# Measure of spectral complexity

Started by February 1, 2006
```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.

```
```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.

I remember seeing a "spectrum flatness" parameter somewhere.
I think it was based on the ratio between the geometric and arithmetic
means of the magnitude spectrum.

Rune

```
```"Ross Clement (Email address invalid - do not use)" <clemenr@wmin.ac.uk>
wrote in message
> 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

```
```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

```
```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:
> 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

```
```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:
> 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

```
```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

```
```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