Analytical expressions for power spectral density issued from one-dimensional continuous piecewise linear maps with three slopes

During the two last decades, chaotic signals have been increasingly considered in telecommunications, signal processing or secure transmissions. Despite the importance of frequency in the telecommunications and transmission security there are few works that explore the spectrum of chaotic signals by considering the bandwidths. Previous works have concerned skew tent maps. In this paper, we derive analytical expressions for the autocorrelation sequence (ACS) and power spectral density (PSD) of chaotic signals generated by one-dimensional continuous piecewise linear maps with three slopes. We obtain similar results to those obtained using the skew-tent map. Our results permit to conjecture that the bandwidth of chaotic signals obtained from piecewise linear continuous map can have the same behaviour whatever be the number of slopes in the map.