# Re: About importance of "phase" in sound recognition

Whoa. I just drifted off there.

500Hz at 1, .25 at 500-4 and 500+4

Or you can use 1khz and then use 1000+4 and 1000-4.

I believe I suffered a change of center frequency between the first and second parts of my post. Sorry.

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-----Original Message-----
From: AUDITORY - Research in Auditory Perception [mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Joachim Thiemann
Sent: Friday, October 08, 2010 8:35 AM
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: [AUDITORY] About importance of "phase" in sound recognition

> By the way, I apologize for not providing the reference for the mathematical
> article that I referred to in the previous email. here is a link to it :
>
> http://www.math.missouri.edu/~pete/pdf/132-painless.pdf
>

Hello Emad, from my quick reading of this paper (since the topic is
quite interesting to me) I notice the following (others feel free to
correct me if I get this wrong):
- to reconstruct a N-dimensional (complex) vector from magnitude only
coefficients you need N^2 coefficients (N(N+1)/2 for real vectors).
An earlier paper (in SPIE 2007) talks about sparse representations
needing as little as 2N-1 coefficients (in the real case). I am not
certain yet if they have generalized it to the complex case, and it
this only applies to a specific set of frames.
- reconstruction from magnitude only will always be within a root of
unity (that is, the solution will be a set of vectors that differ from
each other by e^{-i\phi} \phi=0...2\pi as one expects.

Thanks for the link though!  I am still working in reconstruction from
the basis of Griffin&Lim's iterative reconstruction algorithm, so this
is quite interesting to me.

Joe.
--
Joachim Thiemann :: http://www.tsp.ece.mcgill.ca/~jthiem

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