[sdiy] Waveform analysis into non-sine components

[Tom Wiltshire]

Hi All,

Can anyone give me some useful references for the above topic?

I've been looking into it, but there's not much from the synthesis world. I found a reasonably interesting discussion about using walsh functions to analyse seismic data, but that's about the size of it.

Principally, I'd like to know more about:

1) Basis functions - Sin/cos are a good basis for waveform analysis. Walsh functions are another. Are two phase-shifted squares another? If not, why not? What makes a set of functions a sound basis or not?

2) Analysis - can the same method be used for all basis sets?

3) Pros/cons of various basis function sets for various types of analysis, with particular emphasis on sound waveforms.

I understand Fourier Analysis well enough these days (finally), but I'd like to extend this understanding and grok a bit more of the foundations.
Please bear in mind that hideous pages of academic maths are really only intended for academic mathematicians and don't serve to teach the rest of us anything much. I realise that's a big ask given the topic.

Thanks for any help,
Tom