Applied Introduction to Digital Signal Processing

From the Inside Flap:

PREFACE

The digital signal processing (DSP) revolution has drastically changed the way electronic circuits are designed. It has brought new possibilities that were once deemed impossible using conventional analog circuitry. Digital signal processors are used in CD players, cellular telephones, music synthesizers, and high-speed modems, to name just a few of the items that are now considered among the necessities of life. What magic makes these marvelous devices work? What do readers need to know to start using this technology? The goal of this book is to introduce readers to DSP so that they can incorporate some of this technology into their designs.

This book is based on seven years of experience teaching this subject at the college level. The goal is for readers to understand the fundamentals of DSP so that they may design and implement signal synthesis, signal analysis, filters, and modulators on any digital signal processor. The book provides readers the background necessary to attend seminars and to further their studies.

It is widely recognized that the mathematics supporting DSP prevents many good technically-oriented people from studying the subject. The challenge was to find an approach that would be both intuitive and familiar to undergraduate students. Since vector arithmetic is used very early in most technology programs to explain the basics of most scientific topics, this book relies on these simple arrows along with some of the basic rules of mathematics to introduce the subject. This allows the use of an intuitive graphical approach. Readers will be surprised at how fast they become familiar with the material. They will quickly acquire enough DSP literacy to understand the basics that drive this technology and the major issues that drive practical designs. In the process, they will acquire the basic knowledge to implement simple DSP applications.

This book delivers enough of the basics so readers can use many features of the readily available filter design software packages that automatically perform most of the math. For example, readers will be able to use filter design software packages to design almost any of the standard filters, including Butterworth and Chebyshev filters. Readers will then be able to program these filters onto a digital signal processor of their choice. Additionally, the equations that are developed in this book may be exercised using popular number-calculating software such as spreadsheets. TARGET AUDIENCE

It is assumed that readers are either engineers who have forgotten a good deal of math or undergraduate students who understand the basics of passive circuits such as RC networks. Readers should also have some elementary programming background and an understanding of simple binary systems. Two appendices thoroughly review vector arithmetic and binary manipulation concepts to help readers comprehend the material.

Most of the complicated math and calculus is used only on rare occasions to provide a reference for the curious. In cases of mathematical derivations, readers can skip to the bottom line where the result is explained in simple, practical terms.

This book is well suited to cover an undergraduate course in the second year of a technology or engineering program. It is particularly well adapted to computer engineering or electronics technology programs. The material covered will provide graduates with a fundamental understanding of one of the essential high-tech tools to face today's technological challenges. ORGANIZATION OF THE TEXT

Chapter 1 answers the most common question newcomers ask about DSP: "How do digital signal processors differ from other types of processors?" The chapter links readers' elementary programming knowledge to the DSP environment. It also provides readers the terminology required to comprehend most seminars that cover new processors. The content of this chapter is not essential to cover Chapters 2 through 8, but it does provide some of the background necessary to cover Chapter 9.

Chapter 2 provides a painless introduction to the things that can be done with strings of numbers. Strictly speaking, this chapter does not cover digital signal processing; however, it does provide some of the basics about signals, which readers need to understand the following chapters. It introduces continuous-time and discrete-time concepts and explains periodic signals, as well as harmonic components, by using the practical application of signal synthesis. The material covered in this chapter also provides opportunities to explore many applications in a laboratory environment.

Chapter 3 focuses on some of the most important properties that relate to digital signals. The material covered here is essential to understanding all of the other chapters. Subjects such as the sampling theorem, antialiasing input filters, and reconstructing output filters are concepts that must be learned in order to deal with any DSP system.

Chapter 4 deals with the basic hardware aspects of DSP systems. It examines the system philosophically as a black box and develops theories that explain what happens inside the box. The chapter presents the difference equation, which is used to define the operation of filter systems. It also introduces the impulse response technique that may be used to test systems and develops a simple criterion to determine system stability. The important convolution operation is also developed in this chapter.

Chapter 5 is devoted entirely to spectral analysis. The approach is completely unconventional because it relies on some of the synthesis rules to develop the analysis technique. It is also unconventional in its uses of vectors to illustrate the operation of the discrete Fourier transform.

Chapter 6 is concerned with the frequency response of systems. It develops a technique that uses the value of the difference equation coefficients to compute the gain and phase response of systems. The discrete-time Fourier transform is an invaluable tool to determine the frequency domain behavior of systems. The chapter also examines the response of DAC systems, which are part of almost all DSP systems. The concept of an equalizer is introduced and used to compensate for undesired frequency characteristics.

Chapter 7 develops the Z-transform, which is used to design the response of systems. It uses the concept of poles and zeros to build the system response. A graphical method using vectors provides readers an intuitive approach in positioning poles and zeros. Important concepts such as stability are explored, and practical aspects such as coefficient quantizing are examined. Oscillator systems are designed based on the positioning of poles and on trigonometric identities.

Chapter 8 is a filter primer that describes the various popular types of filters. It covers filter concepts such as filter bands, linear-phase filters, phase equalizers (all pass), and describes the characteristics of standard filters such as the Bessel, Butterworth, and Chebyshev. Design techniques, such as the bilinear transform, windowing, and the positioning of poles and zeros to implement narrowband notch filters, are also described.

Chapter 9 covers the implementation of DSP systems using some of the most popular programming structures. It develops the various structures and identifies the strengths and weaknesses of each. FIR filters are implemented using both the direct form and the cascaded form. IIR filters are implemented using a cascade of both direct form II and transposed structures. Basic concepts of noise control are introduced and applied to programming techniques. Issues of scaling are addressed using practical examples.

Appendix A reviews complex arithmetic as applied to vectors. It covers complex numbers, complex exponentials, and Euler's identity, and develops the algebra necessary to manipulate complex numbers and vectors. It also defines magnitude, angle, and argument and shows how to plot complex numbers and vectors on an Argand diagram.

Appendix B reviews the binary systems, formats, and manipulations necessary for programming DSP applications. It covers fixed-point and floating-point numbers, addition, multiplication, quantization, and tolerance. ACKNOWLEDGMENTS

Writing a book verifies one of Murphy's fundamental laws: "Completing a project will take at least twice as much time as your worst-case estimate." One cannot bring such an endeavor to successful completion and keep one's sanity without the precious support of colleagues, friends, and family.

The material in this book could not have been assembled without the comments and thoughtful reviews of numerous people that provided input. I would like to extend my gratitude to the many students who gave me support and feedback. I am especially indebted to my friends Paul Arseneault and Bob Southern, who have been most generous with their time, spending many long hours reading the draft material.

I also thank the following reviewers for their valuable suggestions: Ray Bashnick, Texas A&M University; David Birkett, Wentworth Institute of Technology; James LeBlanc, New Mexico State University; Mike Tsalsanis, Stevens Institute of Technology; Guoliang Zeng, Arizona State University; and Omar Zia, Southern Polytechnic Institute.

A special note of appreciation goes to my good friend Gerd Schneider with whom I have been playing squash and having breakfast twice a week for more than ten years. His encouragement, support, and ever-present optimism have been important factors in maintaining my enthusiasm for this project.

I also extend my gratitude and special thanks to Brigitte and Catherine, my two teenage daughters, mostly for their patience and understanding during the long hours I spent in front of that computer.

Last but certainly not least, to my beloved Mariette, whose support and presence allowed me to bring this project to fruition. Merçi de to compréhension, de to patience, et de ton amour.

Philippe Déziel
dezielp@algonquincollege

From the Back Cover:

This important book introduces the fundamentals of digital signal processing. Its goal is to help the reader design and implement signal synthesis, signal analysis, filters, and modulators on any digital signal processor. The following unique features differentiate this book from others:

• Use of an intuitive graphical approach
• Use of vector arithmetic
• Includes manipulation of binary numbers
• Presents filter performance issues
• Contains real, practical applications

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