Análise espectral de sinais caóticos gerados por mapas unidimensionais

Abstract

In this work, we investigate characteristics of the Power Spectral Density (PSD) of chaotic signals generated by one-dimensional maps. Usually, these signals are mentioned as having broadband and impulsive Autocorrelation Sequence (ACS). In this work, we verify that chaotic signals can be narrowband or broadband, with their power concentrated in the high or low frequencies. For a particular piecewise linear family of maps, we analytically evaluate the influence of the Lyapunov exponent on the ACS and on the PSD. We relate essential bandwidth to this exponent and to the parameter that defines a map in the family. We also consider the Manneville family of maps. In this case, the analysis is performed via computational simulations, interpreting the signals as sample-functions of a stochastic process. We relate the essential bandwidth to the Lyapunov exponent and to the family's parameter. We also relate this parameter to the return time of the intermittences. From the Telecommunication Engineering point of view, the results are relevant because they allow the emergence of new ideas for applications of chaotic signal in digital communication.