Generalised Filters and Stochastic Sampling Zeros

It is well-known that the zeros of sampled-data models for deterministic systems depend on the hold device used to generate the continuous-time system input. A dual result holds also for stochastic systems. In the latter case, the zeros of the sampled-data model depend on the anti-aliasing filter used before sampling. Generically, extra zeros appear in both deterministic and stochastic discrete-time models. These zeros have no continuous-time counterpart. This paper presents an anti-aliasing filter design, such that the stochastic sampling zeros are asymptotically assigned to the origin, for fast sampling rates. The design procedure relies only on the system relative degree.