THIRD EDITION Discrete-Time Signal Processing Alan V. Oppenheim Massachusetts Institute of Technology Ronald W. Schafer Hewlett-Packard Laboratories · San Francisco · New York Upper Saddle River · London · Toronto · Sydney · Singapore · Tokyo · Montreal Indianapolis Dubai · Madrid · Hong Kong · Mexico City · Munich · Paris · Amsterdam · Cape Town · Boston · Columbus Vice President and Editorial Director, ECS: Marcia J. Horton Acquisition Editor: Andrew Gilfillan Editorial Assistant: William Opaluch Director of Team-Based Project Management: Vince O’Brien Senior Marketing Manager: Tim Galligan Marketing Assistant: Mack Patterson Senior Managing Editor: Scott Disanno Production Project Manager: Clare Romeo Senior Operations Specialist: Alan Fischer Operations Specialist: Lisa McDowell Art Director: Kristine Carney Cover Designer: Kristine Carney Cover Photo: Librado Romero/New York Times—Maps and Graphics Manager, Cover Photo Permissions: Karen Sanatar Composition: PreTeX Inc.: Paul Mailhot Printer/Binder: Courier Westford Typeface: 10/12 TimesTen Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on the appropriate page within the text. LabVIEW is a registered trademark of National Instruments, 11500 N Mopac Expwy, Austin, TX 78759-3504. Mathematica is a registered trademark of Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237. MATLAB and Simulink are registered trademarks of The MathWorks, 3 Apple Hill Drive, Natick, MA 01760-2098. © 2010, 1999, 1989 by Pearson Higher Education, Inc., Upper Saddle River, NJ 07458. All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright and permissions should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use materials from this work, please submit a written request to Pearson Higher Education, Permissions Department, One Lake Street, Upper Saddle River, NJ 07458. Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages with, or arising out of, the furnishing, performance, or use of these programs. Pearson Education Ltd., London Pearson Education Singapore, Pte. Ltd. Pearson Education Canada, Inc., Toronto Pearson Education–Japan, Tokyo Pearson Education Australia Pty. Ltd., Sydney Pearson Education North Asia Ltd., Hong Kong Pearson Education de Mexico, S.A. de C.V. Pearson Education Malaysia, Pte. Ltd. Pearson Education, Inc., Upper Saddle River, New Jersey 10 9 8 7 6 5 4 3 2 1 ISBN-13: 978-0-13-198842-2 ISBN-10: 0-13-198842-5 To Phyllis, Justine, and Jason To Dorothy, Bill, Tricia, Ken, and Kate and in memory of John This page intentionally left blank
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