Signal Processing and Integrated Circuits

Chapter 4

Discrete Signals and Systems

4.1 Introduction

This chapter gives a brief and compact review of the process of analog to digital conversion and the representation of discrete signals and systems. Then the classification of digital systems is given with emphasis on linear shift-invariant types. The forms of realization of finite duration and infinite duration impulse response filters are discussed [11, 12]. This chapter, as in the case of Chapter 2, can be used as a compact review of the material which is normally given early at the junior level.

4.2 Digitization of Analog Signals

A signal f(t) is called a continuous-time or an analog signal if it is defined, somehow, for all values of the continuous variable t. If f(t) is defined only at discrete values of t, it is called a discrete-time signal or an analog sampled-data signal. Suppose that in addition to being discrete-time the signal quantities f(t) can assume only discrete values, and that each value is represented by a code such as the binary code. The resulting signal is said to be a digital signal.

The first step in the digitization process is to take samples of the signal f(t) at regular time intervals: nT (n = 0, ±1, ±2, …). This amounts to converting the continuous-time variable t into a discrete one. This way, we obtain a signal f(nT) which is defined only at discrete instants which are integral multiples of the same quantity T, which is called the sampling period. Such a signal may be thought of as a sequence ...