Page 49 - Fundamentals of Communications Systems

Chapter
2

Signals and Systems Review

This chapter provides a brief review of signals and systems theory usually
taught in an undergraduate curriculum. The purpose of this review is to
introduce the notation that will be used in this text. Most results will be given
without proof as these can be found in most undergraduate texts in signals and
systems [May84, ZTF89, OW97, KH97].

2.1 Signal Classification

A signal, x(t), is defined to be a function of time (t ∈ R). Signals in engi-
neering systems are typically described with five different mathematical
classifications:
1. Deterministic or random
2. Energy or power
3. Periodic or aperiodic
4. Complex or real
5. Continuous time or discrete time

We will only consider deterministic signals at this point as random signals
are a subject of Chapter 9.

2.1.1 Energy versus Power Signals
Definition 2.1 The energy, E x , of a signal x(t)is

T m /2
2
E x = lim |x(t)| dt (2.1)
T m →∞ −T m /2

2.1
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