Digital Filter Design.pdf

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TOPICS IN DIGITAL SIGNAL PROCESSING C. S. BURRUS and T. W. PARKS: DFTIFFT AND CONVOLUTION ALGORITHMS Rice University T. W. PARKS and C. S. BUR RUS: DIGITAL FILTER DESIGN Cornell University and Rice University J. TREICHLER, R. JOHNSON, JR. and M . LARIMORE: THEORY AND DESIGN OF ADAPTIVE FILTERS Cornell University and Applied Signal Technology, Inc. W. KOHN: DIGITAL CONTROL (in preparation) Rice University

Digital Filter Design T. W. Parks School of Electrical Engineering Cornell University Ithaca, New York 14853 C. S. Burrus Department of Electrical and Computer Engineering Rice University Houston, Texas 77251 A WILEY-INTERSCIENCE PUBLICATION JOHN WlLEY & SONS, Inc. New York Chichester Brisbane Toronto Singapore

Copyright 0 1987 by Texas Instruments Incorporated Published by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work . beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. Library of Congress Cataloging-in-Publication Data: Parks, T. W. Digital filter design. "A Wiley-Interscience publication." Includes bibliographies and index. 1. Electric filters, Digital-Design and construction. L Burrus, C. S. 11. Title. TK7872.F5P37 ISBN 0-471 -82896-3 1987 621.3815'324 Printed in the United States of America 86-32500

To our parents William and Mildred Parks and Aleta Huffman

Preface This digital filter design book is addressed to the mathematician, scientist, or engineer who has an understanding of continuous-time signals and who has been introduced to discrete-time signal analysis. The main topic of this book is the frequency-domain analysis and design of linear, constant coefficient, digital filters. The book is divided into two major parts: finite-duration impulse-response (FIR) filters and infinite-duration impulse-response (IIR) filters. Each part consists of a complete, self-contained treatment of the corresponding filter type. All aspects of each filter type are discussed. Each part begins with a discussion of filter properties, which leads into material on design of the filter to meet frequency-domain specifications. This aspect of filter design is called the approximation problem and makes up a major portion of the book. Each of the two parts concludes with a chapter on realization pro- implementation of the filter with fixed-point arithmetic-the blem. The chapters on implementation both include a detailed design example that presents a step-by-step design and implementation of a typical filter. The design examples begin with the frequency-domain specifications for the filter and conclude with a listing of the assembly language program for implementing the filter on a signal-processing chip (the TMS32010 from Texas Instruments). The book begins with an introductory chapter that reviews the concepts of frequency-domain analysis of discrete-time systems and states the major problems in digital filter design. The final chapter summarizes the main results in the book with a discussion of the unique characteristics of the FIR and IIR filter types. An appendix with listings of ten FORTRAN programs for filter design is included. This book may be used in several ways. For some applications one might

viii Preface turn to the appendix, run the appropriate design program to get the coefficients of a filter that meets given frequency-domain specifications, then turn to the listing in the design example, insert the coefficients in the listing, and run the program on a TMS32010. If all goes smoothly in this process, one may not need to read and completely understand the theory in the book. However, if, as often happens, the problem one is faced with is not exactly covered by the programs in the appendix, then with some reading of the theory, one can probably modify the appropriate design program or write a special program to obtain the appropriate filter coefficients. Even if the coefficients can be obtained from a program in the appendix, the implementation in the design example may not be exactly what one wants. For example, the filter may take too much time to execute or may require too much memory or may have undesirable quantization effects. Again, some time spent in reading the theory in the chapters on implementation should allow the reader to develop an appropriate implem- entation of the desired digital filter. This book would not have been written without the support and encourage- ment of Texas Instruments, Inc. We would especially like to thank Mike Hames, who has always been ready with a smile and a helping hand when all of us realized just how much work is involved in writing a book. Maridene Lemmon has continued to patiently correct and improve our writing styles and has carefully read through countless revisions of the manuscript. The engineers at TI have read early versions of the text and helped correct our errors. We would like to thank Professor H. W. Schiissler who helped us begin to understand the issues in digital filter implementation when he was on leave at Rice University. Some of our examples are taken from his notes. We would like also to thank Cole Erskine for working out the two detailed design examples and for providing the necessary TMS32010 code. Jim Kaiser and Dick Roberts provided us with very thorough reviews of the manuscript and made several good suggestions, which we have incorporated in the text. We appreciate the long hours of reading put in by our graduate students Doug Jones and Henrik Sorenson, who have made many good suggestions for improving the book. Thanks also is given to the students at Rice University in our digital signal-processing courses who have helped us develop this book over the years.

Contents Part One INTRODUCTION 1. Introduction to Digital Filters 1.1. Properties of Discrete-Time Systems 1.2. Linear, Stationary, Discrete-Time Systems 1.3. Frequency Response and Transfer Functions 1.4. Digital Filter Design 1.4.1 The Approximation Problem 1.4.2 The Realization Problem 1.5. Properties of FIR and IIR Filters References Part Two FINITE IMPULSE-RESPONSE (FIR) FILTERS 2. Properties of Finite Impulse-Response Filters 2.1. Frequency-Domain Description of FIR Filters 2.2. Linear-Phase FIR Filters 2.2.1. Four Types of Linear-Phase FIR Filters 2.2.2. Calculation of FIR Filter Frequency Response 2.2.3. Zero Locations for Linear-Phase FIR Filters References

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