[sdiy] Truly red noise

[Magnus Danielson]

From: "Theo" <t.hogers at home.nl>
Subject: Re: [sdiy] Truly red noise
Date: Fri, 25 Jun 2004 16:17:56 +0200
Message-ID: <000d01c45abf$360a13e0$93b37ad9 at ensch1.ov.home.nl>

Hi Theo,

> > > Did you notice in the article all the way down Brown noise?
> > > Spectrum given is 1/(f^2) and the color Red is suggested as in this case
> > > Brown is not a color.
> >
> > The usefullness of Brown or Red as describing it have nothing to do with
> what
> > is a "color" in this or that languague. That kind of argument is nonsense!
> > Actually, the whole "color" way of reasoning is all bullocks anyway, it
> > actually have no real meaning, so it boils down to a matter of taste
> rather
> > than actual true meaning.
> >
> 
> Yes sure agreed.
> Just but the correct term is brownian noise, not brown noise, hence the
> remark.

Actually, no. They are distinct noise forms.

Well, that it is called "white noise" is just the Brownian noise, which is due
to the Brownian motion of particles. This is by its nature also called thermal
noise, since the Brownian motion of atoms is due to their temperature (which is
a measure on how much Brownian motion they have).

Brown discovered this form of motion when investigating particles in his
microscope. The first observation of this noise in electronics components is
due to J.B. Johnson of Bell Telephone Laboratories in 1927 and the theoretical
analysis was delivered the next year by his colleague H. Nyquist.

This noise has a flat power spectrum in theory. As you know reality deviates
only slightly from theory, but we usually ignore the discrepance. ;O)

The so belowed "pink noise" is also known as excess noise, current noise and
even flicker noise (due to the flickering effect in tubes).

Then the "red noise" is the 1/f^2 noise.

Also, we have shot-noise, wich has even worse degree (I don't recall now if it
was 1/f^3 or 1/f^4). I think "brown noise" sometimes have been used to describe
shot-noise.

> > What is more useful of the two is Red thought, since it makes sense that
> > "pink noise" (with power-spectra of 1/f) is between "white noise" (with
> flat
> > power-spectra) and "red noise" (with power-spectra of 1/f^2).
> >
> > > A Pink noise filter is basically a LP filter with -3 dB slope.
> > > This is often build as a single RC LP were the R is one resistor and the
> C
> > > made of multiple cap+resistor combinations.
> > > Swapping the resistor and caps+resistors so that the resistor goes to
> ground
> > > and the caps+resistors become the input should change it into a HP
> version
> > > for Brownian noise.
> >
> > Actually, just remove the resistor-cap combinations in parallel with the
> > capacitor and you have it. All you need is a "perfect" integrator.
> >
> 
> Err, I don't get this one.
> Wait I do, wrong color, I was trying to get the inverse spectrum of pink.
> Think that would be some shade of blue.

It would.

"blue noise" could possibly be described for a f power-spectrum and
"purple noise" would then be f^2 I'd guess. I haven't seen any conclusive
definitions on these as I see it.

> Just one question.
> When considering noise "colors" usually only the power-spectra are
> mentioned.

Yes.

> However the distribution of  frequency density across the spectrum also can
> make a quite notable difference.

I'm loosing you here...

> Even when the power spectrum is correct, the sound can be quite different
> from what is expected.
> But never really came across a mention of this frequency distribution
> effect, why?

Can you try to explain what you mean by frequency distribution as distinct
from the power-spectra? The power-spectra "slope" listing gives you the
frequency distribution, i.e. the amount of power and how it depends on the
frequency.

> The effect is most pronounced when the frequency density is relatively low.
> I came across this when cooking up the noise oscillators for a soft synth
> that used narrow noise bands instead of sines for additive synthesis.
> Past tense, cause it ran on Atari ST and results where not too interesting.
> The produced sounds really needed a chorus to live up.

I think you still need to articulate yourself.

However, narrow-band noise is a totally different subject than the noise-colour
scheme which is oh so popular.

Cheers,
Magnus