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Re: About importance of "phase" in sound recognition
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.
Why the "perceptual" issue even arises here, except in that you LISTEN to the results, is beyond me.
Given that I've been doing signal processing for some 35 years, I dare say that I'm well aware of the very basic propreties of the various Fourier transforms. This is also irrelevant,
MAKE THE TWO SIGNALS AND LISTEN TO THEM.
That's what's relevant. I repeat, make two signals, one sines of 500-4 500 and 500+4 Hz, amplitudes .25 1 .25 and then make another amplitude .25 1 -.25, or alternatively -.25 1 .25. Make sure you don't clip this when you render it, (i.e. apply proper gain scaling) and LISTEN.
I repeat LISTEN.
When you're done, you have listened to two signals with the same amplitude spectrum, and different phase spectra.
That's the only point. If you hear a difference, phase is audible. If you don't, then maybe it's not.
There's no "perceptual bias" here, only a signal generator that you apply to your own perception, and a signal generator that goes directly to the heart of the question "is phase audible". Phase has a definition. I am addressing, directly the actual definition of phase, which is the only relevance of Fourier mathematics here. And phase, I gather, is the debate. I PRESUME we all use the standard definition of phase?
MY GOODNESS. Are we to argue about the existance of the Dirac Delta next?
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
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.
Joachim Thiemann :: http://www.tsp.ece.mcgill.ca/~jthiem
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