Approximation of the Wigner distribution for dynamical systems governed by differential equations
EURASIP Journal on Applied Signal Processing
Nonlinear transformation of differential equations into phase space
EURASIP Journal on Applied Signal Processing
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A new method is described to study dynamical systems characterized by linear ordinary differential equations. The method is aimed at studying the time-varying properties of the resulting solution of the differential equation. In contrast to the standard methods where one solves the differential equation and then uses a time-frequency distribution, for example the Wigner distribution, to ascertain the time-frequency properties of the solution we show that one can obtain a differential equation for the Wigner distribution of the solution. We discuss a number of advantages for doing so.