Approximation of the Wigner distribution for dynamical systems governed by differential equations

Authors:
Lorenzo Galleani;Leon Cohen
Affiliations:
Dipartimento di Elettronica, Politecnico di Torino, Torino, Italy;City University of New York, New York, NY
Venue:
EURASIP Journal on Applied Signal Processing
Year:
2002

Citing 2
Cited 1

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EURASIP Journal on Applied Signal Processing

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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.