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Algebraic signal sampling, Gibbs phenomenon and Prony-type systems

Dmitry Batenkov,Y. Yomdin

Published 2013 in arXiv.org

ABSTRACT

Systems of Prony type appear in various signal reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. We propose a novel approach for solving Prony-type systems, which requires sampling the signal at arithmetic progressions. By keeping the number of equations small and fixed, we demonstrate that such "decimation" can lead to practical improvements in the reconstruction accuracy. As an application, we provide a solution to the so-called Eckhoff's conjecture, which asked for reconstructing jump positions and magnitudes of a piecewise-smooth function from its Fourier coefficients with maximal possible asymptotic accuracy -- thus eliminating the Gibbs phenomenon.

PUBLICATION RECORD

  • Publication year

    2013

  • Venue

    arXiv.org

  • Publication date

    2013-06-05

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 1306.1097
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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