Analysis of chaotic signals in the time-frequency plane

In this paper we study chaotic signals generated from Chua’s circuit: in particular we concentrate on the well known spiral attractor. Chaotic signals have a nonstationary nature, and hence the classical Fourier spectrum turns out to be inadequate for the analysis. Instead of it we use TimeFrequency Distributions, a powerful set of tools specifically designed for nonstationary signal analysis. Time-Frequency analysis shows that the considered chaotic signals are multicomponent, and can be thought as the sum of amplitude modulated (AM) signals with a constant carrier frequency. The basic components are extracted with a zero-phase distortion filtering, and the validity of the AM representation with constant carrier frequency is then verified. An approximation of the original chaotic signal is obtained summing up a limited number of its filtered components. The validity of this approach is verified by comparing the original chaotic attractor with that built through the approximated signals.