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