N-dimensional uniform probability distribution in nonlinear autoregressive filter structures

In this brief, we consider a class of nonlinear discrete-time systems and prove conditions for the generation of signals with n-dimensional uniform probability distribution. To obtain this result we prove the invariance of the Frobenius-Perron-Operator on a finite-dimensional function space. Spectral properties of the generated signal, as well as the influence of an input signal on the signal characteristics are discussed.