Technical Report 2003-028

Limiting Properties of Sampled Stochastic Systems

Erik K. Larsson

May 2003

The objective of this paper is to present some general properties of discrete-time systems originating from fast sampled continuous-time stochastic systems. In particular, some results concerning the zero locations and the innovations variance of fast sampled continuous-time autoregressive moving average (ARMA) systems will be stated. Knowledge of these properties is of importance and interest in various fast sampling applications, such as discrete-time simulation of continuous-time systems and identification of continuous-time systems using discrete-time measurements. The main contribution, however, is to provide some insight into questions like: when can simple approximate sampling schemes be applied accurately enough and what determines the characteristic dynamic of a fast sampled system. The results are illustrated by an extensive set of examples.

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