[sdiy] Mixing several noise generators

[Richie Burnett]

Hi Tom,

Independent noise generators that are not correlated add like orthogonal 
signals.  This applies to a bunch of analogue thermal noise generators, or a 
bunch of digital shift-register based noise generators using very long 
sequence lengths.

When you add two un-correlated sources together the amplitude goes up by 
only 3dB.  i.e. the resulting amplitude goes up by sqrt(2).  This can be 
contrasted to the doubling (+6dB) of amplitude that you'd get when you add 
two identical signals together.

It's easiest to think of the two independent noise sources as being 
orthogonal signals.  i.e. at 90 degrees to each other in space, like X and Y 
on a graph, or like a Sine and Cosine in the time domain.  When you add the 
two together the resultant is equal to the square-root of the sum of the 
squares of the other two amplitudes.  You can extend this analogy to three 
un-correlated noise sources, representing the X, Y and Z dimensions, and so 
on for more and more independent sources.

You are quite right that it has an effect in synthesis.  If you generate a 
flute sound with an equal balance of pitched tone and noise, then this 
balance will be upset in a polyphonic instrument that only uses one shared 
noise source.  As you add notes together, the different pitches of the tonal 
parts are orthogonal so add geometrically but the noise sources are all 
identical and add arithmetically.  The result is an overall change in 
tone-to-noise ratio for the complete sound.

As far as implementations go, I don't know of any synths that use 
independent noise sources for each voice.  If any synth does, it's probably 
going to be something like the Alesis Ion or its siblings as these use 
seperate mini-DSP chips for each voice.  In this case it is surely easier to 
have a seperate noise source running in each DSP than to pipe-in a common 
digital noise source to all eight voice DSPs.  Of course this still assumes 
that they don't just load all 8 voice DSPs with the same seed for their 
random number generators at startup resulting in eight independent but 
highly correlated noise sources!

I hope this helps,

Cheers,

-Richie Burnett,