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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:


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 distributions
  • nonstationary signals
  • linear systems
  • differential equations

Authors’ Affiliations

Department of Physics and Astronomy, Hunter College, City University of New York, 695 Park Avenue, New York, NY 10021, USA
Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129, Italy


© Cohen and Galleani 2004