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As digital signal processing parts become more easily available (and cheaper), more and more engineers are being forced to use them when doing design work. Although several excellent books cover the theory and rigorous mathematics of DSP, few—if any—have focused on the practical aspects of doing design work in DSP. This volume provides not only a solid introduction to communications theory and digital signal processing, but also provides practical information on DSP as it applies to telecommunications. KEY TOPICS: Discusses communications theory, mathematics, and notation; introduces the concepts, tools, and shortcomings of DSP; provides solved mathematical examples and computer program listings for implementing the algorithms; and devotes an entire section to applications of DSP in telecommunications—echo cancellation, transmultiplexers, voice-compression, and waveform generation. MARKET: For design engineers in the field of communications, engineers in the fields of defense and bio-electronics, and engineering managers.
I. INTRODUCTION TO COMMUNICATIONS THEORY.
1. Introductory Concepts. 2. Representation of Signals. 3. Linear Time Variant Systems. 4. Modulation. 5. Probability, Random Variables, and Stochastic Processes. 6. Filters.
II. DIGITAL SIGNAL PROCESSING.
1. The Sampling Theorem. 2. Elementary A/D and D/A Conversion. 3. Discrete-Time Linear Time Invariant Systems. 4. Models for Digital Filters. 5. The Discrete Fourier Transform (DFT). 6. Fast Fourier Transform (FFT) Algorithms. 7. Design of Digital Filters. 8. Delta- Sigma-Modulation Techniques Applied to A/D and D/A Conversion. 9. The Least Mean Square Algorithm and Basic Adaptive Filters. 10. Fundamental Considerations in the Hardware Implementation of Digital Filters.
III. APPLICATIONS OF DSP IN TELECOMMUNICATIONS.
1. The North American Hierarchy for Digital Signals. 2. Analog-to-Digital Conversion. 3. Linear Prediction and Speech Compression. 4. Implementation of Banks of Bandpass Filters. 5. The LMS Algorithm and Its Application in Echo Cancellers. 6. Waveform Generation.
This book is intended to be of use to two broad groups of readers. The first group comprises those who have good familiarity with Digital Signal Processing (DSP) and/or Telecommunications. The second group consists of those who need at least a casual or, perhaps, detailed, knowledge of the applications of DSP in telecommunications. A typical member of the second group is someone who is involved in a design project utilizing DSP but whose area of expertise is a different branch of electrical engineering, such as software, hardware, systems engineering, or application-specific integrated circuit (ASIC) design. Included in the second group are students who wish to get a feel for how DSP is applied.
The book is comprised of nine chapters.
The intent of Chapter 1 is to provide the spectrum of readership a preamble that puts the material in the subsequent chapters in perspective.
Chapters 2 and 3 are targeted toward the second group and cover the fundamental concepts of communication theory and digital signal processing.
Readers in the first group could skip directly to Chapter 4 or skim Chapters 2 and 3 to get a feel for the notation used.
Chapters 4 through 9 are reasonably self contained and draw on material from the first three chapters. Those well versed in telecommunications would find the material useful in understanding the concepts of DSP; experts in DSP would find a description of some telecommunications concepts in a familiar jargon.
Except for Chapters 1 and 5, one section of each chapter consists of selected exercises. For Chapters 2 and 3 these exercises are chosen to enhance the understanding of the material in a mathematical sense. Applying pencil and paper remains the best way to develop a proficiency in dealing with the mathematical, and sometimes abstract, notions introduced. The exercises in the later chapters assume the availability of some form of computing power, either a PC or ad workstation, or some other form of desktop computing. These exercises are better described as suggestions for computer programs to simulate the structures and execute the algorithms described in the text.
Chapter 1 discusses some of the unique characteristics and thought processes associated with the telephone channel. In particular, the implications of the access portion of a telephone channel, the coding requirements for conversion between analog and digital formats, and the need for echo control in circuits that have substantial transmission delay. From the viewpoint of transmission, the subscriber's signal is affected first by the cable plant that is used to physically connect the station set to the network. This connection, called the subscriber loop, materially impacts the signal, especially when the subscriber is geographically distant from the central office, a distance that could be in excess of three miles. At the central office the signal experiences bandlimiting; the telephone network principally supports channels that have a (nominal) cutoff frequency of about 4 kHz.
Furthermore, the signal is converted from analog to digital format using a nonlinear encoding proces s. The subscriber loop is full duplex, or "two-wire," with the cable pair supporting signals in both directions. The Network is "four-wire," assigning separate (possibly logically separate) paths for signals in the two directions. This split is achieved by a hybrid and the non ideal nature of the hybrid gives rise to the phenomenon of echo. The focus of Chapter 1 is an explanation of the principal characteristics and impairments of the subscriber loop, signal processing in the "line circuit, " signal processing in the trunking network, and the need for echo control. Since telecommunications has its own jargon with several acronyms, which often times have lost their origin, an appendix is provided where several commonly used acronyms are expanded and a short description provided in some cases.
The fundamental concepts of communication theory and signal processing are presented in Chapter 2. In particular, the essentials of signal theory, transforms, and linear time-invariant systems are discussed. The principles of modulation, with emphasis on amplitude modulation, as well as the basic signal processing associated with data transmission, is treated in a unified, though simple, fashion.
Chapter 3 extends these concepts to discrete-time and digital signal processing. The cornerstone of DSP, the sampling theorem, is discussed in detail and the notions of Fourier transforms and frequency response of discrete-time filters are developed as extensions of the concepts introduced in the derivation of the sampling theorem.
Chapter 3 also covers the essentials of the Z-transform, and FIR and IIR filters. Finite-word length effects in A/D and D/A conversion, as well as in the implementation of digital filters, are treated in a generic fashion as additive noise. Analog-to-digital and digital-to-analog conversion are implied whenever we use digital techniques to process real-world, i.e., analog, information-bearing signals. In telecommunications the main information signal is speech or speech-like. For such signals the conversion process can be tailored to achieve a desired behaviour.
Chapter 4 discusses the principles of quantization, a fundamental component of an A/D converter. Quantization can be "uniform," as in traditional converters, or "compan ded," the term used to describe the nonuniform quantization charateristics used in A-law and m-law converters. Quantization also plays a part in the digital implementation of discrete- time filters.
The impact of "finite wordlength" of information bearing (analog) signals. The fundamentals of differential encoding, adaptive quantizers, Adaptive Differential Pulse Code Modulation (ADPCM), linear predictive coding (LPC) techniques, and Digital Speech Interpolation (DSI) are introduced. The ADPCM algorithm described follows the world-wide standard agreed upon and additional performance information, not commonly available in the open literature, is provided. The applicability of LPC for speech compression is presented via an example: the EIA-IS-54 standard for digital cellular telephony, which includes the description of the encoding of the speech signal. In the same vein, the application of DSI to speech compression is described via a discussion of the key facets of an available product, the TC421 from DSC Communications Corp.
Chapter 6 covers techniques for echo control in detail. The approach taken is to describe the manner in which echo control is accomplished by the use of echo suppressors and echo cancelers. The latter is the method of choice in all new deployment. Echo cancelers are basically adaptive digital filters and one section of Chapter 6 is devoted to the underlying theory of adaptive filters used in this application.
The Discrete Fourier Transform (DFT), first introduced in Chapter 3, is treated in greater detail in Chapter 7 along with its companion, the Discrete Cosine Transform (DCT). From the viewpoint of telecommunications, the principal usage of the DFT and the DCT is in applications calling for a collection of bandpass filters. Two such applications are described. The popularity of the DFT, in a general sense, stems from the availability of algorithms, generically referred to as Fast Fourier Transforms (FFTs), which drastically reduce the computational burden associated with a DFT. The study of FFT algorithms is quite mature and the bibliography provides numerous articles and books that the interested reader can refer to for details. Bandpass filtering is usually accompanied by a change in sampling rate, that is interpolation, whereby the rate is increased, or decimation, whereby the rate is decreases. Chapter 7 provides an introduction to interpolation and decimation and discusses the use of "polyphase schematics," which are block diagram representations of signal processing accompanied by sampling rate changes.
Chapter 8 explains the principles of Delta Sigma Modulation, especially as applied to analog-to-digital and digital-to-analog conversion. The principal contribution of Chapter 8 is an explanation of the manner in which conversion wordlength can be traded-off with sampling frequency. Such converters, even when used to convert speech signals, operate at a high sampling rate, of the order of 1 MHz, and hence providing digital filters that operate at this high rate can be an expensive proposition unless the filters are simple. The use of the rectangular and triangular windows, simple filters that can be implemented very cost-effectively, is covered in detail and a guideline as to the performance of Delta Sigma Modulation in conjuction with such filters is quantified.
Digital filters are completely described by their transfer functions, that is, the coefficients of the polynomials that define the poles and zeros of the digital filter. The notion of designing a digital filter is thus equivalent to obtaining either the poles and zeros or the coefficients in such a manner that we obtain a stable filter whose frequency response approximates a desired shape.
Chapter 9 describes one particular design method, especially useful for recursive filter design, and that is not readily available in text books, in detail. One of the best ways to learn about DSP is to experiment with it. There are several software packages available that would automate many of the operations described in this book and provide wonderful, graphical, output so as to "visualize" the operation. Simulation of digital filters is quite straightforward since the description of the operations is in a form that is well suited for translation into a computer program. Further, computing power is sufficiently inexpensive such that desktop machines can run most, if not all, the programs available.
To the reader who has such computing power available, I strongly recommend the actual coding of algorithms since the process of so doing does add insight into the computational and control complexity of an actual implementation.
I have been fortunate in my career to have had the opportunity to apply DSP techniques in a variety of applications. I have been doubly blessed in having many associates whose field of expertise was not DSP, but who displayed a fierce desire to understand the principles of DSP as applied to the projects we were working on jointly. By demanding that I explain, to their satisfaction, not just what DSP principle was being applied but why it was appropriate, they planted the seed of this book. Since 1985 1 have been involved in teaching "Communication Theory and Applications," "Digital Signal Processing I," and "Digital Signal Processing II," under the auspices of The University of California, Berkeley, Extension Program. The lecture notes and general course content I generated in that effort form the basis for the Chapters 2 and 3. Chapters 4 through 9 are related very closely to the research and development efforts I have been personally involved with, starting as a graduate student at Stanford in the early 1970s, and subsequently at the ITT-Advanced Technology Center, Granger Associates/DSC Communications Corporation, and continuing at present at Telecom Solutions Inc.
Over the past 20 years of involvement with DSP, I have had the good fortune to be associated with some very bright people. I am indebted to my advisers at Stanford, the late Prof. A. M. Peterson and Dr. M.J. ("Sim") Narasimha, with whom I still have a close professional, and personal association; several colleagues at ITT, most notably Dr. B.P. Agrawal and Dr. Hyokang Chang, as well as Sarma Jayanthi and Doug Sutherland; Dr. Moon Song, Dr. Raphael Montalvo, Paul Yang, Pat Hanagan, Conne Skidan Enko, and Helena Ho at Granger/DSC; and several others, too numerous to list. Each one has contributed something to my own understanding of the subject and thus has made a contribution to this book.
More than any professional colleague, the one person who has made a significant impact is my wife, Amita, who dedicated a great deal of her time to the production of this book for publishing. While maintaining a household, raising our pre-schooler, and meeting the needs of her clients, she found the time and energy for the design and desktop-publishing effort associated with the production of this book, and its cover. Although my name appears as the author, the book is as much her creation as it is mine.
Kishan Shenoi
Saratoga, California