a finite discrete-time signal as:

1/(Nend-Nstart) sum_{k = Nstart}^{Nend} | x_k |^2

( And that is not average power, that is simply power, isn't it? )

--

As for the pattern recognition: by saying that the signals have distinctive
spectra, I meant that they have different shapes, with different peaks and
different extension in frequency.

The problem is, I don't see why I should use "features" as the maximum
peak, the frequency in which the maximum peak is, and so on, when I can
exploit all the informations I have and evaluate the difference,
cross-correlation, etc etc. At least to my eyes that is a better use of
what I have, if you will.

Some of you've been talking about overfitting: but ( pardon my ignorance in
the subject ), doesn't that refer exclusively to neural networks and other
algorithms of that kind? Were you then suggesting to use these methods to
accomplish my goal? If so, what should I feed the network with?

On Monday, May 27, 2013 12:34:32 AM UTC-7, pater wrote:
> Ok, I think I now understand correctly. See, the problem was that none of
> my academic books actually contextualized power in this manner, though as
> some of you pointed out, you may be interested in the power released by a
> detonation, and that is not ( hopefully ) a periodic event! I would
> therefore define the power of a finite discrete-time signal as:
> 
> 1/(Nend-Nstart) sum_{k = Nstart}^{Nend} | x_k |^2
> 
> ( And that is not average power, that is simply power, isn't it? )
> 

This topic has been discussed here before.

On Saturday, April 7, 2012 10:40:20 AM UTC-7, dbd wrote:
...
> Some signal components are correctly described by a power spectrum, some by a power spectral density, and some by an energy spectral density. Each is calculated differently. See:
> 
> Bo0438.pdf
> Choose your Units! (PWR, PSD, ESD)
> www.bksv.com/doc/bo0438.pdf
> 
> Bv0031.pdf
> Technical review No. 3 - 1987
> http://bruel.ru/UserFiles/File/Review3_87.pdf
> or
> www.bksv.com/pdf/bv0031.pdf
> (The bksv.com site seems to request registration.)
> The article on page 29 this file is
> "Signal and Units"
> by Svend Gade and Henrik Herlufsen
> see page 30
> 
> Dale B. Dalrymple

pater <95187@dsprelated> wrote:

(snip)

> Some of you've been talking about overfitting: but ( pardon my ignorance in
> the subject ), doesn't that refer exclusively to neural networks and other
> algorithms of that kind? Were you then suggesting to use these methods to
> accomplish my goal? If so, what should I feed the network with?

No. The word in your original post that reminded me of overfitting was
"classifier".

Any system that uses training data, is susceptible to overfitting.

Easier to see the effect, and explain, are polynomial fitting.

-- glen

pater <95187@dsprelated> wrote:
>Now, I've been reading a lot around the web, but every definition I found
>refers to the Cross Power Spectral Density of the signals!

Information on the Internet is often like a tip at a race track.  If
someone tells you that they got it straight from the horses mouth;
make sure they weren't talking to the wrong end of the horse.

Regarding coherence, I guess it can be a little confusing because you
can find slightly different definitions of cross-spectra, derivations
of coherence from the cross-spectra, and analysis.  One common
definition of coherence, for example, is:

http://www.ni.com/white-paper/4278/en

The above definition and subsequent analysis (and confusion) can be
found in a number of places on the web.  But in "The Analysis of Time
Series" by C. Chatfield (pps. 174-177 + 217-219) (published in the US
by Chapman + Hall, 1975, 1980), he uses a similar definition, but then
recommends against doing things that I've seen others do!  He also
mentions (p. 175) that: "The cross-spectrum is sometimes called the
cross-power spectrum, although its physical interpretation in terms of
power is more difficult than for autospectrum (see Lee, 1966, p.
348)."

The Lee mentioned above is: LEE, Y. W. (1960) Statistical Theory of
Communication, New York: Wiley.

On p. 177, Chatfield mentions that the squared coherence C(omega) is
between 0 and 1, and is analogous to the square of the usual
correlation coefficient. The closer it is to 1, the more closely
related are the two processes at frequency omega.

So maybe you could just use the squared correlation coefficient.

Regarding overfitting - there's a recent book that includes a few
examples: "The Signal and the Noise: Why So Many Predictions Fail -
But Some Don't" by Nate Silver.

http://www.amazon.com/dp/159420411X

Maybe there's a copy at your local library.  It's not a textbook, so
it doesn't go into a lot of technical detail, but it's interesting.

Kevin McGee