Signal Modeling Using Piecewise Linear Chaotic Generators

In this paper the modeling of a signal by a chaotic generator with respect to a specified signal statistic will be considered. To accomplish that, the considered class of n-dimensional piecewise linear Markov generators will first be analyzed analytically, yielding an algebraic expression for the statistical quantity in question. Based on this analytical result an optimal set of parameters minimizing the modeling error with respect to the considered statistical quantity will be calculated. 1 MOTIVATION Statistical signal modeling is an important method in modern digital signal processing. Specifically, parametric signal models have been widely used for the estimation of the power density spectrum, but also for higher order spectra. Usually, linear (AR, MA, ARMA) models are preferred due to the relatively straight-forward estimation of their parameters. Linear models have the disadvantageous necessity to be driven by a noise source (due to their stability). In contrast, chaotic syste..