I am a beginner here , so take my analysis with a grain of salt. I
would think the highest complexity is associated with randomness since
essentially you cannot compress any of the information . This might
mean that if you take the inverse FFT of your spectrum, then the
autocorrelation of that would be sharply peaked around zero.

Best

Looking at the page:

http://web.gfi.uib.no/~ngbnk/kurs/notes/node123.html

I find a set of formulae that make a measurement of coherence expressed
as a "coherence spectrum" analogous with a correlation coefficient. I'm
tempted to adopt the above measure until I get further through Bendat
et. al's books.

Cheers,

Ross-c

I've obtained these books from the library, but haven't really looked
into them yet. The copy of "Measurement and Analysis of Random Data" I
have is from 1966. I'll see what happens when I can sit down and start
reading.

Cheers,

Ross-c

Ross Clement (Email address invalid - do not use) wrote:
> It will take me some time to get my mitts on this book. Would his older
> books "Engineering applications of correlation and spectral analysis"
> or "Measurement and analysis of random data" be relevant?

I have just had a look at the book "Engineering applications of
correlation
and spectral analysis". It seems to go deeper into the workings of
coherence than "Random Data" does. It even mentions the tautology
cxy(f) == 1 I have had problems with. I haven't had the time to look
into the details, but it seems that the clue is what estimator one uses
for the various spectra that go into the coherence estimator.

Rune

Ross Clement (Email address invalid - do not use) wrote:
> It will take me some time to get my mitts on this book. Would his older
> books "Engineering applications of correlation and spectral analysis"

Probably. I don't have my copy of this one easily available, but I
remember
noticing there was a lot of common material in this one and "Random
Data".
The difference would be that "Random Data" is heavier on the theory,
while
"Engineering applications..." is more hands-on.

> or "Measurement and analysis of random data" be relevant?

Maybe. I wouldn't be surprised if this is one of the first couple of
editions 
of "Random Data".

Rune

It will take me some time to get my mitts on this book. Would his older
books "Engineering applications of correlation and spectral analysis"
or "Measurement and analysis of random data" be relevant?

Cheers,

Ross-c

Ross Clement (Email address invalid - do not use) wrote:
> After reading these answers and thinking carefully, I've decided to
> redesign my experiments so that "spectral complexity" becomes
> "difference from a known spectrum". That makes things much more
> objective.

Seems to be the definition of "coherence"? See chapter 11 of

Bendat & Piersol: Random Data, 4th edition, Wiley 2000.

Rune

After reading these answers and thinking carefully, I've decided to
redesign my experiments so that "spectral complexity" becomes
"difference from a known spectrum". That makes things much more
objective.

Cheers,

Ross-c

Ross Clement (Email address invalid - do not use) wrote:
> Hi. Are there any widely used measures of spectral complexity. What I
> mean is something that would say how spectrally complex a sound is such
> that a pure sine wave would be mapped to 0 and white noise would be
> mapped to 1. I could use a goodness of fit test comparing the
> distribution of amplitude among spectral bins (after an fft) to a
> uniform distribution, but imagine there are much better tests.

In DTMF decoding, Parseval's theorem is often used to calculate
the ratio of energy in the expected bins versus the total energy
of the signal for evaluating signal validity.  Is this something
like what you were looking for?


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M

"Ross Clement (Email address invalid - do not use)" <clemenr@wmin.ac.uk> 
wrote in message 
news:1138781594.249117.90320@z14g2000cwz.googlegroups.com...
> Hi. Are there any widely used measures of spectral complexity. What I
> mean is something that would say how spectrally complex a sound is such
> that a pure sine wave would be mapped to 0 and white noise would be
> mapped to 1. I could use a goodness of fit test comparing the
> distribution of amplitude among spectral bins (after an fft) to a
> uniform distribution, but imagine there are much better tests.
>

That sounds like a reasonable starting place.
What does "complexity" mean to you?  That's another good starting place.

Fred