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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: About importance of "phase" in sound recognition*From*: Joachim Thiemann <joachim.thiemann@xxxxxxxxx>*Date*: Sat, 9 Oct 2010 20:23:25 -0400*Approved-by*: joachim.thiemann@xxxxxxxxx*Delivery-date*: Sat Oct 9 20:24:49 2010*In-reply-to*: <20101009201652.43CD7983C@xxxxxxxxxxxxxxxxxxxxxxx>*List-archive*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>*List-help*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>, <mailto:LISTSERV@LISTS.MCGILL.CA?body=INFO AUDITORY>*List-owner*: <mailto:AUDITORY-request@LISTS.MCGILL.CA>*List-subscribe*: <mailto:AUDITORY-subscribe-request@LISTS.MCGILL.CA>*List-unsubscribe*: <mailto:AUDITORY-unsubscribe-request@LISTS.MCGILL.CA>*References*: <20101007213645.637317165@xxxxxxxxxxxxxxxxxxxxxxx> <20101008094422.E19A78110@xxxxxxxxxxxxxxxxxxxxxxx> <20101008130215.358FE5685@xxxxxxxxxxxxxxxxxxxxxxx> <20101008133504.CC22085FA@xxxxxxxxxxxxxxxxxxxxxxx> <20101008160133.69E225590@xxxxxxxxxxxxxxxxxxxxxxx> <20101008194629.9A4FD9857@xxxxxxxxxxxxxxxxxxxxxxx> <20101009125332.E4B616022@xxxxxxxxxxxxxxxxxxxxxxx> <20101009201652.43CD7983C@xxxxxxxxxxxxxxxxxxxxxxx>*Reply-to*: Joachim Thiemann <joachim.thiemann@xxxxxxxxx>*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

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

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