数字信号处理——基于计算机的方法（第2版）（英文影印版）

书籍
通信书籍
　　 本书选材以数字信号处理的基础内容为主，同时也给出了现代信号处理部分内容。书中以主要篇幅讨论离散信号和离散系统的基本概念及其时域分析、变换域分析、数字滤波器的结构域设计、有限字长分析及随机信号的基本概念等。这是数字信号处理中的经典内容，也是进一步学习和掌握更多信号处理理论的基础。此外，本书讨论了多抽样率信号处理问题，其中的滤波器组（Filter Bank）是近十年来非常活跃的内容，广泛应用于带编码和小波变换。本书最后一章介绍数字信号处理的应用，并讨论现代谱估计的部分内容。
　　 本书具有丰富的例题、习题以及基于Matlab的信号处理算法的程序。
　　 本书非常适合电类专业高年级本科生用作教材，也可作为研究生的参考资料和工程技术人员的自学用书。
　　

preface xiii
1 signals and signal processing 1
1.1 characterization and classification of signals 1
1.2 typical signal processing operations 3
l.3 examples of typical signals 12
l.4 typical signal processing applications 22
l.5 why digital signal processing 37
2 discrete-time signals and systems in the time-domain 41
2.l discrete-time signals 42
2.2 typical sequences and sequence representation 53
2.3 the sampling process 60
2.4 discrete-time systems 63
2.5 time-domain characterization of lti discrete-time systems 71
2.6 finite-dimensional lti discrete-time systems 80
2.7 correlation of signals 88
2.8 random signals 94
2.9 summary 105
2.10 problems 106
2.11 matlab exercises 115
3 discrete-time signals in the transform-domain 117

　　 The field of digital signal processing (DSP) has seen explosive growth during the past three decades, as phenomenal advances both in research and application have been made. Fueling this growth have been the advances in digital computer technology and software development. Almost every electrical and computer engineering department in this country and abroad now offers one or more courses in digital signal processing. with the first course usually being offered at the senior level. This book is intended for a two-semester course on digital signal processing for seniors or first-year graduate students. It is also written at a level suitable for self-study by the practicing engineer or scientist.
　　 Even though the first edition of this book was published barely two years ago, based on ale feedback received from professors who adopted this book for their courses and many readers, it was clear that a new edition was needed to incorporate the suggested changes to the contents. A number of new topics have been included in the second edition. Likewise, a number of topics that are interesting but not practically useful have been removed because of size limitations. It was also felt that more worked-out examples were needed to explain new and difficult concepts.
　　 The new topics included in the second edition are: calculation of total solution, zero-input response, zero-state response, and impulse response of finite-dimensional discrete-time systems (Sections 2.6. l-2.6.3), correlation of signals and its applications (Section 2.7), inverse systems (Section 4.9), system identification (Section 4. IO), matched filter and its application (Section 4. 14), sampling of bandpass signals (Section 5.3), design of highpass, bandpass, and bandstop analog filters (Section 5.5), effect of sample-and-hold operation (Section 5.11 ), design of highpass, bandpass, and bandstop IIR digital filters (Section 7.4),design of FIR digital filters with least-mean-square error (Section 7.8), constrained least-square design of FIR digital filters (Section 7.9), perfect reconstruction two-channel FIR filter banks (Section IO.9), cosine- modulated L-channel filter banks (Section I0. 11), spectral analysis of random signals (Section l l .4), and sparse antenna array design (Section l l. 14). The topics that have been removed from the first edition are as follows: state-space representation of LTI discrete-time systems from Chapter 2, signal How-graph representation and state-space structures from Chapter 6, impulse invariance method of IIR filter design and HR filter design based on the frequency-sampling approach from Chapter 7, reduction of product round-off errors from state-space structures from Chapter 9, and voice privacy system from Chapter l l .The fractional sampling rate conversion using ale Lagrange interpolation has been moved to Chapter I0. Materials in each chapter are now organized more logically.
　　 A key feature of this book is the extensive use of MATLAB -based examples that illustrate the program's powerful capability to solve signal processing problems. The book uses a three-stage pedagogical structure designed to take full advantage of MATLAB and to avoid the pitfalls of a "cookbook" approach to problem solving. First, each chapter begins by developing the essential theory and algorithms. Second, the material is illustrated with examples solved by hand calculation. And third, solutions are derived using MATLAB. From the beginning, MATLAB codes are provided with enough details to permit the students to repeat ale examples on their computers. In addition to conventional theoretical problems requiring analytical solutions. each chapter also includes a large number of problems requiring solution via MATLAB. This book requires a minimal knowledge of MATLAB. I believe students learn the intricacies of problem solving with MATLAB faster by using tested, complete programs, and then writing simple programs to solve specific problems that are included at the ends of Chapters 2 to 11 .
　　 Because .computer verification enhances the understanding of the underlying theories and, as in the first edition, a large library of worked-out MATLAB programs are included in the second edition. The original MATLAB programs of the first edition have been updated to run on the newer versions of MATLAB and the Signal Processing Toolbox. In addition, new MATLAB programs and code fragments have been added in this edition. The reader can run these programs to verify the results included in the book. Altogether there are 90 MATLAB programs in the text that have been tested under version 5.3 of MATLAB and version 4.2 of the Signal Processing Toolbox. Some of the programs listed in this book are not necessarily the fastest with regard to their execution speeds, nor are they the shortest. They have been written for maximum clarity without detailed explanations.
　　 A second attractive feature of this book is the inclusion of 23t simple but practical examples that expose the reader to real-life signal processing problems which has been made possible by ale use of computers in solving practical design problems. This book also covers many topics of current interest not normally found in an upper-division text. Additional topics are also introduced to the reader through problems at the end of each chapter. Finally. the book concludes with a chapter that focuses on several important, practical applications of digital signal processing. These applications are easy to follow and do not require knowledge of other advanced-level courses.
　　 The prerequisite for this book is a junior-level course in linear continuous-time and discrete-time systems, which is usually required in most universities. A minimal review of linear systems and transforms is provided in the text, and basic materials from linear system theory are included, with important materials summarized in tables. This approach permits the inclusion of more advanced materials without significantly increasing the length of the book.
　　 The book is divided into l l chapters. Chapter l presents an introduction to the field of signal processing and provides an overview of signals and signal processing methods. Chapter 2 discusses the time-domain representations of discrete-time signals and discrete-time systems as sequences of numbers and describes classes of such signals and systems commonly encountered. Several basic discrete-time signals that play important roles in the time-domain characterization of arbitrary discrete-time signals and discrete-time systems are then introduced. Next, a number of basic operations to generate other sequences from one or more sequences are described. A combination of these operations is also used in developing a discrete-time system. The problem of representing a continuous-time signal by a discrete-time sequence is examined for a simple case. Finally, the time-domain characterization of discrete-time random signals is discussed.
　　 Chapter 3 is devoted to the transform-domain representations of a discrete-time sequence. Specifically discussed are the discrete-time Fourier transform (DTFT), the discrete Fourier transform (DFT), and the z-transform. Properties of each of these transforms are reviewed and a few simple applications outlined. The chapter ends with a discussion of the transform-domain representation of a random signal.
　　 This book concentrates almost exclusively on the. linear time-invariant discrete-time systems, and Chapter 4 discusses their transform-domain representations. Specific properties of such transform-domain representations are investigated, and several simple applications are considered.
　　 Chapter 5 is concerned primarily with the discrete-time processing of continuous-time signals. The conditions for discrete-time representation of a bandlimited continuous-time signal under ideal sampling and its exact recovery from the sampled version are 8rst derived. Several interface circuits are used for the discrete-time processing of continuous-time signals. Two of these circuits are the anti-aliasing filter and the reconstruction filter, which are analog lowpass filters. As a result, a brief review of the basic theory behind some commonly used analog filter design methods is included. and their use is illustrated with MATLAB. Other interface circuits discussed in this chapter are the sample-and-hold circuit, ale analog-to-digital convener. and the digital-to-analog convener.
　　 A structural representation using interconnected basic building blocks is the first step in the hardware or software implementation of an LTI digital filter. The structural representation provides the relations between some pertinent internal variables with the input and the output, which in turn provides the keys to the implementation. There are various forms of the structural representation of a digital filter, and two such representations are reviewed in Chapter 6, followed by a discussion of some popular schemes for the realization of real causal IIR and FIR digital filters. In addition, it describes a method for the realization of IIR digital filter structures that can be used for the generation of a pair of orthogonal sinusoidal sequences.
　　 Chapter 7 considers the digital filter design problem. First, it discusses the issues associated with the filter design problem. Then it describes the most popular approach to IIR filter design, based on the conversion of a prototype analog transfer function to a digital transfer function. The spectral transformation of one type of IIR transfer function into another type is discussed. Then a very simple approach to FIR filter design is described. Finally, the chapter reviews computer-aided design of both IIR and FIR digital filters. The use of MATLAB in digital filter design is illustrated.
　　 Chapter 8 is concerned with the implementation aspects of DSP algorithms. Two major issues concerning implementation are discussed first. The software implementations of digital filtering and DFT algorithms on a computer using MATLAB are reviewed to illustrate the main points. This is followed by a discussion of various schemes for the representation of number and signal variables on digital machines, which is basic to the development of methods for the analysis of finite wordlength effects considered in Chapter 9. Algorithms used to implement addition and multiplication, the two key arithmetic operations in digital signal processing, are reviewed next, along with operations developed to handle overflow. Finally, the chapter outlines two general methods for the design and implementation of tunable digital 81ters,followed by a discussion of algorithms for the approximation of certain special functions.
　　 Chapter 9 is devoted to analysis of the effects of the various sources of quantization errors; it describes structures that are less sensitive to these effects. Included here are discussions on the effect of coefficient quantization .
　　 Chapter 10 discusses multirate discrete-time systems with unequal sampling rates at various pans. The chapter includes a review of the basic concepts and properties of sampling rate alteration, design of decimation and interpolation digital filters, and multirate filler bank design.
　　 The final chapter. Chapter l 1, reviews a few simple practical applications of digital signal processing to provide a glimpse of its potential.
　　 The materials in this book have been used in a two-quarter course sequence on digital signal processing at the University of California, Santa Barbara, and have been extensively tested in the classroom for over IO years. Basically, Chapters 2 through 6 form the basis of an upper-division course, while Chapters 7 through 10 form the basis of a graduate-level coarse.
　　 Many topics included in this text can be omitted from class discussion, depending on the coverage of other courses in the curriculum. Because a senior-level course on random signals and systems is required of all electrical and computer engineering majors in most universities, materials in Sections 2.7, 3. 10, and 4.9 can be excluded from an upper-division course on digital signal processing. However, these topics ale important in the analysis of wordlength effects discussed in Chapter 9, and readers not familiar with this subject are encouraged to review these sections before reading Chapter 9. Likewise, Section 8.4 on number representation and Section 8.5 on arithmetic operations can similarly be omitted from discussion since most students taking a digital signal processing course usually take a course on digital hardware design.
　　 This text contains 231 examples, 90 MATLAB programs, 684 problems, and 186 MATLAB exercises.

　　 Digital SignalProcessing—A Computer-Based Approach(第2版)影印版序
　　 清华大学出版社为配合清华大学创建世界一流大学的规划，决定批量引进国外著名大学最新出版的高水平的原版教材。这不但对清华大学，而且对全国所有高校的学科建设及人才培养都有着重要的意义。现在出版的《Digital Signal Processing—— A Computer-Based Approach》一书即是最新引进的一种。这是一本值得推荐的好教材。
　　 该书的中文名字可以译为《数字信号处理——基于计算机的方法》。它由国际著名的McGraw—Hi11出版社于2001年最新出版。该书是美国加利福尼亚大学圣·巴巴拉分校的教材，作者是Sanjit K．Mitra教授。
　　 Mitra教授是国际上著名的信号处理专家。他在加利福尼亚大学伯克利分校获得硕士和博士学位，先后在康奈尔大学、AT＆T贝尔实验室、加利福尼亚大学戴维斯分校、圣·巴巴拉分校任教和工作。他曾任圣·巴巴拉分校电气与计算机工程系主任、IEEE电路与系统学会的主席，IEEE、AAAS和SPIE学会的Fellow，多个国际著名杂志的编委，获得过多项企业和学术界的奖励。他发表学术论文500多篇，出版了11本著作。本书在两年前出版了第l版，现在影印出版的是该书的第2版。
　　 在介绍本书的特点之前，有必要先谈一下本书所讨论的主题——“数字信号处理”。
　　 随着计算机和信息学科的飞速发展，数字信号处理(DSP)的理论与应用在过去的三十多年中获得了飞越式的发展，并已成长为一门极其重要的高新技术学科。简单地说，数字信号处理是利用计算机或专用处理设备，以数值计算的方法对信号进行采集、变换、综合、估值与识别等加工处理，借以达到提取信息和便于应用的目的。采用数字的方法处理信号比传统的模拟处理方法有着无法比拟的优点。
　　 数字信号处理的特点是其理论性和实践性都很强。理论性强，是指在综合应用众多的数学、电路理论、信号、系统和信息等领域知识的基础上，发展并形成了自己丰富的理论体系。实践性强，一方面指的是该学科的理论目前已成为众多新兴学科(如现代通信理论、自动控制、模式识别、故障诊断等)的重要理论基础；另一方面，是指数字信号处理的应用极其广泛，如在通信、控制、仪器、仪表、电力系统、电力电子、生物医学工程、机械及力学等领域。
　　 可以说，凡是和“信号”有关的学科领域都要用到DSP。
　　 目前，以数字信号处理器(DSP)为代表的高新技术产业正在世界范围内蓬勃兴起。另外，美国MathWork公司推出的Matlab科技应用软件现正在风靡全世界，其中的信号处理(Signal Processing)工具箱，以及和信号处理有关的工具箱(如小波、高阶谱分析等)更是学习和应用DSP的有力工具。DSP芯片的飞速发展及Matlab信号处理软件的不断完善又有力地促进了数字信号处理理论的发展，并为其开拓了更加广阔的应用空间。
　　 成功地将数字信号处理理论和DSP芯片用于实际，需要大批既掌握DSP的理论，同时又具有DSP硬件知识的高水平人才。现在，国内外重点大学的电气、通讯与计算机类的大部分院、系都为本科生或研究生开设了“数字信号处理”课程，有的还开设了“现代信号处理”课程。
　　 凡是从事过数字信号处理教学的老师，或是学习过该课程的同学都有一个共同的体会，即由于数字信号处理的理论性特别强、内容又特别多，所以非常希望能有一本或几本高水平的教材。本人在阅读了Mitra教授的《Digital Signal Processing—A Computer-Based Approach》一书后，感到该书确实是一本值得推荐的好教材。该书的特点是：
　　 1．本书的选材以数字信号处理的基础内容为主，同时也给出了现代信号处理的部分内容。书中以主要篇幅讨论了离散信号和离散系统的基本概念及其时域分析、变换域分析、数字滤波器的结构与设计、有限字长分析及随机信号的基本概念等。这是数字信号处理中的经典内容，也是进一步学习和掌握更多信号处理理论的基础。此外，本书用一章讨论子多抽样率信号处理问题，其中的滤波器组(Filter Bank)是近十年来非常活跃的内容，广泛应用于子带编码和小波变换。本书最后一章介绍了数字信号处理的应用，并讨论了现代谱估计的部分内容。所以，从本书的选材看，它非常适合电类专业高年级本科生用作教材，当然，也可作为研究生的参考用书和工程技术人员的自学用书。
　　 2．本书说理清楚，疑难处讨论得比较详尽。如书中关于FT、DTFT存在性的讨论，关于各种离散系统性质的讨论以及滤波器设计的讨论等都很有特色。这样，当学生预习或是自学书中的内容时，一般不会遇到困难。
　　 3．本书给出了大量的例子来讨论所要介绍的理论问题，这些例子共有231个，再加上说理清楚的特点，就使本书更具有可读性。这一方面有利于读者掌握书中的理论，另一方面有利于读者知道如何把这些理论应用于实际。
　　 4．本书另外一个重要的特点是把传统理论的讨论和Matlab相结合。前面已指出，Matlab是当前最优秀的科技应用软件，其中信号处理的内容极其丰富，包含了绝大部分信号处理算法的程序。二者的结合可以帮助读者在学习了信号处理理论的同时也学习了Matlab，并可以互相促进。书中给出了如个Matlab的子程序，基本上覆盖了本书要讨论的内容。这一特点也正是本书书名“基于计算机的方法”的内涵。
　　 5．本书的习题也很有特色，一是多，计684个；二是习题的质量相当高，有利于培养读者的思考能力和创新能力；三是给出了186个Matlab的练习，这非常有利于读者在计算机上去实践信号处理的众多理论和算法，同时也为把这些理论和算法用于工程实际打下了很好的基础。
　　 总之，由这本书可以看出，Mitra教授在数字信号处理教学方面有着丰富的经验；也可以看出，他在这本书的编写中确实下了很大的功夫，并把自己的教学经验反映在书中。所以，作为在国内长期从事数字信号处理教学的教师，我向国内的读者推荐Mitra教授的这本好教材。
　　 胡广书教授
　　 清华大学电机工程与应用电子技术系
　　 2001年5月