Preface xix
discussed; definitions of signal energy and signal power are given. The idea of impulse
decomposition of a signal is presented in preparation for the discussion of convolution oper-
ation in later chapters. The concept of a phasor is introduced for continuous-time sinusoidal
signals. The chapter includes MATLAB exercises that focus on techniques for generating
and graphing signals, developing functions for basic building blocks, and simulating signal
operations.
In Chapter 2 the concept of a continuous-time system is introduced. Simplifying assump-
tions of linearity and time invariance that are useful in building a framework for analysis and
design of systems are discussed. The chapter proceeds with the use of constant-coefficient
linear differential equations for describing the behavior of linear systems. Rather than as-
suming prior background in solving differential equations or simply referring the student to
math textbooks, differential equation solution methods are explained at a level sufficient
for working with linear and time-invariant systems. If the students have already been ex-
posed to a course on differential equations, corresponding sections of this chapter could be
skipped or reviewed quickly. Representation of a differential equation by a block diagram
is also briefly discussed. The concepts of impulse response and convolution are developed,
and their link to the differential equation of the system is shown. Definitions of stability
and causality as well as the time-domain conditions for a system to achieve them are given.
MATLAB exercises are provided for testing linearity and time invariance of continuous-time
systems and for obtaining approximate numerical solutions to differential equations.
Chapter 3 provides a treatment of time-domain analysis for discrete-time systems, and
parallels the coverage of Chapter 2. After the introduction of linearity and time invari-
ance from a discrete-time system perspective, it proceeds with the analysis of discrete-time
systems by means of their difference equations. Solution methods for difference equations
are summarized for the sake of completeness. Representation of a difference equation by
a block diagram is discussed. Impulse response and convolution concepts are developed
for discrete-time systems, and their relationship to the difference equation of the system is
shown. Stability and causality concepts are also detailed for discrete-time systems. The
chapter includes MATLAB exercises that focus on software implementation of discrete-time
systems from difference equations or by using discrete-time convolution.
Chapter 4 is on Fourier analysis of continuous-time signals and systems. It begins with
the analysis of periodic continuous-time signals in terms of their frequency content. First,
the idea of finding the best approximation to a periodic signal through the use of a few
trigonometric functions is explored in order to build intuition. Afterwards trigonometric,
exponential and compact variants of the Fourier series are discussed. The Fourier trans-
form for non-periodic signals is then introduced by generalizing the exponential Fourier
series representation of a periodic signal with infinitely large period. A discussion of Par-
seval’s theorem is provided leading to the concepts of energy and power spectral density
for deterministic signals. System function concept is introduced for continuous-time sys-
tems. Response of linear and time-invariant systems to both periodic and non-periodic
input signals is studied. The chapter includes a number of MATLAB exercises dealing with
finite-harmonic approximations to periodic signals and the problem of graphing system
functions.
The development of Chapter 5 mirrors that of Chapter 4 for discrete-time signals. Anal-
ysis of periodic discrete-time signals through the use of discrete-time Fourier series (DTFS)
is presented. Afterwards the discrete-time Fourier transform (DTFT) is developed by gen-
eralizing the discrete-time Fourier series. The relationship between the DTFS coefficients
of a periodic signal and the DTFT of a single isolated period of it is emphasized to high-
light the link between the indices of the DTFS coefficients and the angular frequencies of