1/f

Hello there tuners....

Can anybody in layman's terms please explain to me what "1/f noise" is, and
also what is ment by the term "power spectrum", and I think that this is
called "spectral density" is it not?

It's just that I have heard that white noise is 1/f^0, and brown noise is
1/f^2, and knowing me, and knowing that the n-bonaccis lye between
1-------->2, I though a little sonic alchemy would be in order.

Get my drift?

----Sarn.

thcdelta@ihug.co.nz (Sarn Richard Ursell) wrote:

> Hello there tuners....
>
> Can anybody in layman's terms please explain to me what "1/f noise" is,
> and
> also what is ment by the term "power spectrum", and I think that this is
> called "spectral density" is it not?

In layman's terms, "1/f noise" is the sound a television makes when it
isn't tuned in. Unless that sound is gated, of course.

I don't think "power spectrum" can be explained in layman's terms. It
isn't something laymen usually worry about. It's a way of representing a
sound showing power as a function of frequency rather than time. You
generate it from the time-signal using a Fourier transform, which is
similar to the Fourier series for strengths of overtones but for
continuous frequencies. You use power rather than amplitude so that you
only get positive numbers.

Or something like that. It's actually an "auto correlation" that gets
plotted.

I don't know what "spectral density" is.

> It's just that I have heard that white noise is 1/f^0, and brown noise
> is
> 1/f^2

This is correct. It means that in white noise, all frequencies are as
strong. This is by analogy to white light. It doesn't mean the power
spectrum is a straight line, as is sometimes stated, because noise has to
be random. But the power doesn't depend on frequency. 1/f^0 is merely a
clever way of saying "nothing to do with frequency.

This "brown noise" is what you would get by plotting a random walk as
amplitude against time, hence modelling Brownian motion.

1/f noise is also called "pink noise" because the lower frequencies are
more prominent, like with pink light.

>, and knowing me, and knowing that the n-bonaccis lye between
> 1-------->2, I though a little sonic alchemy would be in order.
>
> Get my drift?

There is a body of literature relating music to 1/f noise. All music,
with some exceptions (Stockhausen and Xenakis apparently, I don't have
precise references) looks like 1/f noise if you send it through a spectrum
analyser. "Chaos Under Control" by Peak&Frame is the book I got all this
from.

I have C code for generating noise for a given frequency ratios. It can
be compiled for PCs, and outputs WAV files. I could dig it out and send
it to you (either source or executable) if you like. It's not very big.
I find the brown region is more pleasing on the ear.

Graham

> Can anybody in layman's terms please explain to me what "1/f noise" is,

Noise where the intensity at a particular frequency is inversely
proportional to the frequency. Also called "pink noise".

> and
> also what is ment by the term "power spectrum"

How much power (or intensity) is at each particular frequency.

> and I think that this is
> called "spectral density" is it not?

I think so.

>It's just that I have heard that white noise is 1/f^0, and brown noise is
>1/f^2,

Yup, and pink noise is 1/f (or 1/f^1).

All your questions will be much better answered by the one book I keep
recommending:

_Fractals, Chaos, Power Laws_ by Manfred Schroder. Get this book!