Understanding Digital Signal Processing by Richard Lyons

From the Publisher

This is undoubtedly the most accessible book on digital signal processing (DSP) available to the beginner. Using intuitive explanations and well-chosen examples, this book gives you the tools to develop a fundamental understanding of DSP theory. The author covers the essential mathematics by explaining the meaning and significance of the key DSP equations. Comprehensive in scope, and gentle in approach, the book will help you achieve a thorough grasp of the basics and move gradually to more sophisticated DSP concepts and applications.

Booknews

Begins with a complete explanation of periodic sampling followed by a lucid introduction to Fourier transform and its fast Fourier transform (FFT) implementation. Includes extensive information on both finite impulse response (FIR) and infinite impulse response (IIR) digital filters, as well as coverage of the benefits of signal averaging. In addition, the abstruse topics of the Convolution theorem and complex signals are demystified, and the practical uses of various binary number formats are carefully described and compared. Annotation c. by Book News, Inc., Portland, Or.

Product Details

• Table of Contents
• Forewords & Introductions
• Read an Excerpt

Table of Contents

Forewords & Introductions

When I first tried to learn DSP it was the best of times, it was the worst of times, it was a period of understanding, it was a period of confusion, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, I had everything before me, I had nothing before me, I was approaching enlightenment, I was doomed to ignorance. There were kings of DSP with large jaws and mathematical minds on their thrones in universities and industry research centers bestowing their knowledge in cryptic form. In both places it was clearer than crystal to the lords of technology, that things in general were settled forever. (With thanks, apologies, to Charles Dickens.)

Now that I'm finished "clowning around", I want you to know that learning DSP is not quite as dismal as the above paragraph implies. In fact, you're opportunity to learn DSP has never been better, and I hope my book further improves this situation. With that said, here are a few thoughts about the book:

Oh no, not another book on digital signal processing! Don't we have enough of those mysterious books with confusing diagrams and pages filled with equations? Yes, we do, but Understanding Digital Signal Processing is not one of those books. Understanding Digital Signal Processing, written specifically for beginners by someone who's been there, is new and different. A gentle introduction to digital signal processing (DSP), this book is DSP without tears.

Years ago, I realized that the DSP textbook market was in need of a "DSP For the Complete Idiot" kind of book. That is, a book that would enable the practicing engineer to understand the fundamental principles and speak the language of DSP without formal training. I was convinced that a book that provided a slow, gentle introduction, with well-chosen examples and plenty of drawings, would be useful to many people. I was sure that learning DSP just wasn't as hard to learn as it appeared.

If that's true, then why does the subject have the reputation of being hard to understand? The answer lies partially in how the material is typically presented in the literature. It's difficult to convey technical information, with its mathematical subtleties, in written form. It's one thing to write equations, but it's another matter altogether to explain what those equations really mean from a practical standpoint, and that's the goal of this book.

Too often written explanation of DSP theory appears in one of two forms: mathematical miracles occur and you're simply given a short and sweet equation without further explanation; or you face a flood of complex variable equations and phrases such as "it is obvious that," "such that W(f) is greater than or equal to 0 å f," and "with judicious application of the homogeneity property." In their defense, DSP authors provide the needed information, but too often the reader must grab a pick and shovel, put on a miner's helmet, and try to dig the information out of a mountain of mathematical expressions. How many times have you been forced to follow the derivation of an equation, after which the author states they're going to illustrate that equation with a physical example, which turns out to be just another equation? A recipe for technical writing that's too rich in equations is hard for the beginner to digest.

The broad field of digital signal processing (DSP) covers the processes of analyzing, filtering, generating, and transmitting signals that are in digital form. Due to the proliferation of computer hardware, and the power of DSP techniques, our technical world is rapidly going from analog to digital. Applications for DSP abound and are growing: from below us with deep-sea geological mapping to above us with deep-space communications and radio astronomy; from products as superfluous as talking greeting cards to applications as serious as medical imaging. Without DSP there would be no on-ramps to the Information Super Highway (Internet), no digital television, cellular phones or CDs, and special effects in the movies would still be clay models. This overwhelming change in technology, commercial products, and information from analog to digital sets the stage for the fundamental topics all practicing and future engineers and scientists must understand.

While the primary audience for this book is practicing electrical and software engineers, with no background in DSP, the book is useful for anyone analyzing, or manipulating data of any kind using a computer. This audience includes a wide array of professions because technology has switched its signal analysis and data communications processes from analog to digital. Understanding Digital Signal Processing can be beneficial to Electrical and Communications Engineers, Computer Programmers, Mechanical Engineers, Chemical Engineers, Physicists, and college students.

I wrote this book with one goal in mind; to provide an introduction to DSP that's readable, understandable, and comprehensive. With full sympathy for the struggling DSP beginner, I've tried to write a book that uses just enough mathematics to develop a fundamental understanding of DSP theory, and then illustrate that theory with examples.

The book attempts to:

• Enable the reader to understand the fundamental principles and speak the language of DSP without having to attend formal training.
• Concentrate on practical signal processing fundamentals as opposed to mathematically rigorous discussions of discrete system theory.
• Provide just enough mathematics to develop a fundamental understanding of the theory and then illustrate that theory using practical examples.
• Explain the meaning of every mathematical equation in the book and illustrate key equations with figures.
• Provide, in addition to a comprehensive index, a list of references at the end of each chapter for the DSP reader who wants to explore further

Next, you'll encounter the concepts used in advanced periodic sampling. The digital filter and advanced sampling chapters demystify the abstruse topics of the Convolution theorem and complex signals. The practical utility of binary number formats are also described and compared. Finally, a collection of tricks-of-the-trade, used by professionals to make DSP algorithms more efficient, is provided to help you apply DSP concepts successfully.

The appendices include a number of topics to help the beginner understand the mathematics of DSP, such as the arithmetic of complex numbers, complex signals and negative frequency, statistics fundamentals, and the use of the logarithmic decibel scale. The last appendix provides a glossary of the terminology used in the field of digital filters.

With Best Regards, and Wishes,

[-Rick-]

Read an Excerpt

Learning Digital Signal Processing

Learning the fundamentals, and how to speak the language, of digital signal processing does not require profound analytical skills or an extensive background in mathematics. All you need is a little experience with elementary algebra, knowledge of what a sinewave is, this book, and enthusiasm. This may sound hard to believe, particularly if you've just flipped through the pages of this book and seen figures and equations that appear rather complicated. The content here, you say, looks suspiciously like the material in technical journals and textbooks, material that is difficult to understand. Well, this is not just another book on digital signal processing.

This book's goal is to gently provide explanation followed by illustration, not so that you may understand the material, but that you must understand the material "Here we have the opportunity of expounding more clearly what has already been said" (Rene Descartes).

Remember the first time you saw two people playing chess? The game probably appeared to be mysterious and confusing. As you now know, no individual chess move is complicated. Given a little patience, the various chess moves are easy to learn. The game's complexity comes from deciding what combinations of moves to make and when to make them. So it is with understanding digital signal processing. First we learn the fundamental rules and processes and, then, practice using them in combination.

If learning digital signal processing is so easy, then why does the subject have the reputation of being difficult to understand? The answer lies partially in how the material is typically presented in the literature.It's difficult to convey technical information, with its mathematical subtleties, in written form. It's one thing to write equations, but it's another matter altogether to explain what those equations really mean from a practical standpoint, and that's the goal of this book.

Too often, written explanation of digital signal processing theory appears in one of two forms: either mathematical miracles occur and you are simply given a short and sweet equation without further explanation, or you are engulfed in a flood of complex variable equations and phrases such as "it is obvious that," "such that W(f) is greater than or equal to 0 å f," and "with judicious application of the homogeneity property." Authors usually do provide the needed information, but, too often, the reader must grab a pick and shovel, put on a miner's helmet, and try to dig the information out of a mountain of mathematical expressions. (This book presents the results of several fruitful mining expeditions.) How many times have you followed the derivation of an equation, after which the author states that he or she is going to illustrate that equation with a physical example-and this turns out to be another equation? Although mathematics is necessary to describe digital signal processing, I've tried to avoid overwhelming the reader because a recipe for technical writing that's too rich in equations is hard for the beginner to digest.

The intent of this book is expressed in a popular quote from E. B. White in the introduction of his Elements of Style (New York: Macmillan Publishing, 1959):

Will (Strunk) felt that the reader was in serious trouble most of the time, a man floundering in a swamp, and that it was the duty of anyone attempting to write English to drain the swamp quickly and get his man up on dry ground, or at least throw him a rope.

I've attempted to avoid the traditional instructor-student relationship, but, rather, to make reading this book like talking to a friend while walking in the park. I've used just enough mathematics to develop a fundamental understanding of the theory, and, then, illustrate that theory with examples.

The Journey

Learning digital signal processing is not something you accomplish; it's a journey you take. When you gain an understanding of some topic, questions arise that cause you to investigate some other facet of digital signal processing. Armed with more knowledge, you're likely to begin exploring further aspects of digital signal processing much like those shown in the following diagram. This book is your tour guide during the first steps of your journey.

You don't need a computer to learn the material in this book, but it would help. Digital signal processing software allows the beginner to verify signal processing theory through trial and error. "One must learn by doing the thing; for though you think you know it, you have no certainty until you try it" (Sophocles). In particular, software routines that plot signal data, perform the fast Fourier transform, and analyze digital filters would be very useful.

As you go through the material in this book, don't be discouraged if your understanding comes slowly. As the Greek mathematician Menaechmus curtly remarked to Alexander the Great, when asked for a quick explanation of mathematics, "There is no royal road to mathematics." Menaechmus was confident in telling Alexander that the only way to learn mathematics is through careful study. The same applies to digital signal processing. Also, don't worry if you have to read some of the material twice. While the concepts in this book are not as complicated as quantum physics, as mysterious as the lyrics of the song "Louie Louie," or as puzzling as the assembly instructions of a metal shed, they do get a little involved. They deserve your attention and thought. So go slow and read the material twice if you have to; you'll be glad you did. If you show persistence, to quote a phrase from Susan B. Anthony, "Failure is impossible."

Coming Attractions

Chapter 1 of this book begins by establishing the notation used throughout the remainder of our study. In that chapter, we introduce the concept of discrete signal sequences, show how they relate to continuous signals, and illustrate how those sequences can be depicted in both the time and frequency domains. In addition, Chapter 1 defines the operational symbols we'll use to build our signal processing system block diagrams. We conclude that chapter with a brief introduction to the idea of linear systems and see why linearity enables us to use a number of powerful mathematical tools in our analysis.

Chapter 2 introduces the most frequently misunderstood process in digital signal processing, periodic sampling. Although it's straightforward to grasp the concept of sampling a continuous signal, there are mathematical subtleties in the process that require thoughtful attention. Beginning gradually with simple examples of low-pass sampling and progressing to the interesting subject of bandpass sampling, Chapter 2 explains and quantifies the frequency-domain ambiguity (aliasing) associated with these important topics. The discussion there highlights the power and pitfalls of periodic sampling.

Chapter 3 is devoted to one of the foremost topics in digital signal processing, the discrete Fourier transform (DFT). Coverage begins with detailed examples illustrating the important properties of the DFT and how to interpret DFT spectral results, progresses to the topic of windows used to reduce DFT leakage, and discusses the processing gain afforded by the DFT. The chapter concludes with a detailed discussion of the various forms of the transform of rectangular functions that the beginner is likely to encounter in the literature. That last topic is included there to clarify and illustrate the DFT of both real and complex sinusoids.Chapter 4 covers the innovation that made the most profound impact on the field of digital signal processing, the fast Fourier transform (FFT). There we show the relationship of the popular radix-2 FFT to the DFT, quantify the powerful processing advantages gained by using the FFT, demonstrate why the FFT functions as it does, and present various FFT implementation structures. Chapter 4 also includes a list of recommendations to help us when we use the FFT in practice.

Chapter 5 ushers in the subject of digital filtering. Beginning with a simple low-pass finite impulse response (FIR) filter example, we carefully progress through the analysis of that filter's frequency-domain magnitude and phase response. Next we learn how window functions affect and can be used to design FIR filters. The methods for converting low-pass FIR filter designs to bandpass and highpass digital filters are presented, and the popular Remez Exchange (Parks McClellan) FIR filter design technique is introduced and illustrated by example. In that chapter we acquaint the reader with, and take the mystery out of, the process called convolution. Proceeding through several simple convolution examples, we conclude Chapter 5 with a discussion of the powerful convolution theorem and show why it's so useful as a qualitative tool in understanding digital signal processing.

Chapter 6 introduces a second class of digital filters, infinite impulse response (IIR) filters. In discussing several methods for the design of IIR filters, the reader is introduced to the powerful digital signal processing analysis tool called the z-transform. Because the z-transform is so closely related to the continuous Laplace transform, Chapter 6 starts by gently guiding the reader from the origin, through the properties, and on to the utility of the Laplace transform in preparation for learning the z-transform. We'll see how IIR filters are designed and implemented, and why their performance is so different from FIR filters. To indicate under what conditions these filters should be used, the chapter concludes with a qualitative comparison of the key properties of FIR and IIR filters.

Chapter 7 discusses two important advanced sampling techniques prominent in digital signal processing, quadrature sampling and digital resampling. In the chapter we discover why quadrature sampling is so useful when signal phase must be analyzed and preserved, and how this special sampling process can circumvent some of the limitations of traditional periodic sampling techniques. Our introduction to digital resampling shows how we can, and when we should, change the effective sample rate of discrete data after the data has already been digitized. We've delayed the discussion of digital resampling to this chapter because some knowledge of low-pass digital filters is necessary to understand how resampling schemes operate.

Chapter 8 covers the important topic of signal averaging. There we learn how averaging increases the accuracy of signal measurement schemes by reducing measurement background noise. This accuracy enhancement is called processing gain, and the chapter shows how to predict the processing gain associated with averaging signals in both the time and frequency domains. In addition, the key differences between coherent and incoherent averaging techniques are explained and demonstrated with examples. To complete the chapter, the popular scheme known as exponential averaging is covered in some detail.

Chapter 9 presents an introduction to the various binary number formats that the reader is likely to encounter in modern digital signal processing. We establish the precision and dynamic range afforded by these formats along with the inherent pitfalls associated with their use. Our exploration of the critical subject of binary data word width (in bits) naturally leads us to a discussion of the numerical resolution limitations of analog to digital (A/D) converters and how to determine the optimum A/D converter word size for a given application. The problems of data value overflow roundoff errors are covered along with a statistical introduction to the two most popular remedies for overflow, truncation and rounding. We end the chapter by covering the interesting subject of floating-point binary formats that allow us to overcome most of the limitations induced by fixed-point binary formats, particularly in reducing the ill effects of data overflow.

Chapter 10 provides a collection of tricks of the trade that the professionals often use to make their digital signal processing algorithms more efficient. Those techniques are compiled into a chapter at the end of the book for two reasons. First, it seems wise to keep our collection of tricks in one chapter so that we'll know where to find them in the future. Second, many of these schemes require an understanding of the material from the previous chapters, so the last chapter is an appropriate place to keep our collection of clever tricks. Exploring these techniques in detail verifies and reiterates many of the important ideas covered in previous chapters.

The appendices include a number of topics to help the beginner understand the mathematics of digital signal processing. A comprehensive description of the arithmetic of complex numbers is covered in Appendix A, while Appendix B derives the often used, but seldom explained, closed form of a geometric series. Appendix C strives to clarify the troubling topics of complex signals and negative frequency. The statistical concepts of mean, variance, and standard deviation are introduced and illustrated in Appendix D, and Appendix E provides a discussion of the origin and utility of the logarithmic decibel scale used to improve the magnitude resolution of spectral representations. In a slightly different vein, Appendix F provides a glossary of the terminology used in the field of digital filters.

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