Chaotic signals and physical systems

The methods for establishing a phase space or state space for a physical system from measurements of a scalar time series are reviewed, and the implications for the analysis of signals of the geometry of strange attractors are discussed. Classifying the physical systems by invariants on the attractor is seen to be the analog of classifying linear systems by the resonant response frequencies. The statistical properties of deterministic systems are used to perform this classifying. Methods for separating a chaotic signal of interest from contamination such as high dimensional noise are discussed. An example of a signal from a nonlinear circuit whose equations of evolution are unknown is discussed in detail and all the items mentioned are illustrated