Dynamic Response of Discrete-Time Systems

In earlier chapters we have seen that the Laplace transform provides a convenient way of analyzing the dynamic behavior of continuous-time systems. The Laplace transform is also applicable to discrete-time systems but is somewhat awkward to use. Thus we consider a related transform for discrete-time systems, the z-transform. The z-transform has the same utility as the Laplace transform in that its use leads to a compact mathematical description of a dynamic system and permits the use of algebraic operations for system analysis. By using z-transforms, transfer functions for discrete-time processes can be defined. This procedure facilitates subsequent analysis of sampled-data control systems, namely systems where a sampled signal appears. In this chapter we introduce z-transforms and pulse transfer functions and show how they can be used to calculate transient responses.