Mitra: Digital Signal Processing

Mitra: Digital Signal Processing, 2/e

Preface

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 the feedback received from professors who adopted the 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 2.6.1-2.6.3), correlation of signals and its applications (Section 2.7), inverse systems (Section 4.9), system identification (Section 4.10), 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 10.9), cosine-modulated L-channel filter banks (Section 10.11), spectral analysis of random signals (Section 11.4), and sparse antenna array design (Section 11.14). 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 flow-graph representation and state-space structures from Chapter 6, impulse invariance method of IIR filter design and FIR 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 11. The fractional sampling rate conversion using the Lagrange interpolation has been moved to Chapter 10. Materials in each chapter are now organized more logically.

A key feature of this book is the extensive use of MATLAB®-based¹ examples that illustrate the program's powerful capability to solve digital 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 the 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 writing simple programs to solve specific problems that are included at the ends of Chapters 2 to 11.

¹MATLAB is a registered trademark of The MathWorks, Inc., 24 Prime Park Way, Natick, MA 01760-1500, Phone: 508-647-7000, http://www.mathworks.com.

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 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 231 simple but practical examples that expose the reader to real-life signal processing problems which has been made possible by the 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-leve 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 11 chapters. Chapter 1 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 first 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, the analog-to-digital converter, and the digital-to-analog converter.

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 discussed 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 filters, 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 parts. The chapter includes a review of the basic concepts and properties of sampling rate alteration, design of decimation and interpolation digital filters, and multirate filter bank design.

The final chapter, Chapter 11, 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 10 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 course.

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 are 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.

Every attempt has been made to ensure the accuracy of all materials in this book, including the MATLAB programs. I would, however, appreciate readers bringing to my attention any errors that may appear in the printed version for reasons beyond by control and that of the publisher. These errors and any other comments can be communicated to me by e-mail addressed to: mitra@ece.ucsb.edu .

Finally, I have been particularly fortunate to have had the opportunity to work with the outstanding students who were in my research group during my teaching career, which spans over 35 years. I have benefited immensely, and continue to do so, both professionally and personally, from my friendship and association with them, and to them I dedicate this book.

Sanjit K. Mitra

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