Digital chaotic noise using tent map without scaling and discretization process

Abstract

This work shows how to improve the statistical distribution of signals produced by noise generators designed with one-dimensional chaotic maps. It also shows that in a electronic design the piecewise linear chaotic maps should be considered because they do not have stability islands in its chaotic behavior region, as it occurs with the logistic map commonly used to build noise generators. The design and implementation problems of the noise generators are analyzed and a solution is proposed. This solution relates the tent map output, defined in the real numbers' domain, with a codebook of S elements. The proposed scheme produces digital noise signals using tent map without scaling and discretization process. Finally, this work shows that it is possible to have control over the statistical distribution of the noise signal by selecting the control parameter of the tent map and using, as a design criterion, the bifurcation diagram. © 2012 Springer-Verlag.