Representation of Discrete (Sampled) Systems

Summary

This chapter explores Shannon sampling, the Z‐transform and parametric representation. Sampling and interpolation are inseparable concepts for continuous systems considered by automatic control and signal processing. In addition, in order for signals to be usable by digital computers, quantification should be conducted. The Z‐transform (ZT), for discrete signals, can be considered as a generalization of the Fourier transform. It is an indispensable tool for the analysis of discrete signals and systems. There is a formulation close to Fourier's using Cauchy's theorem. More often, to calculate the inverse of a ZT, practical methods are employed such as simple elements decomposition or polynomial division. The chapter presents sampling associated with exact interpolation and indicates how this theoretical principle can be applied in practice. A discrete system is an operator or an algorithm that transforms an input sequence x (n) into an output sequence y (n).