信号与系统全面探索：理论与应用详解

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《信号与系统》是一本针对本科水平课程编写的教材，全面探讨了信号与系统的概念和方法，特别注重连续时间和离散时间理论的平行发展，强调两者之间的相似性和差异性。作者Mahmood Nahvi以加州理工学院圣路易斯奥比斯波分校的荣誉电气工程教授身份编写此书，它旨在为读者提供一个相对独立的学习框架，无需预先掌握系统分析、卷积、傅立叶分析或拉普拉斯和z变换等基础知识。该书的结构设计使得初学者能够轻松理解信号处理的基本原理，包括但不限于滤波、通信技术、连续时间信号的离散处理以及反馈控制等领域。作者通过实例和应用来介绍这些基本方法，使理论知识更具实际操作意义。值得注意的是，版权方面，《信号与系统》由McGraw-Hill出版，受《麦格劳-希尔公司》所有。根据版权法，未经该公司事先书面许可，任何部分内容均不得以任何形式复制、分发或存储，包括但不限于网络传输、电子存储或远程学习等。此外，作者和出版商虽已尽力确保内容的准确性，但并不对书中材料或程序的完整性和适用性做出保证，也不承担因出版而产生的任何间接损失。该教材可能还包含一些辅助材料，如电子版和印刷版组件，但具体哪些资源可供使用可能会有所限制。《信号与系统》是一本旨在为学生提供扎实信号处理基础，并引导他们进入实际应用领域的核心教材，适合那些希望深入理解信号处理及其在现代信息技术领域中作用的读者。

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Contents xv

17.12 Problems 983

17.13 Project: DFT Spectral Analysis 993

Chapter 18

System Function, the Frequency

Response, and Digital Filters 1005

Introduction and Summary 1005

18.1 The System Function H(z) 1006

18.2 Poles and Zeros 1011

18.3 The Frequency Response

H(ω) 1015

18.4 Vectorial Interpretation of H(z)

and H(ω) 1025

18.5 Transforming Continuous Time

to Discrete Time 1029

18.6 Digital Filters 1036

18.7 Simple Filters 1039

18.8 Filter Design 1044

18.9 Filter Design by Pole-Zero

Placement 1046

18.10 FIR Filter Design 1047

18.11 IIR Filter Design 1052

18.12 Filter Structures 1055

18.13 Problems 1060

18.14 Project 1: FIR Filter Design by

Windowing 1081

18.15 Project 2: Discrete-Time Modeling

and Control of a Dynamic

System 1084

18.16 Project 3: Modeling a Random Trace

Generator 1090

Appendix ElectricCircuits 1093

Index 1107

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PREFACE

The subject of signals and systems is a requirement in undergraduate electrical and

computer engineering programs. The subject provides the student a window through

which he or she can look into and examine the ﬁeld. In addition, it provides the necessary

background for more specialized subjects, including communication, control, and signal

processing. Several other engineering majors offer similar courses in the same subject

matter.

This book is designed to serve as the primary textbook for a course in signals and

systems at the junior undergraduate level. It is to be used mainly in the electrical, elec-

tronics, and computer engineering programs but is also appropriate for other engineering

majors. It may be used in a one- or two-semester or two-quarter sequence according to the

criteria of the curriculum and depending on an appropriate selection of material which

meets the needs and backgrounds of students.

This book treats the continuous- and discrete-time domains separately in two parts.

Part One (Chapters 1–9) covers continuous-time signals and systems; Part Two

(Chapters 10–18) covers discrete-time signals and systems. Both parts stand alone

and can be used independently of each other. This allows instructors to use the text

for instruction on either domain separately, if desired. The book may also be used for

courses that teach the two domains simultaneously in an integrated way, as the chapters

in Parts One and Two provide parallel presentations of each subject. The parallelism

of the chapters on the continuous- and discrete-time domains facilitates the integra-

tion of the two parts and allows for ﬂexibility of use in various curricula. The chapter

topics and the parallelism between the time-domain treatments are listed in the table

below.

Part One, Continuous-Time Domain Part Two, Discrete-Time Domain

Chapter Topic Chapter Topic

1 Introduction to Signals 10 Time-Domain Sampling and Reconstruction

2 Sinusoids 11 Discrete-Time Signals

3 Systems, Linearity, and Time Invariance 12 Linear Time-Invariant Discrete-Time Systems

4 Superposition, Convolution, and Correlation 13 Discrete Convolution

5 Differential Equations and LTI Systems 14 LTI Difference Equations

6 The Laplace Transform and Its Applications 15 The z-Transform and Its Applications

7Fourier Series 16 Discrete-Time Fourier Transform

8Fourier Transform 17 Discrete Fourier Transforms

9 System Function, the Frequency Response, 18 System Function, the Frequency Response,

and Analog Filters and Digital Filters

Whether the subject of signals and systems in the continuous- and discrete-time

domains is taught separately or in integrated form, the present organization of the book

provides both pedagogical and practical advantages. A considerable part of the subject

matter in signals and systems is on analysis techniques (such as solution methods in the

time and frequency domains) which, although conceptually similar, use different tools.

xvii

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xviii Preface

Introducing the tools and applying them separately simpliﬁes the structure of the course.

Another advantage of the present organization is that the analyses of signals and systems

in the continuous- and discrete-time domains can stand on their own (both conceptually

and in terms of analysis tools). Each domain may be taught without requiring the other.

Thus, for programs that are designed to offer a DSP course, the discrete-time part of the

book will satisfy the prerequisites of such a course.

Each part begins with the introduction of signals and their models in the time do-

main. It then deﬁnes systems, linearity, and time invariance, along with examples. Time-

domain solution methods, such as convolution and differential/difference equations, are

presented next, followed by the transform domains. These are brought together in cap-

stone chapters on the system function and frequency response. Chapter 10 on sampling

provides a bridge between the continuous- and discrete-time domains.

Each chapter is made of sections and no subsections. Each section addresses a

single discussion item, starting with the introduction of a topic, mathematical tools

used to address that topic, the application of those tools, and one or two examples. To

a large extent, therefore, each section is a learning unit and can provide the student

with a concluding marker in learning the subject. In that sense the sections are modular

and convenient for instruction. The modular organization of the book provides a direct

approach and an effective tool for learning the fundamentals of signals and systems. As

avehicle for lectures, 5 to 10 essential sections may be covered in an hour, while others

may be assigned as outside reading or homework.

Reference to other sections, ﬁgures, formulas, and other chapters is kept to a min-

imum. This provides easy and direct access to material, a feature much preferred by

students and instructors. The modular structure of the chapters and sections also makes

the book a convenient tool for instructional needs in a wide range of teaching scenarios

at various levels of complexity.

Illustrative examples, end-of-chapter problems, and supplementary problems with

solutions comprise other important components of the book. The book contains a total

of nearly 475 examples, 175 problems with solutions, and 750 end-of-chapter problems.

The examples and problems are of two types: (1) mathematical analyses and exercises

that represent abstractions of engineering subjects and (2) contextual problems, such

as those seen in electric circuits and devices, communication, and control. For the EE

and CPE student these subjects provide a context to convey and develop fundamental

concepts in signals and systems.

Examples from familiar signals and tangible systems in engineering can illustrate the

utility of the relevant mathematical analysis. They can make the subject more attractive

and generate motivation. In accordance with the above pedagogy, the book assumes

that the reader is familiar with the operation of basic circuits and devices (such as

passive RLC circuits and active circuits including dependent sources and operational

ampliﬁer models) and uses these to illustrate and reinforce the mathematical concepts.

It also assumes familiarity with elementary trigonometric functions, complex numbers,

differentiation/integration, and matrices. The Appendix at the end of the book can be

used to refresh the reader’s memory on electric circuits.

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Preface xix

ORGANIZATION OF CHAPTERS

The detailed outline of the ﬁrst part, covering signals and systems in the continuous-time

domain, is as follows.

Chapter 1 introduces various signal types (such as those that are natural, societal, or

human-made) and their models.Itshowsthat,asfunctionsof time, signals are speciﬁed by

a wide set of parameters and characteristics (e.g., rate of change, time course, periodicity,

and ﬁne, coarse, and nested-loops structures). Time averages are discussed, along with

some simple operations on signals.

Chapter 2 is on sinusoids and contains a review of basic trigonometry. The examples

in this chapter employ simple sinusoids in illustrating some topics of practical interest

such as phase and group delay, power, and more.

Chapter 3 introduces the deﬁnitions of linearity and time invariance. Examples teach

the student how to test for these properties. This initial chapter is not intended to cover all

properties of LTI systems, but only as much as is needed at this stage in such a course on

signals and systems. More exposure will be provided throughout other parts of the book.

Chapter 4 discusses the time-domain solution of LTI systems by convolution.Convo-

lution of a system’s unit-impulse response with the input produces the system’s response

to that input. The chapter starts with convolution as a method of obtaining the response

of a linear system. It uses the linearity and superposition properties to develop the convo-

lution sum and integral. It then illustrates their evaluation by numerical, analytical, and

graphical methods. The ﬁltering property of convolution is explained next. The chapter

also brieﬂy touches on deconvolution. This latter concept is brought up in future chapters

on solutions in the frequency domain.

Chapter 5 presents the time-domain solution of LTI systems by an examination of

their describing differential equations in classical form. Parallels are drawn between

the homogeneous and particular components of the total solution and the familiar com-

ponents in the response of physical systems; that is, the natural and forced parts of the

response from system analysis and design. The homogeneous and particular components

of the total solution are then also related to the zero-input and zero-state responses. An

example of a numerical computation of a response is provided at the end of the chapter.

Chapter 6 analyzes the solution of LTI systems by the Laplace transform in the

frequencydomain. Both the unilateral and bilateral forms of the transform are considered.

The ﬁrst half of the chapter focuses on the unilateral version, its inverse evaluation by the

partial fraction expansion method, and some applications. The residue method of ﬁnding

the inverse is also presented. The second half addresses the bilateral Laplace transform

and its inverse. Comprehensive examples demonstrate how to obtain the response of an

LTI system by the frequency domain approach and observe parallels with those in the

time domain.

Chapters 7 and 8 are on Fourier analysis in the continuous-time domain. Chapter

7 discusses the Fourier series expansion of periodic signals, in both trigonometric and

exponential forms, and visualizes methods of extending the expansion to nonperiodic

signals, which is a topic presented in detail in Chapter 8. Introduction of the impulse

function in the frequency domain provides a uniﬁed method of Fourier analysis for a

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