Compressive sampling of pulse trains: Spread the spectrum!

  • Authors:

  • Farid M. Naini;Remi Gribonval;Laurent Jacques;Pierre Vandergheynst

  • Affiliations:

  • Signal Processing Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Switzerland;Centre de Recherche INRIA Rennes, IRISA Campus de Beaulieu, F-35042 Rennes cedex, France;Signal Processing Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Switzerland;Signal Processing Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Switzerland

  • Venue:
  • ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
  • Year:
  • 2009

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Abstract

In this paper we consider the problem of sampling far below the Nyquist rate signals that are sparse linear superpositions of shifts of a known, potentially wide-band, pulse. This signal model is key for applications such as Ultra Wide Band (UWB) communications or neural signal processing. Following the recently proposed Compressed Sensing methodology, we study several acquisition strategies and show that the approximations recovered via ℓ1 minimization are greatly enhanced if one uses Spread Spectrum modulation prior to applying random Fourier measurements. We complement our experiments with a discussion of possible hardware implementation of our technique.