Once upon a time I tried to expand audio data into a series of sin(w*x+d), using

LMS
optimization by w. FFT basically does the same thing for a fixed set of frequencies.

So it worked, and was able to detect parameters of a single sinus wave, which looked cool.

But then I tried to implement compression using it, and it turned out that real files are not made from

such simple functions - there was some compression, but results were worse than rar.

Basically, the audio signal is not mixed from such fixed functions, and there's noise and inter-channel

correlation, so afaik whatever nice serial approximation doesn't help much for lossless compression.

As an example, here's a lossless MDCT-based spectral coder.

http://nishi.dreamhosters.com/u/fast08sh4.rar
(it doesn't store the header nor precise wav length, so not 100% lossless)

Hopefully your results can prove that I was wrong somewhere?