Signals and Systems - Electrical Engineering

CHAPTER 8 Discrete-Time Signals and Systems.........................................................

It’s like dej ́a-vu,`

all over again.

Lawrence “Yogi” Berra (1925)

Yankees baseball player

8.1 Introduction.....................................................................................

As you will see in this chapter, the basic theory of discrete-time signals and systems is very much like
that for continuous-time signals and systems. However, there are significant differences that need to
be understood. Specifically in this chapter we will consider the following contrasting issues:

n Discrete-time signals resulting from sampling of continuous-time signals are only available at
uniform times determined by the sampling period; they are not defined in-between sampling
periods. It is important to emphasize the significance of sampling according to the Nyquist sam-
pling rate condition since the characteristics of discrete-time signals will depend on it. Given the
knowledge of the sampling period, discrete-time signals depend on an integer variablen, which
unifies the treatment of discrete-time signals obtained from analog signals by sampling and those
that are naturally discrete. It will also be seen that the frequency in the discrete domain differs
from the analog frequency. The radian discrete frequency cannot be measured, and depends on
the sampling period used whenever the discrete-time signals result from sampling.
n Although the concept of periodicity of discrete-time signals coincides with that for continuous-
time signals, there are significant differences. As functions of an integer variable, discrete-time
periodic signals must have integer periods. This imposes some restrictions that do not exist in
continuous-time periodic signals. For instance, continuous-time sinusoids are always periodic as
their period can be a positive real number; however, that will not be the case for discrete-time
sinusoids. It is possible to have discrete-time sinusoids that are not periodic, even if they resulted
from the uniform sampling of continuous-time sinusoids.
n Characteristics such as energy, power, and symmetry of continuous-time signals are conceptually
the same for discrete-time signals. Integrals are replaced by sums, derivatives by finite differences,
and differential equations by difference equations. Likewise, one can define a set of basic signals

Signals and Systems Using MATLAB®. DOI: 10.1016/B978-0-12-374716-7.00012-0
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