existence and uniqueness of an invariant probability measure, ergodicity properties as well as the existence of moments w.r.t. the invariant probability are proved using Markov process theory. Considering ē as n random perturbation of the orbits of sn+1 = λ(sn) the structure of the power spectrum of the quantizer error is studied approximately for small values of the white noise variance using the deterministic signal sn under a uniform invariant distribution.

Representations and statistical properties of the process ē defined by ēn+1 = λ(ēn + ξn), where λ(u) := u - b sign(u) + m are given, when ξn is a Gaussian white noise. The process ē represents the binary quantizer error in a model for (single loop) Sigma Delta modulation, see [3,6]. The existence and uniqueness of an invariant probability measure, ergodicity properties as well as the existence of moments w.r.t. the invariant probability are proved using Markov process theory. Considering ē as n random perturbation of the orbits of sn+1 = λ(sn) the structure of the power spectrum of the quantizer error is studied approximately for small values of the white noise variance using the deterministic signal sn under a uniform invariant distribution.