Subject: Re: About importance of "phase" in sound recognition From: Joachim Thiemann <joachim.thiemann@xxxxxxxx> Date: Sat, 9 Oct 2010 20:23:25 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>On Sat, Oct 9, 2010 at 16:15, James Johnston <James.Johnston@xxxxxxxx> wrote: > To the below. I'm describing how to make a signal for which phase is audible. The fact I'm using an FFT to generate the signal is, frankly, not relevant to this discussion. I could as well just describe it as the sum of sines with different signs on the amplitude. Hi, I never disputed that signals with same Fourier transform magnitude spectrum can sound very different, and in fact am quite in agreement. In fact I think yours is a very good example of why the FFT magnitude spectrum is not sufficient as a signal representation. My comment was more on the paper by Casazza which deals with reconstruction from magnitude coefficients alone, and that the algorithm requires a frame which is highly redundant. The Fourier transform is not a redundant transform so that it shouldn't be expected that one can reconstruct a signal even within perceived similarity from magnitude coefficients. Here's the 2 signals you described, in the sum-of-sines construction (if I understand your description correctly): x1 = sin(2*pi*500*(1:L)/fs)+.25*sin(2*pi*496*(1:L)/fs)+.25*sin(2*pi*504*(1:L)/fs); x2 = sin(2*pi*500*(1:L)/fs)+.25*sin(2*pi*496*(1:L)/fs)-.25*sin(2*pi*504*(1:L)/fs); I also add x3 = sin(2*pi*500*(1:L)/fs)-.25*sin(2*pi*496*(1:L)/fs)-.25*sin(2*pi*504*(1:L)/fs); x4 = sin(2*pi*500*(1:L)/fs)-.25*sin(2*pi*496*(1:L)/fs)+.25*sin(2*pi*504*(1:L)/fs); for comparison. SInce it is possible to have a change in phase that IS imperceptible, I think it is interesting to consider transforms that represent the sound in such a way that the phase component of the transform coefficient can be discarded without perceptual distortion. Joe. -- Joachim Thiemann :: http://www.tsp.ece.mcgill.ca/~jthiem