Subject: Re: About importance of "phase" in sound recognition From: Joachim Thiemann <joachim.thiemann@xxxxxxxx> Date: Sat, 9 Oct 2010 08:51:14 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>On Fri, Oct 8, 2010 at 15:44, James Johnston <James.Johnston@xxxxxxxx> 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