Re: About importance of "phase" in sound recognition

[Joachim Thiemann <joachim.thiemann@xxxxxxxxx>]

On Sat, Oct 9, 2010 at 16:15, James Johnston <James.Johnston@xxxxxxx> 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