What is the Use of Frobenius-Perron Operator for Chaotic Signal Processing?

In this paper we demonstrate the application of the Frobenius-Perron operator to the statistical analysis of chaotic systems. The Frobenius-Perron operator is the main analysis tool whenever statistical properties of the generated and processed signals are of interest. One important field of application are systems, where information is located in a particular statistic of the chaotic signal. For those systems we present a general structure which includes Chaotic Ranging, DCSK, a particular CSK and Code-coherent communication systems. By use of the Frobenius-Perron Operator a statistical analysis is possible, which gives as results performance measures in analytical form. So analytical expressions for the bit error rate as a function of the bit energy to noise ratio for systems with complex polyphase chaotic sequences will be derived. 1 Introduction In recent years the statistical analysis of discrete-time chaotic systems and its application have attracted the attention of many resear..