Nonlinear transformation of differential equations into phase space

Authors:
Leon Cohen;Lorenzo Galleani
Affiliations:
Department of Physics and Astronomy, Hunter College, City University of New York, New York, NY;Dipartimento di Elettronica, Politecnico di Torino, Torino, Italy
Venue:
EURASIP Journal on Applied Signal Processing
Year:
2004

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Abstract

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.