Hello,

This would seem to be of interest to Codec2: a Faster-than-Fast
Fourier Transform designed especially for sparsely filled spectra:

News article:
http://web.mit.edu/newsoffice/2012/faster-fourier-transforms-0118.html

Paper (free download, as public-funded research ought to be):
http://arxiv.org/abs/1201.2501v1

The algorithm achieves O(k.log(n)) if the input signal has at
most k non-zero Fourier coefficients.  In terms of Codec2, we
could expect k=10 over 320 samples, so O(2663) becomes O(133).

Roughly -- and background noise would worsen these figures.
The Codec2 encoder spends about 1/3 of its time in FFT.


Cheers,
 -Rick

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