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Boundary Control approach to the spectral estimation problem: the case of multiple poles

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Abstract

There exist many methods for solving the spectral estimation problem. This paper proposes a new approach to this problem based on the Boundary Control method. We show that the problem of decomposition of a signal modeled by a sum of exponentials with polynomial coefficients can be reduced to an identification problem for a discrete time linear dynamical system. It follows that values of exponentials can be found solving a generalized eigenvalue problem as in the Matrix Pencil method. We also give exact formulas for the polynomial amplitudes.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, 99775-6660, USA

    Sergei Avdonin

  2. Seismology Department, Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK, 99775, USA

    Anna Bulanova

Authors
  1. Sergei Avdonin
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  2. Anna Bulanova
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Correspondence to Anna Bulanova.

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Avdonin, S., Bulanova, A. Boundary Control approach to the spectral estimation problem: the case of multiple poles. Math. Control Signals Syst. 22, 245–265 (2011). https://doi.org/10.1007/s00498-010-0052-5

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  • DOI: https://doi.org/10.1007/s00498-010-0052-5

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