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  • Research Article
  • Open Access

Nonlinear Transformation of Differential Equations into Phase Space

EURASIP Journal on Advances in Signal Processing20042004:903519

Received: 7 September 2003

Published: 29 September 2004


Time-frequency representations transform a one-dimensional function into a two-dimensional function in the phase-space of time and frequency. The transformation to accomplish is a nonlinear transformation and there are an infinite number of such transformations. We obtain the governing differential equation for any two-dimensional bilinear phase-space function for the case when the governing equation for the time function is an ordinary differential equation with constant coefficients. This connects the dynamical features of the problem directly to the phase-space function and it has a number of advantages.

Keywords and phrases

time-frequency distributionsnonstationary signalslinear systemsdifferential equations

Authors’ Affiliations

Department of Physics and Astronomy, Hunter College, City University of New York, New York, USA
Dipartimento di Elettronica, Politecnico di Torino, Torino, Italy


© Cohen and Galleani 2004