[PD] The (not) doppler distortion (was: overdriven speaker)
Mathieu Bouchard
matju at artengine.ca
Sat Nov 13 18:01:22 CET 2010
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.
_______________________________________________________________________
| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
More information about the Pd-list
mailing list