Efficient generation of random signals with prescribed probability distribution and spectral bandwidth via ergodic transformations

Abstract

A novel random signal generator design that accommodates the specification of both the sample probability distribution as well as the signal bandwidth is presented in this paper. The generator achieves a high degree of computational efficiency through the nonlinear transformation of trajectories produced by a discrete–time dynamical system which has an ergodic map as evolution rule. The ergodic map is designed using a recently proposed solution of the inverse Frobenius–Perron problem that allows for the selection of the map’s invariant distribution as well as its spectral characteristics. The nonlinear transformation is obtained via a novel piecewise polynomial fitting algorithm, which facilitates the approximation of absolutely continuous probability distributions over compact support with greater accuracy than existing techniques. Numerical experiments indicate that the proposed design achieves a reduction in signal generation time of up to 22% compared to a conventional generator, while at the same time using a smaller lookup table, maintaining a comparable level of accuracy, and offering flexibility in the selection of the signal bandwidth. It is concluded that the proposed approach is suitable for signal generation in applications where low computational complexity is a critical requirement.