[sdiy] Handy DIY tip #213/noise color

[Magnus Danielson]

From: Tim Parkhurst <tparkhurst at siliconbandwidth.com>
Subject: RE: [sdiy] Handy DIY tip #213/noise color
Date: Wed, 15 Jan 2003 16:37:41 -0800

> Hi All,
> 
> Correct me if I'm wrong (like I have to ask, wink), but I thought I had read
> that white noise has equal frequency distribution (all frequencies are
> perceived to be the same volume across the range of human hearing) whereas
> pink noise has an equal energy distribution (all frequencies have the same
> power level which, due to the frequency response of the human ear, makes
> pink noise sound "darker").

Not quite... This is how it works:

White noise has equal energy over frequencies, i.e. if you used say a 1 Hz
bandpass filter, whatever center frequency you pick up, the same RMS value you
would read.

Pink noise has equal energy over octaves, i.e. over a one octave range you
have the same energy as over any other octave. Since an octave ranges more
frequencies at higher frequencies, the energy per frequency must be lower.
The math comes out such that when viewed in frequency you have a slope of -3 dB
per octave in relation to the white noise, since the white noise is perceived
to "rise" 3 dB per octave, but it isn't, it's just that it's the doubled
frequencies per octave, and double frequency means doubled energy, and that
means +3 dB per octave.

Doing a - 3dB per octave filter is "unnatural" so it becomes quite ugly
actually.

Did it make sense?

> If I've got this right, then I would guess this would be at least part of
> what you would look for in analyzing the "quality" of a noise source. 

Well, I was taking it as in noisiness, not in noise-slope. Due to the wounders
of math, I think that it will also will "flat out" on a number when you have
the wrong slope (for white noise) since noise with negative slope has the
property of not converging in the averaging, so you have to differentiate the
signal until no negative slope remains, and only then will it converge towards
zero, or whatever level that non-noise would render.

Statistics on non-white noise is kind of interesting. ;O)
(That is my way of saying that this is where you probably will be falling
asleep on the lecture.)

> Right? Wrong? Fell asleep during that lesson? Criminally insane?

No. Yes. Wasn't there. Probably not, but you never know. ;O)

Cheers,
Magnus