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Canonical basis; fourrier dictionary or wavelets?-SPARSE SIGNAL REPRESENTATION

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Sherra

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Hi all,

Does anyone know how to construct a basis function (Fourier, Bayesian, wavelet function, generalized basis function...) in matlab to represent a sparse signal.
The problem is I have a signal in time domain (THAT SIGNAL REPRESENTS THE CHANNEL COEFFICIENTS OF A 20-PATH OR 2-SIGNIFICANT SCATTERERS MULTIPATH CHANNEL), I know it is sparse (20-sparse) in some basis, but how to find that basis? Since i only have the channel coefficients in the frequency domain.
The problem could be reformulated as as : knowing h (1000,1) in some conventional basis, I am looking for the matrix "Phi" such that , < h=Phi*h_sparse >.
h_sparse is the same as h, only represented in another basis and having lots of zeros entries.
Thanks for any help!!!

I wanted to add something to make myself clear enough. How do I choose a dictionary (overcomplete basis) in which to represent a signal, that is in time domain,
to get its sparse representation?

thank you!!
 

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