Mathematical Methods

13

Z-Transforms and Solution of Difference Equations

13.1 Introduction

Let A and B be the domain and range sets of specified functions. A transform is a mapping T : A → B from A into B. Recall that we have earlier studied Laplace and Fourier transforms. These are integral transforms by which we mean that these mappings are defined through integrals. Further, these transforms belong to a class of transforms dealing with functions of continuous variables. Now we consider a transformation called the Z-transformation which deals with functions of discrete variables. Indeed the Z-transform is the discrete analogue of the Laplace transform. Consequently, for every operational rule and application of Laplace transform we have an operational rule and ...