A Friendly Guide to Wavelets

I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of

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To Yadwiga-Wanda and Stanisiaw Wiodek, to Teofila and Franciszek Kowalik, and to their children Janusz, Krystyn, Mirek, and Renia. Risking their collective lives, they took a strangers' infant into their homes and hearts. Who among us would have the heart and the courage of these simple country people? To my mother Cesia, who survived the Nazi horrors, and to my father Bernard, who did not. And to the uncounted multitude of others, less fortunate than I, who did not live to sing their song.

A Friendly Guide t o Wavelets

Gerald Kaiser

Reprint of the 1994 Edition §? Birkhauser

Gerald Kaiser Center for Signals and Waves 3608 Govalle Avenue Austin, TX 78702 U.S.A. [email protected] www.wavelets.com

Originally published as a hard cover edition.

ISBN 978-0-8176-8110-4 DOI 10.1007/978-0-8176-8111-1

e-ISBN 978-0-8176-8111-1

ISBN 978-0-8176-8110-4 e-ISBN 978-0-8176-8111-1 Library of Congress Control Number: PCN applied for DOI 10.1007/978-0-8176-8111-1 Mathematics Subject Classification (2010): 15-XX, 30-XX, 31-XX, 32-XX, 35-XX, 41-XX, 42-XX, 44-XX, 46-XX, 65-XX, 78-XX, 94-XX © Gerald Kaiser 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper birkhauser-science.com

§? Birkhauser

G E R A L D

KAISER

A Friendly Guide to Wavelets

Birkhauser Boston • Basel • Berlin 1994

Gerald Kaiser The Virginia Center for Signals and Waves 1921 Kings Road Glen Allen, VA 23060

Library of Congress Cataloging-in-Publication Data Kaiser, Gerald. A friendly guide to wavelets / Gerald Kaiser. p. cm. Includes bibliographical references and index. ISBN 0-8176-3711-7 (acid-free). - ISBN 3-7643-3711-7 (acid-free) 1. Wavelets. I. Title. OA403.3.K35 1994 94-29118 515'.2433-dc20 CIP

Printed on acid-free paper v v

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© Gerald Kaiser 1994 Sixth printing, 1999 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhauser Boston, c/o Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trade