ABSTRACT
This chapter deals with the statistical description of chaotic signals and systems. Although chaotic systems are purely deterministic they can be modelled, analysed and designed by using probability measures and statistical characteristics, such as probability density functions and correlation functions, widely used in signal theory and in engineering applications. The chapter describes the problem of statistical analysis, the performance evaluation of chaotic signal processing schemes. This requires the introduction of an extended calculus because random processes interact with chaotic signals. The chapter examines the solution of inverse problem, the synthesis and design of chaotic systems from prescribed statistical characteristics of signals to be generated. Chaos communication schemes are analysed and the results are presented in terms of performance criteria commonly used in communication engineering. The fundamentals of statistical analysis of chaotic systems are explained systematically. The theory is mainly developed for multidimensional systems and illustrated with examples for one-dimensional case. The chapter presents and develops tools for the statistical analysis.
