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Sparsity in Time-Frequency Representations

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Abstract

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 ℂn with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S≤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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Authors and Affiliations

  1. School of Engineering and Science, Jacobs University Bremen, 28759, Bremen, Germany

    Götz E. Pfander

  2. Hausdorff Center for Mathematics & Institute for Numerical Simulation, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Holger Rauhut

Authors
  1. Götz E. Pfander
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  2. Holger Rauhut
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Corresponding author

Correspondence to Holger Rauhut.

Additional information

Communicated by Thomas Strohmer.

H.R. acknowledges support by the European Union’s Human Potential Programme through an Individual Marie Curie Fellowship, contract number MEIF CT-2006-022811.

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Pfander, G.E., Rauhut, H. Sparsity in Time-Frequency Representations. J Fourier Anal Appl 16, 233–260 (2010). https://doi.org/10.1007/s00041-009-9086-9

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  • DOI: https://doi.org/10.1007/s00041-009-9086-9

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