[sdiy] Waveform analysis into non-sine components

[Neil Johnson]

Olivier Gillet wrote:
> The most common approach is to break down the signal into small
> overlapping windows, and perform an analysis on each window
> (assuming that the signal is stationary over the segment) ; but this
> is not the only approach. A very intuitive technique is matching
> pursuit. You have a "dictionary" of reference signals. You search for
> the element the most correlated with your signal, you subtract it,
> and you repeat the procedure on the residual until your residual has
> low energy. If your dictionary contains sustained sine waves, this is
> equivalent to Fourier analysis. But you can use clicks, sine waves
> with envelopes, etc, to get a representation more detailed than
> Fourier analysis, and in which most coefficients are null for a large
> palette of audio signals. - it's a bit like trying to approximate a
> song with a simple ROMpler with a programmable envelope generator.
> Hot stuff for low-bitrate coding! See the figures in this:
> http://ismir2008.ismir.net/papers/ismir2008_261.pdf

This sounds a bit like CELP as used in mobile phones for example.  Just
replace "element" with "codebook" and the similarity is there.

http://en.wikipedia.org/wiki/CELP

Neil
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