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Re: About importance of "phase" in sound recognition

I would think that the signals x1, x2, x3, and x4 would sound different
because of their different audible beat patterns, i.e. their temporal
envelopes would be different. To my way of thinking, phase is more
inaudible when temporal envelope differences are not obvious to the ear. 
I'm especially thinking about "relative phases" of the harmonics of a
harmonic signal that may have a slowly moving fundamental. 
The model would be:

  s(t) =  SUM 1,K: A[k](t)*cos(2*pi*k*integral(f0(t)dt)+ph0[k])
  where k = harmonic no., K = no. of harmonics, f0 = fund. freq,
  and ph0[k] are the harmonic relative phases. Except for the
  residual, wouldn't this be a good model for a solo voice or wind
  or string musical instrument?

I hope I'm not missing the point here.


Original message:
>From: Joachim Thiemann <joachim.thiemann@xxxxxxxxx>
>Date: Sat, 9 Oct 2010 20:23:25 -0400
>To: AUDITORY@xxxxxxxxxxxxxxx
>Subject: Re: [AUDITORY] About importance of "phase" in sound recognition
>On Sat, Oct 9, 2010 at 16:15, James Johnston <James.Johnston@xxxxxxx>
>> 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.
>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
>                                                              1819,1        93%
>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.