Subject: Re: About importance of "phase" in sound recognition From: Joachim Thiemann <joachim.thiemann@xxxxxxxx> Date: Fri, 8 Oct 2010 11:35:20 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>On Fri, Oct 8, 2010 at 09:33, emad burke <emad.burke@xxxxxxxx> 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