Obtaining order in a world of chaos [signal processing]

Measurements of a physical or biological system result in a time series, s(t)=s(t/sub 0/+n/spl tau//sub s/)=s(n) sampled at intervals of /spl tau//sub s/ and initiated at t/sub 0/. When a signal can be represented as a superposition of sine waves with different amplitudes, its characteristics can be adequately described by Fourier coefficients of amplitude and phase. In these circumstances, linear and Fourier based methods for extracting information from the signal are appropriate and powerful. However, the signal may be generated by a nonlinear system. The waveform can be irregular and continuous and broadband in the frequency domain. The signal is noise-like, but is deterministic and may be chaotic. More information than the Fourier coefficients is required to describe the signal. This article describes methods for distinguishing chaotic signals from noise, and how to utilize the properties of a chaotic signal for classification, prediction, and control.