[music-dsp] [ot] DSP, complex numbers, fractals, and crazy stuff

Anig Browl anig_browl at yahoo.com
Sun Oct 28 06:23:32 EST 2001


Following on from the DSP vs. Analog thread, I have a really off-the-wall
question that does not quite fit into that thread but is related to it.

Much of the problem with simulating analog circuits with DSP for music is
that analog circuits distort in interesting ways that tell us something
about the properties of the materials in the circuit. And because we find
this so interesting to listen to, digital emulations often fail to satisfy
us. I don't want to call this distortion 'noise' - while it is noise
compared to the pure signal that an analog circuit may be *meant* to
generate, the musical character of the distortion depends on an interaction
between the signal and the components, so to me it's more chaotic.  (I'm
probably giving the list mathematicians fits - sorry.)

As we know, chaos is all around us. Maybe I'm excessively holist, but to me
the distortions in an analog circuit are not essentially different from
turbulence in a set of plumbing pipes. A great deal of research has been
devoted to minimising or exploiting turbulence in physical systems from
aeroplane wings to internal combustion engines, and I wonder how this can be
applied to music-DSP.

In the same vein, I can't help being struck by the fact that much DSP
cleverness takes place in the complex plane. I have always liked complex
numbers and I've had loads of fun looking at fractals in the complex plane
since the late 80s. You see where this is going, don't you? Fractals exhibit
all sorts of complex, beautiful, and chaotic behaviour in their boundary
zones, analog filters can exhibit all sorts of complex, beautiful, and
chaotic behaviour around their cutoff points...

Now fractal pictures are usually maps of the complex plane with 0,0 as their
centre point, while filter curves (or fft plots, or...) are usually shown in
the positive quadrant of amplitude and frequency (0-1). So I started
imagining these DSP graphs like filter curves mirrored in the negative of
both real and imaginary axes, and the resulting 'butterflies' begin to
strike me as the kind of shapes that I get out of things like fractint when
I can find time to play with it.

Well - am I drinking waaay too much coffee, or has anyone investigated the
application of fractal math technique to music-DSP?

Anig Browl




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