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Re: About importance of "phase" in sound recognition
I never disputed that signals with same Fourier transform magnitude
spectrum can sound very different, and in fact am quite in agreement.
Excellent. Now can we get the entire AES to listen? Sorry, I've been told "phase is irrelevant" enough times that I am about to beat somebody about the head with a 999th order schroder section
(that would be ( .99 + z^999)/(z^999 + .99) ... tell me that's not an audible effect :) :)
In fact I think yours is a very good example of why the FFT magnitude
spectrum is not sufficient as a signal representation.
Well, magnitude alone is missing half of the information, certainly, give or take. But I agree, if we are talking about auditory perception, an FFT of any length just doesn't cut it. Yes, I'm well aware I used an FFT in the MPEG Psychoacoustic Model 2, simply so that it could be calculated by a 1990-era processor , but the time resolution of any uniform decomposition of any length is, by itself, pretty much hopeless in terms of the auditory system. So we don't even need to worry about "magnitude", even "uniform frequency" isn't going to do it.
You understood the two signals well enough, indeed. It's fun to play things like that for an audience that is still back with the old 60 Hz/7kHz "phase is inaudible" crowd.
Sorry, being in audio as well as acoustics and psychoacoustics, I meet a lot of people with "belief", as it were...
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