Digital Filters Design for Signal and Image Processing

2.1. Introduction

The study of discrete-time signals is based on the z-transform, which we will discuss in this chapter. Its properties make it very useful for studying linear, time-invariant systems.

This chapter is organized as follows. First, we will study discrete, invariant linear systems based on the z-transform, which plays a role similar to that of the Laplace transform in continuous systems. We will present the representation of this transform, as well as its main properties; then we will discuss the inverse-z-transform, From a given z-transform, we will present different methods of determining the corresponding discrete-time signal. Lastly, the concepts of transfer functions and difference equations will be covered. We also provide a table of z-transforms.