Pink noise

[françois]

Hello all,

There was these late days a discussion on the SDIY mailing list about making pink noise from a (supposedly good) source of white noise (I personnally prefer the good old analog reverse-biased junction quantic noise, rather than shift-register noise, matter of taste probably).

It is easy to find many passive networks that approximate a -3dB/oct slope lowpass filter. It is far less easy to design one... I tried to analyze existing networks (they ususally consist of a series of lowpass/bandpass cells so that poles and zeroes cancel out very carefully, although I could do the calculations by hand it is awkward, and SPICE does a very good job there) but I could just have to admit that they do the job, no understanding how or why.

But the point is that a -3dB/oct slope is mathematically a "half-integrator", with Laplace transfer function 1/sqrt(s). Being mathematically oriented, I know this is a fractal operator, and I wondered if some kind of chaotic circuit could generate such a slope. To no avail, of course.

Let me be clear. A precise -3dB/oct slope is ideal for calibrating audio equipment, but is not really required for musical applications. A good approximation is enough. But I's like to understand generally how to design such a thing.

And, even more generally, a varying-slope filter (ideally voltage controlled) would certainly have a musical utility (modulating e.g. from +12dB/oct to -12dB/oct slope).

If any of you has ever thought of this, please let me know !

-- françois

[frijitz]

[françois]

Thank you, Ian.

It seems that the various feedback "cells" have to approximate a multi-band equalizer -- I did that with a 1/3oct band graphic equalizer and obtained a *very* good approximation to a -3dB/oct slope, at the cost of having 48 feedback elements... I could have even more if I wanted the pink noise to be "accurate" over 20 octaves. That is pure delirium, of course. Fortunately SPICE comes in handy, I didn't have to breadboard this monstruosity. But I got the point.

Now I would really be interested in a variable slope filter, whatever this means. I don't know if it would be of great musical interest, but it is an interesting problem in itself. My first idea was very similar to a vocoder : separating the audio spectrum into many frequency bands and reshaping the spectrum with VCAs. Much too complicated obviously. What I'd like is to have a Laplace transfer function of the form 1/(s^n) with voltage controlled n. This is (relatively) easy in software but with RC cells (and opamps maybe) it is far from obvious.

Yours,

-- françois

EDIT : BTW, Ray Wilson's (MFOS) "Pink enough for me" noise generator is very similar to your suggestion. He mentions he tweaked the values of the components until he could hear a "satisfactorily pink" noise... maybe this is the most practical way to go.

[frijitz]