Re: About importance of "phase" in sound recognition

[Joachim Thiemann <joachim.thiemann@xxxxxxxxx>]

On Fri, Oct 8, 2010 at 15:44, James Johnston <James.Johnston@xxxxxxx> wrote:
> Do a 2^20th fft.
> In the bin corresponding to 500Hz, your choice of sampling frequencies, put a '1'.
> In the bins corresponding to 996 and 1004, put a .25.
[...]
> Repeat, using the same gain so as to avoid intensity differences.
[...]
> To me, at least, they are different sounds.

But the Fourier transform as used here is a 1-1 transform, without
redundancy.  All reconstruction from magnitude methods rely on
redundancy - Griffin & Lim use FFT blocks that overlap fully, and the
algorithms by Cassaza et al for polynomial time inversion rely on N^2
magnitude coefficients.

The Fourier transform is a projection of a signal onto infinite-length
sinusoids, (or in the case of the STFT, a circulant projection onto
short-time sinusoids) which is not very perceptually based.

Joe.
-- 
Joachim Thiemann :: http://www.tsp.ece.mcgill.ca/~jthiem