Sparsity in time-frequency representations

Details Sparsity in time-frequency representations Sparsity in time-frequency representations

2007-11-15

arxiv.org/abs/0711.2503v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We consider signals and operators in finite dimension which have sparse time-frequency representations. As main result we show that an $S$-sparse Gabor representation in $\mathbb{C}^n$ with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that $S\leq Cn/\log(n)$. Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing.

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