[sdiy] Truly red noise

[Magnus Danielson]

From: allenre at umich.edu
Subject: Re: [sdiy] Truly red noise
Date: Fri, 25 Jun 2004 10:48:38 -0400
Message-ID: <1088174918.40dc3b46f049f at mail.umich.edu>

> I noticed that, but there are inconsistencies throughout the page and I've
> seen literature describe 1/(f^2) noise as red, not brown.

Exactly. I just checked and verified.

> The page says that 'purple noise' is differentiated white noise, but if white
> noise has a distribution of 1, then differentiating it gives you 0 (silence).

No. It's has the power-spectrum of f^2 (f in amplitude). The diffrentiation is
in time and not frequency.

> I think it should go something like this:
> 
> .
> .
> .
> 'infrared noise', 1/(f^3) distribution
> 'red noise', 1/(f^2) distribution
> 'pink noise', 1/f distribution
> 'white noise', unity distribution
> 'blue noise', f distribution (given on page)
> 'violet noise', f^2 distribution
> 'ultraviolet noise', f^3 distribution
> .
> .
> .

I agree. If we are going to use color references, this is the same listing I
would be making.

As for filtering, for a 1/f^2 we have an integrator (with respect to time),
f^2 is a diffrentiation (with respect to time). 1/f and f variants are harder.
The 1/f is a "half-pole" integrator and the f is a "half-zero" diffrentiator.
For those we only make approximations.

Anyone got the NBS article on noise simulation? I'd love to get my hands on
that one?

Cheers,
Magnus