Practical Signals Theory with MATLAB Applications

Discrete Signals

LEARNING OBJECTIVES

By the end of this chapter, the reader will be able to:

• Describe the difference between discrete time and continuous time signals
• Compute a suitable sampling rate for a bandlimited signal
• Explain how a signal can be recovered from its samples
• Explain the concept of aliasing and the use of an anti-aliasing filter
• Describe the discrete time Fourier transform (DTFT) and discrete Fourier transform (DFT)
• Use MATLAB to find the Fourier transform of sampled signals
• Apply the DFT to frequency-domain filtering
• Explain time-domain filtering in terms of delays

8.1 Introduction

A signal described by a continuous function of time has a unique value at every definable instant. For example, given the continuous cosine signal c(t) = cos(2πf₀t), its value at an arbitrary time such as t = 5.00012 s can be determined by computing c(5.00012) with the aid of a pocket calculator. This chapter deals with discrete time signals of the form {c(nT)} for constant T and integer n, which do not exist at every point in time, but which are generally representative of an underlying continuous signal c(t).

8.2 Discrete Time vs. Continuous Time Signals

Consider the task of plotting by hand some continuous signal s(t). It is usually not necessary to compute s(t) for every point on a graph. Instead, the desired shape of s(t) can be reproduced by drawing a smooth line through ...