[sdiy] Digital noise generation

[Magnus Danielson]

From: Tim Ressel <madhun2001 at yahoo.com>
Subject: Re: [sdiy] Digital noise generation
Date: Tue, 8 Mar 2005 10:38:37 -0800 (PST)
Message-ID: <20050308183837.43707.qmail at web54610.mail.yahoo.com>

> Yo,

Tjena Tim!

> I believe it has to du with distribution. I saw a blurb (in EDN?) about
> summing together 12 analog noise gens to make the distribution gaussian
> instead of, um , whatever. Perhaps the extra taps is messing with the
> distribution?

It only really works when the sources are not synchronous to each other, like
true noise sources are. This works for sines for instance, which amplitude
distribution is like a bathtub. Add a bunch of those at same amplitude but
different frequency and the distribution becomes more and more gaussian the
more of them you add. The interesting is what happends when you double the
amount of sine waves but lower the amplitude to maintain equal power, then the
resulting signal becomes more gaussian of the same power, but the peak-to-peak
also spreads farther and farther away until it approximates infinity (but not
really, there is a *really* good reasoning about it relating to the lifetime of
universe and how far out that would get you, and it is not as far as you would
just expect from the asymtotes).

Anyway, shaping the noise amplitude distribution does *nothing* to the
frequency distribution. However, the amplitude distribution may be important
for a number of other processing stages. Especially when non-linearity comes in
play. Clipping in particular.

For synchronous noise addition cases (like multiple tapping of the same noise
source) I would rather consider frequency-distribution colouring, but that
should surely affect the amplitude distribution too. It would be interesting
to plot these against each other.

A typical pseudo-random noise source has an evenly spreat amplitude
distribution. Any particular value is equally probable. Actually this is an
oversimplification, it is rather such that all of the discrete amplitudes it
assumes is equally probable, since they all occur onces in every cycle.
Thus, the source has a white frequency distribution but is not gaussian.
A number of these (of different polynomial and length) can be added to shape
a more gaussian source if needed. Hint: Use a power of 4, like in 4, 16 or 64
since that way will the effective power be an easy shift away when normalizing
the power relative to the original source.

Cheers,
Magnus