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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: About importance of "phase" in sound recognition*From*: Joachim Thiemann <joachim.thiemann@xxxxxxxxx>*Date*: Fri, 8 Oct 2010 11:35:20 -0400*Approved-by*: joachim.thiemann@xxxxxxxxx*Comments*: To: emad burke <emad.burke@xxxxxxxxx>*Delivery-date*: Fri Oct 8 12:01:04 2010*In-reply-to*: <20101008133504.CC22085FA@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>*Reply-to*: Joachim Thiemann <joachim.thiemann@xxxxxxxxx>*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

On Fri, Oct 8, 2010 at 09:33, emad burke <emad.burke@xxxxxxxxx> wrote: > 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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