[PD] Waveform Analysis?

[Mathieu Bouchard]

On Wed, 14 Apr 2004, Ian Smith-Heisters wrote:

> For general analysis I'd try looking for beats with the usual methods,
> maybe try a discrete cosine transform to look for patterns of
> harmonics... I'm not really sure.

I think DCT/FFT may be a little limited for that, but at the same time
would be very much useful in performing the task. It's part of a larger
family of methods (mathheads may call it "orthogonal function
decomposition"... whatever). It includes Fourier transforms, but also
Laplace's, Legendre's, Bessel's, Laguerre's, Hermite's, Chebyshev's, and
the many variants of wavelet transforms as well.

I'm listing those because some of those transforms correspond to actual
patterns you are likely to find in music. One such transform may be used
for each kind of pattern you want to find in music:

1. Fourier transforms would of course take a signal and find the spectrum
associated to it. The ear is a biological Fourier transform device and the
brain processes the result of it at a sample rate below 100 Hz instead of
anything like 44100 Hz ...

2. log-transforming each spectrum (so that frequency units are
octaves/halftones instead of Hz) may outline some extra patterns in music
(scale-oriented), but also _not_ log-transforming already outlines a
different bunch of patterns (harmonics-oriented).

3. something like a Laplace transform (maybe a modified version of
it) would find natural decay patterns like when you pluck a guitar string
and the note slowly fades away, and consider it as only one event.

4. a square-wave transform (and/or step-function wavelet transform) would
find repetitions in the sequences of notes on a long-term basis.

5. if anyone cares about analysing drum sounds (i mean membrane waves
instead of string waves), i think they make sense using Bessel transforms
(?), whereas with Fourier you get a weird set of partial-harmonics.

And of course, getting all that stuff to actually work with Pd is an
exercise left to the reader...

> certainly genetic algorithms written that recognize stylistic
> similarities in music, and probably some implementation of neural nets
> that do similar things.

I wonder how much Markov-chain modeling would be appropriate for this. I
mean, if music is a language, then why not analyse it using Natural
Language Processing (NLP) techniques like Markov's... :-)

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