[PD] The (not) doppler distortion (was: overdriven speaker)

[Mathieu Bouchard]

On Wed, 10 Nov 2010, - wrote:

> haut-parleur-doppler.pd is the original file from Martin,
[...]
> Please correct me if I'm wrong somewhere.

Yes, that file is from me and not from Martin. (but that's just a few 
kilometres off)

> The parallel up/downshifting leads to a chaotic spectrum change. With a 
> speed of .7 ms/ms we have at the same time the signal with 30% and 170% 
> playback speed. Which clearly has no relation to the original pitch and 
> no harmonic relation left.

Why is that clear to you ?

The apparent slowdown and acceleration of the sound goes on at the same 
rate as the contents of the signal itself. Therefore, you don't even have 
the time to hear a change of pitch... it's not even possible to detect 
one... there isn't one.

Suppose you have an input signal f(t). Then the output signal is 
f(t-b-a*f(t)). Then suppose the input signal has period k. This means 
f(t)=f(t+k). Then the output signal at time t+k is f(t+k-b-a*f(t+k)). But 
f(t+k) = f(t), so the output signal at time t+k is also f(t-b-a*f(t)) 
because the argument of f is modulo k. Thus the output signal has period 
k. Thus all the component tones of the output are harmonics of period k. 
This fact does not depend on a and b, it depends on the lack of 
nonperiodic components and differently-periodic components in the formula.

Even if I use f(t-b-tanh(a*f(t))) instead, it remains periodic because 
tanh of a k-period signal is a function with a k-period signal... it only 
depends on f(t).

> The more I think about it the more fascinated I am that this results in 
> something interesting to the ear.

It remains consonant to the ear so easily simply because it only produces 
harmonics.

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| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC