DISCRETE SYSTEMS and DIGITAL SIGNAL PROCESSING with M ATLAB ® Electrical Engineering Textbook Series Richard C. Dorf, Series Editor University of California, Davis Forthcoming and Published Titles Applied Vector Analysis Matiur Rahman and Isaac Mulolani Continuous Signals and Systems with MATLAB ® Taan ElAli and Mohammad A. Karim Discrete Systems and Digital Signal Processing with MATLAB ® Taan ElAli Electromagnetics Edward J. Rothwell and Michael J. Cloud Optimal Control Systems Desineni Subbaram Naidu Taan S. ElAli CRC PRESS Boca Raton London New York Washington, D.C. DISCRETE SYSTEMS and DIGITAL SIGNAL PROCESSING with M ATLAB ® This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. Visit the CRC Press Web site at www.crcpress.com © 2004 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-1093-8 Library of Congress Card Number 2003053184 Library of Congress Cataloging-in-Publication Data Elali, Taan S. Discrete systems and digital signal processing with MATLAB / Taan S. Elali. p. cm. (Electrical engineering textbook series) Includes bibliographical references and index. ISBN 0-8493-1093-8 (alk. paper) 1. Signal processing--Digital techniques--Mathematics. 2. MATLAB. I. Title II. Series. TK5102.9.E35 2003 621.382’2—dc21 2003053184 Catalog record is available from the Library of Congress This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” ISBN 0-203-48711-7 Master e-book ISBN ISBN 0-203-58523-2(Adobe eReader Format) Preface All books on linear systems for undergraduates cover both the discrete and the continuous systems material together in one book. In addition, they also include topics in discrete and continuous filter design, and discrete and continuous state-space representations. However, with this magnitude of coverage, although students typically get a little of both continuous and discrete linear systems, they do not get enough of either. A minimal coverage of continuous linear systems material is acceptable provided there is ample coverage of discrete linear systems. On the other hand, minimal coverage of discrete linear systems does not suffice for either of these two areas. Under the best of circumstances, a student needs solid background in both of these subjects. No wonder these two areas are now being taught separately in so many institutions. Discrete linear systems is a big area by itself and deserves a single book devoted to it. The objective of this book is to present all the required material that an undergraduate student will need to master this subject matter and to master the use of M ATLAB 1 in solving problems in this subject. This book is primarily intended for electrical and computer engineering students, and especially for the use of juniors or seniors in these undergrad- uate engineering disciplines. It can also be very useful to practicing engi- neers. It is detailed, broad, based on mathematical basic principles and focused, and contains many solved problems using analytical tools as well as M ATLAB . The book is ideal for a one-semester course in the area of discrete linear systems or digital signal processing where the instructor can cover all chap- ters with ease. Numerous examples are presented within each chapter to illustrate each concept when and where it is presented. In addition, there are end-of-chapter examples that demonstrate the theory presented. Most of the worked-out examples are first solved analytically and then solved using M ATLAB in a clear and understandable fashion. The book concentrates on understanding the subject matter with an easy- to-follow mathematical development and many solved examples. It covers all traditional topics plus stand-alone chapters on transformations and con- tinuous filter design, which should be covered before attempting the IIR digital filter design. These chapters (transformation and continuous filter design) plus the two comprehensive chapters on IIR and FIR digital filter design make this book unique in terms of its thorough and comprehensive 1 MATLAB is a registered trademark of The Mathworks, Inc. For product information, please contact: The Mathworks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098. Tel: 508-647-7000. www.mathworks.com. treatment. A complete chapter on state-space is presented. Another chapter summarizes all representations used in describing discrete linear systems with many examples and illustrations. A very comprehensive chapter on the DFT and FFT is also unique in terms of the FFT applications. In working with the examples that are solved with M ATLAB , the reader will not need to be fluent in this powerful programming language, because they are presented in a self-explanatory way. To the Instructor: All chapters can be covered in one semester. In a quarter system, Chapters 8 and 9 can be skipped. The M ATLAB m-files used with this book can be obtained from the publisher. To the Student: Familiarity with calculus, differential equations and pro- gramming knowledge is desirable. In cases where other background material needs to be presented, that material directly precedes the topic under con- sideration (just-in-time approach). This unique approach will help the stu- dent stay focused on that particular topic. In this book there are three forms of the numerical solutions presented using M ATLAB , which allows you to type any command at its prompt and then press the Enter key to get the results. This is one form. Another form is the M ATLAB script which is a set of M ATLAB commands to be typed and saved in a file. You can run this file by typing its name at the M ATLAB prompt and then pressing the Enter key. The third form is the M ATLAB function form where it is created and run in the same way as the script file. The only difference is that the name of the M ATLAB function file is specific and may not be renamed. To the Practicing Engineer: The practicing engineer will find this book very useful. The topics of discrete systems and signal processing are of most importance to electrical and computer engineers. The book uses M ATLAB , an invaluable tool for the practicing engineer, to solve most of the problems. Author Taan S. ElAli, Ph.D., is a full professor of engineering and computer science at Wilberforce University, Wilberforce, Ohio. He received his B.S. degree in electrical engineering in 1987 from The Ohio State University, Columbus, an M.S. degree in systems engineering in 1989 from Wright State University, Dayton, Ohio and an M.S. in applied mathematics and Ph.D. in electrical engineering, with a specialization in systems, from the University of Dayton in 1991 and 1993, respectively. He has more than 12 years teaching and research experience in the areas of discrete and continuous signals and systems. He was listed in “Who’s Who Among America’s Teachers” for 1998 and 2000. He is also listed in “Who’s Who in America” for 2004. Dr. ElAli has contributed many journal articles and conference presenta- tions in the area of systems. He has been extensively involved in the estab- lishment of the electrical and computer degree programs and curriculum development at Wilberforce University. He is the author of Introduction to Engineering and Computer Science with C and M ATLAB and Continuous Signals and Systems with M ATLAB . Dr. ElAli has contributed a chapter to The Engineer- ing Handbook published by CRC Press.