Fourier Series and Transforms PDF
Preview Fourier Series and Transforms
Fourier Series and Transforms A Computer Illustrated Text FOURIER SERIES AND TRANSFORMS R D Harding University of Cambridge First published 1985 by Taylor & Francis Group Published 2019 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 1985 by Taylor & Francis Group, LLC CRC Press is an imprint of the Taylor & Francis Group, an informa business No claim to original U.S. Government works ISBN-13: 978-0-85274-809-1 (pbk) ISBN-13: 978-1-138-41333-7 (hbk) 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. 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CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been 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 Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library' of Congress > Contents Preface vii Introduction 1 Part 1 Sampling and Resolution 3 Part 2 Periodic Functions, Harmonics and Fourier Series 7 Part 3 Fourier Transforms 22 Appendix 1 The FFT Algorithm 46 Appendix 2 Proof of the DFT Inverse Relations 48 Appendix 3 Program Outlines 50 Program User's Notes Apple Pascal Version 64 Program User's Notes BBC Basic Version 71 Index 75 > Preface There are several topics in mathematics at advanced secondary school level or early university course level whose teaching I have always thought would benefit by being more extensively illustrated than is possible in conventional texts. Many such topics are of interest not only to specialist mathematicians but also to scientists and engineers, and from many years experience of teaching them, what seems to be lacking from the normal treatment is a visual and qualitative feel for the properties of the mathematics. The widespread and rapid growth of cheap microcomputers means that it is possible to try to remedy this lack through the use of computer graphics. In this computer illustrated text normal figures and diagrams are replaced with screen displays which can be produced dynamically by the reader, offering a far greater variety of illustrations than would be possible with printed diagrams alone. Of course I have had to assume that the reader has access to, and is reasonably familiar with one of the computers and its programming language which I have chosen to write for. In principle the idea could be applied to an entire textbook but it is felt that to start with it is better to concentrate on a few topics for which this treatment seems especially useful, and also to concentrate on imparting an overall feel for these topics since it is not being suggested that existing texts are inadequate in technical detail. This text is therefore meant to be complementary to a standard textbook or lecture course. Some may wonder whether it would not be better to have the computer reproduce the text as well as the diagrams. There certainly are such packages available, but unless the topic is either very elementary or capable of being discussed very briefly indeed, the present state of computer technology does not allow these to run on a cheap home vn viii PREFACE microcomputer such as the BBC Microcomputer or the Apple II. Another problem is that mathematics requires a wide range of special symbols and again the technology is not widely and cheaply available which would allow these symbols to be shown on a screen. There is also the fact that a printed text can be more easily browsed through. These considerations have led to the design of this monograph, which it is hoped will be the first of several such titles. As it is experimental, comments and criticisms will be particularly welcome. I hope it will make learning more interesting and enjoyable for you, the reader. Good luck. RDM March 1984 > Acknowledgments The author gratefully acknowledges the hospitality and help of the Algebra Institute, University of California, Santa Barbara, where much of this text was written. The author also acknowledges Acornsoft Ltd for permission to use routines from Graphs and Charts on the BBC Microcomputer.
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