RELATIONS BETWEEN CONTINUOUS-TIME AND DISCRETE-TIME LINEAR-SYSTEMS
In this paper the concept of a basic linear system [Takahara 1981] is used to explore relations between continuous-time and discrete-time systems from two directions. First, preservation of systems structure through sampling is considered. Two sampling methods are defined and it is shown that both preserve linearity, causality, stationarity, and finite dimensionality of system core. These preservation makes the resultant discrete-time system a basic linear system. Secondly, we investigate what is the minimal basic linear system for all of discrete-time basic linear systems which are made from sampling of a basic linear system. A continuous-time basic linear system is said to be minimal in the sense that any element of the set of discrete-time basic linear systems can be embedded into it and there is no greater basic linear system that can embed them. It is shown that the original continuous-time basic linear system is the minimal system.
basic linear system, simple sampling, 0-th hold-sampling discrete-time system, continuous-time system, category of basic linear systems, minimal embedding of sampled systems