Filter Banks and DWT

The study of digital signal processing normally concentrates on the design, realization, and application of single-input, single-output digital filters. There are applications, as in the case of spectrum analyzer, where it is desired to separate a signal

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Series Editors Stan Zdonik Peng Ning Shashi Shekhar Jonathan Katz Xindong Wu Lakhmi C. Jain David Padua Xuemin Shen Borko Furht V. S. Subrahmanian Martial Hebert Katsushi Ikeuchi Bruno Siciliano

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K. K. Shukla Arvind K. Tiwari •

Efficient Algorithms for Discrete Wavelet Transform With Applications to Denoising and Fuzzy Inference Systems

123

Arvind K. Tiwari GE India Technology Center Bangalore India

K. K. Shukla Banaras Hindu University Indian Institute of Technology Varanasi Uttar Pradesh India

ISSN 2191-5768 ISBN 978-1-4471-4940-8 DOI 10.1007/978-1-4471-4941-5

ISSN 2191-5776 (electronic) ISBN 978-1-4471-4941-5 (eBook)

Springer London Heidelberg New York Dordrecht Library of Congress Control Number: 2013930141 Ó K. K. Shukla 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science?Business Media (www.springer.com)

Preface

Transforms occupy an important compartment of an engineer’s tool kit for solving signal processing and polynomial computation problems efficiently. By resolving a time-varying signal into sinusoidal components, engineers transform a problem from that of studying time domain phenomena to that of evaluating frequency domain properties. These properties often lead to simple explanations of otherwise complicated occurr