Nonlinear and possibly chaotic dynamical systems are a source of a very wide range of signals that could be used for solving a variety of signal processing tasks. Given a time series measured (or generated) from a known or an unknown dynamical system we address a series of problems, such as section-wise approximation of the measured signal by pieces of trajectories from a chosen nonlinear dynamical system (model); signal restoration when the measured signal has been corrupted e.g. by quantization; signal coding and compression. All these problems can be approached via estimating the initial conditions for a dynamical system under consideration (generator of approximating waveforms) giving rise to an orbit which is optimal in the sense of distance from the measured (or prescribed) transient output waveform.

23.1 Introduction

In various real-life applications processing of data measured from a physical object/process or generated by a nonlinear dynamical system ^{[1] , [2] , [12] , [15] , [21]} is of paramount importance. This is the case for example in observations taken in meteorology, seismic data, physiology, medical observations and measurements, measurements taken in electronic circuits or telecommunication channels. Signal processing is understood here in a very wide way encompassing storage, compression, feature extraction, interpretation, any kind of filtering, shaping etc.

Looking at the literature one can see that researchers from different backgrounds have different approaches to signal processing tasks - some concentrate on just...