[PD] Waveform Analysis?

[Mathieu Bouchard]

On Fri, 16 Apr 2004, vanDongen/Gilcher wrote:

> Besides the analytical tools with orthonormal function-spaces (fourier
> etc.) I am also looking into classification based on the
> geometric/topological properties of the wave.  Things like the fractal
> dimension of the waveform over either a short window, like fft's, or
> on longer segments. They use this kind of stuff to analyse
> heart-rythms f.i.

Sorry, but I thought the fractal dimension (assuming Hausdorff's) doesn't
make sense with mixed dimensions (such as time/space or
time/amplitude) and _especially_ doesn't make sense on a noncontinuous
domain, as there has to be ever-smaller details for the Hausdorff's to be
noninteger.

However I can figure out how given an arbitrarily obfuscated
continuous-domain function I'd find out a fractal dimension. I'd do a
Fourier transform, and then convert it to logarithmic frequency
(Hz->semitones), and then possibly make another Fourier on that to find
periodic patterns. Theoretically, a fractal sound would show, in that
latter spectrum, a periodic or near-periodic pattern that starts but does
not end (converging to zero but not vanishing), but that's not really
possible using discrete data: you can't do anything that makes sense past
the Nykvist frequency.

I think this type of analysis (fft->log->fft) is interesting way beyond
anything fractal.

> And the biggest problem for me, is that computer-analysis is almost
> always after the fact, the note(beginning) or the phrase.  The human
> ear is much better at hitting a running target.

We try to be predictive when following a beat. An algorithm may find where
the pattern is at a given moment, and maybe at the same time as a human,
but the human would stay silent until the next beat so that s/he can be on
time, whereas the algorithm may not care (i.e. not designed to care) about
emitting imitative beats that are on time.

________________________________________________________________
Mathieu Bouchard                       http://artengine.ca/matju