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

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