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EURASIP Journal on Advances in Signal Processing
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Approximation of the Wigner Distribution for Dynamical Systems Governed by Differential Equations

EURASIP Journal on Advances in Signal Processing volume 2002, Article number: 514609 (2002) Cite this article

Abstract

A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exact Wigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in time and frequency. We then show how it lends itself to effective approximation methods because in the time frequency plane there is a high degree of localization of the signal. Numerical examples are given and compared to exact solutions.

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Authors and Affiliations

  1. Dipartimento di Elettronica, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy

    Lorenzo Galleani

  2. City University of New York, 695 Park Avenue, New York, NY, 10021, USA

    Leon Cohen

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  1. Lorenzo Galleani
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  2. Leon Cohen
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Correspondence to Lorenzo Galleani.

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Galleani, L., Cohen, L. Approximation of the Wigner Distribution for Dynamical Systems Governed by Differential Equations. EURASIP J. Adv. Signal Process. 2002, 514609 (2002). https://doi.org/10.1155/S1110865702000458

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  • DOI: https://doi.org/10.1155/S1110865702000458

Keywords

  • differential equations
  • Wigner distribution
  • time-frequency analysis