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DISCRETE AND CONTINUOUS FOURIER TRANSFORMS
ANALYSIS, APPLICATIONS AND FAST ALGORITHMS

DISCRETE AND CONTINUOUS FOURIER TRANSFORMS
ANALYSIS, APPLICATIONS AND FAST ALGORITHMS

University of Guelph Guelph, Ontario, Canada

Eleanor Chu

MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in thisbook. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.

Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2008 by Taylor & Francis Group, LLC Chapman & Hall/CRC is animprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4200-6363-9 (Hardcover) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information,but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The Authors and Publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged pleasewrite and let us know so we may rectify in any future reprint Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without writtenpermission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that havebeen granted a photocopy license by the CCC, a separate system of payment has been arranged. 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 Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents
List of Figures List of Tables Preface Acknowledgments About the Author xi xv xvii xxi xxiii

I Fundamentals, Analysis and Applications
1 Analytical and Graphical Representation of Function Contents 1.1 Time and Frequency Contents of a Function . . . . . . . . 1.2 The Frequency-Domain Plots as Graphical Tools . . . . . 1.3 Identifying the Cosine and Sine Modes . . . . . . . . . . . 1.4 UsingComplex Exponential Modes . . . . . . . . . . . . 1.5 Using Cosine Modes with Phase or Time Shifts . . . . . . 1.6 Periodicity and Commensurate Frequencies . . . . . . . . 1.7 Review of Results and Techniques . . . . . . . . . . . . . 1.7.1 Practicing the techniques . . . . . . . . . . . . . . 1.8 Expressing Single Component Signals . . . . . . . . . . . 1.9 General Form of a Sinusoid in SignalApplication . . . . . 1.9.1 Expressing sequences of discrete-time samples . . 1.9.2 Periodicity of sinusoidal sequences . . . . . . . . 1.10 Fourier Series: A Topic to Come . . . . . . . . . . . . . . 1.11 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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