xii Preface
The organization of the material in the book follows the assumption that the student has been exposed to the
theory of linear circuits, differential equations, and linear algebra, and that this material will be followed by
courses in control, communications, or digital signal processing. The content is guided by the goal of nurturing
the interest of students in applications, and of assisting them in becoming more sophisticated mathematically.
In teaching signals and systems, the author has found that students typically lack basic skills in manipulating
complex variables, in understanding differential equations, and are not yet comfortable with basic concepts in
calculus. Introducing discrete-time signals and systems makes students face new concepts that were not explored
in their calculus courses, such as summations, finite differences, and difference equations. This text attempts to
fill the gap and nurture interest in the mathematical tools.APPROACH
In writing this text, we have taken the following approach:- The material is divided into three parts: introduction, theory and applications of continuous-time signals
and systems, and theory and applications of discrete-time signals and systems. To help students under-
stand the connection between continuous- and discrete-time signals and systems, the connection between
infinitesimal and finite calculus is made in the introduction part, together with a motivation as to why com-
plex numbers and functions are used in the study of signals and systems. The treatment of continuous- and
discrete-time signals and systems is then done separately in the next two parts; combining them is found to
be confusing to students. Likewise, the author believes it is important for students to understand the connec-
tions and relevance of each of the transformations used in the analysis of signals and systems so that these
transformations are seen as a progression rather than as disconnected methods. Thus, the author advocates
the presentation of the Laplace analysis followed by the Fourier analysis, and the Z-transform followed by the
discrete Fourier, and capping each of these topics with applications to communications, control, and filter-
ing. The mathematical abstraction and the applications become more sophisticated as the material unfolds,
taking advantage as needed of the background on circuits that students have. - An overview of the topics to be discussed in the book and how each connects with some basic mathematical
concepts—needed in the rest of the book—is given in Chapter 0 (analogous to the ground floor of a build-
ing). The emphasis is in relating summations, differences, difference equations, and sequence of numbers
with the calculus concepts that the students are familiar with, and in doing so providing a new interpreta-
tion to integrals, derivatives, differential equations, and functions of time. This chapter also links the theory
of complex numbers and functions to vectors and to phasors learned in circuit theory. Because we strongly
believe that the material in this chapter should be covered before beginning the discussion of signals and
systems, it is not relegated to an appendix but placed at the front of the book where it cannot be ignored. A
soft introduction to MATLAB is also provided in this chapter. - A great deal of effort has been put into making the text “student friendly.” To make sure that the student does
not miss some of the important issues presented in a section, we have inserted well-thought-out remarks—
we want to minimize the common misunderstandings we have observed from our students in the past.
Plenty of analytic examples with different levels of complexity are given to illustrate issues. Each chapter
has a set of examples in MATLAB, illustrating topics presented in the text or special issues that the student
should know. The MATLAB code is given so that students can learn by example from it. To help students
follow the mathematical derivations, we provide extra steps whenever necessary and do not skip steps that
are necessary in the understanding of a derivation. Summaries of important issues are boxed and concepts
and terms are emphasized to help students grasp the main points and terminology. - Without any doubt, learning the material in signals and systems requires working analytical as well as com-
putational problems. It is important to provide problems of different levels of complexity to exercise not
only basic problem-solving skills, but to achieve a level of proficiency and mathematical sophistication.
The problems at the end of the chapter are of different types, some to be done analytically, others using