[AH] Red noize

[Magnus Danielson]

From: Martin Czech <martin.czech at intermetall.de>
Subject: Re: [AH] Red noize
Date: Mon, 7 Feb 2000 09:39:26 +0100 (MET)

Hi There!

> :::The trouble with the shift register is that it produces 2**N-1 number of
> :::frequencies (at most). These are single frequencies evenly spread appart.
> :::XORing with noise will not do very well since the modulation would have a DC
> :::term which would let too much of the original waveform thru.
> :::
> 
> This is true, since it is (at most) a repeating sequence of 2**N-1
> samples length, and you think of the DFT of it.

Right.

> But I think if the sequence is very long (usuall) you can't apply
> this DFT model for the hearing result, because the ear-brain machine
> seems to do a short time DFT, otherwise the change of spectra 
> wouldn't be noticed every 1/20 seconds or so.

It is true that the ear will not view the full DFT length...

> I  mean a first order
> model of the ear-brain would be hopping DFTs with 1/20 s window size.
> This would smear , well and give much fewer frequencys.
> But each hop would sound slighly different, which makes it sound like noise
> and not like a harmonic rich wave...

You really can't view the ear this way. The ear is a very obscure set of real
time continous time frequency analysis thingie, the time is not sampled, there
are no fixed frequencies and the amplitude of the frequency components is not
either very sampled.

The ear will however group noise type energies together into a suitable lump
of frequencies. The ear has a diffrent sensitivity to narrow bandwidth noise
than it has for single sines of the same frequency (as the center of that
bandpass filter - usually 1 Hz wide for reference purposes). Also, the masking
effects, time constants of burst etc. all differ for noise than for sines.

However, I think the original question was relating to musically usefull, and
then one can identify the diffrence between some noise sources as you pass it
throgh a high-Q filter, if you have too few frequency components of a PRBS type
of noise source, you will not precieve it as a continous noise as you did with
the "true" noise. Those, a PRBS which migth give white noise migth not work
well with high-Q filtering.

> And XORing with pulses from a diode e.g. will cause a causal impulse response,
> so there is correlation... but still the output should be more random
> than the shifter allone, really unpredictable.

Randomness can be so deceiving, you migth THINK that you have added randomness,
but you migth totallt destroy the effect.

I'm not fully convinced, XORing or even multiplying (which would be the correct
analog equalent in this case) would cause the ring modulation of the PRBS
fixed frequencies with the random (and assumed low frequency content) noise,
this would mean that we split the PRBS peaks and spread the energy out on
adjacent frequencies, which is good. However, these adjacent frequencies would
still correlate too much with each other. The XORed version makes this even
more distinct than the analog multiplication. Yes, you have spread the
energies. Yes, you have added some further noisiness, but I am not sure it
behaves as noisy as we would like.

> Consider the case were you use the random source as pitch modulation.
> Very time you power up the synth you will hear the same modulation
> pattern (I think a POR is needed for the shift register, to avoid
> the 0 state, maybe even a false state detector, to avoid getting trapped).
> Using some extra noise will certainly give more variety.

Yes, some added noise can really make things less static.

> :::> 2nd Idea:
> :::> 
> :::> I've read about mathematical theory about poles with rational order,
> :::> or in general network transfer functions with non integer order.
> :::> 
> :::> There is no reason why math should prefer x**2 instead of x**2.18973,
> :::> we do this every day using the pocket calculator.
> :::> Has anything useable grown out of this roots since 1970??
> :::
> :::Actuall, there are good reasons for some restrictions of that sort. It is
> :::still a mystery how the Columbs law of fources between two round objects
> :::being electrically charged could be so accurate on r**2. It was simple
> :::reasoning behind that and the conclusion has hold for remearsurements to the
> :::16thies digit without disturbance in the force.
> :::
> 
> Sure the laws of physics seem to be against it (today).
> But math has nothing to do with the real world since long...

Until Donald Knuth et.al. published "Concrete Math" ;)

Just the motivation for writing the book gives you an insigth into the subject.

For noise generation purposes there are many ways to do noise generation on
involving diffrent arithmetical operations. For a good treatment of that
subject I direct your attention to Donald Knuth's "The Art of Computer
Programming, Vol 2 - Seminumerical Algorithms" and the chapter 3 "Random
Numbers" a mere 177 page chapter.

Interestingly the PRBSs are really 2 pole oscillators in the Gallois field.

Cheers,
Magnus