Nonuniform Sampling: Theory and Practice PDF
Preview Nonuniform Sampling: Theory and Practice
Nonuniform Sampling Theory and Practice Information Technology: Transmission, Processing, and Storage Series Editor: Jack Keil Wolf University of California at San Diego La Jolla, California Editorial Board: James E. Mazo Bell Laboratories, Lucent Technologies Murray Hill, New Jersey John Proakis Northeastern University Boston, Massachusetts William H. Tranter Virginia Polytechnic Institute and State University Blacksburg, Virginia Multi-Carrier Digital Communications: Theory and Applications of OFDM Ahmad R. S. Bahai and Burton R. Saltzberg Nonuniform Sampling: Theory and Practice Edited by Farokh Marvasti Principles of Digital Transmission: With Wireless Applications Sergio Benedetto and Ezio Biglieri Simulation of Communication Systems, Second Edition: Methodology, Modeling, and Techniques Michel C. Jeruchim, Philip Balaban, and K. Sam Shanmugan A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher. Nonuniform Sampling Theory and Practice Edited by Farokh Marvasti King's College London, United Kingdom and Sharif College of Technology Tehran, [ran Springer Science+Business Media, LLC Library of Congress Cataloging-in-Publication Data Marvasti, Farokh A. Nonuniform sampling: theory and practice/Farokh A. Marvasti. p. cm. -(Information technology: transmission, processing, and storage) Includes bibliographical references and index. ISBN 0-306-46445-4 1. Signal theory (Telecommunication)-Mathematics. 2. Sampling. 3. Time-series analysis. 1. Title. II. Series. TK5102.5 ..M 2953 2000 621.382'23-dc21 00-062213 Additional material to book can be downloaded from http://extra.springer.com. ISBN 978-1-4613-5451-2 ISBN 978-1-4615-1229-5 (eBook) DOI 10.1007/978-1-4615-1229-5 ©2001 Springer Science+Business Media New York Originally published by Kluwer Academic/Plenum Publishers, New York in 2001 http://www.wkap.nll ro 9 8 7 6 5 4 3 2 1 A C.I.P. record for this book is available from the Library of Congress All rights reserved No pari of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher. Dedicated to: The late Prof. 1. L. Yen who introduced interpolation formulae from special nonuniform samplesl The late Claude Shannon, father of information theory, who popularized the field of sampling theory in the engineering communi!)? The Portuguese government, University of Aveiro, and the Portuguese people who hosted me while I was writing several chapters of this book My family, Maryam, Salman, Laleh, Ali, and Narges for their understanding and help My mother who instilled motivation and curiosity in me My late father who cared so much about education 1S ee his biography and the photo in Chapter 1. 2See more comments and photos in Chapters 1 and 2. Contributors Andreas Austeng • University of Oslo, Oslo, Norway Sonali Bagchi • Mobilian Corporation, Hillsboro, OR, USA John Thomas Barnett • Space and Naval Warfare Systems Center, San Diego, CA, USA John Benedetto • University of Maryland, College Park, MD, USA M. Bourgeois • Universite LYON I-CPE, Villeurbanne, France P. L. Butzer • RWTH Aachen, Aachen, Germany Willem L. de Koning • Delft University of Technology, Delft, The Netherlands A. 1. W. Duijndam • Philips Medical Systems, The Netherlands Paulo 1. S. G. Ferreira • Universadade de Aveiro, Aveiro, Portugal D. Graveron-Demilly • Universite LYON I-CPE, Villeurbanne, France Karlheinz Grochenig • University of Connecticut, Storrs, CT, USA Mohammed Hasan • King's College London, London, UK C. O. H. Hindriks • Delft University of Technology, Delft, The Netherlands Sverre Holm • University of Oslo, Oslo, Norway Jon-Fredrik Hopperstad • University of Oslo, Oslo, Norway Karnran Iranpour • University of Oslo, Oslo, Norway Timo I. Laakso • Helsinki University of Technology, Espoo, Finland B. Lacaze • Lab TeSA, Cedex, France Farokh Marvasti • King's College London, London, UK & Sharif University of Technology, Tehran, Iran vii viii Contributors Sanjit K. Mitra • University of California at Santa Barbara, Santa Barbara, CA, USA Dale H. Mugler • University of Akron, Akron, OH, USA M. Sandler • King's College London, London, UK G. Schmeisser • University of Erlangen-Nurenberg, Erlangen, Germany M. A. Schonewille • PGS Onshore, Houston, TX, USA Sherry Scott • University of Maryland, College Park, MD, USA Atif Sharaf • King's College London, London, UK R. L. Stens • RWTH Aachen, Aachen, Germany G. H. L. A. Stijnrnan • Delft University of Technology, Delft, The Netherlands Thomas Strohmer • University of California at Davis, Davis, CA, USA Vesa Vlilimiiki • Helsinki University of Technology, Espoo, Finland D. van Ormont • Delft University of Technology, Delft, The Netherlands L. Gerard van Willigenburg • Wageningen University, Wageningen, The Netherlands F. T. A. W Wajer • Delft University of Technology, Delft, The Netherlands YanWu • University of Akron, Akron, OH, USA Ahmed I. Zayed • University of Central Florida, Orlando, FL, USA Foreword I was very pleased when Farokh Marvasti asked me to write a Foreword to this volume. I can certainly recommend it to the scientific community in the confidence that its readers will get a real sense of the flavour, style and innovative character of nonuniform sampling and its applications. The importance of sampling as a scientific principle, both in theory and practice, can hardly be in doubt. The reader who cares to glance through the Table of Contents cannot fail to be convinced as to the ubiquity of the subject and its broad scope; and if we allow that the subject finds its root in the finite interpolation problems that were already being studied in the middle part of the seventeenth century (and there are cogent reasons for taking this view), nonuniformity of the distribution of sample points has been present in sampling from its very beginnings. A basic idea, one that lies at the foundations of sampling, is that it is very convenient to consider a signal, or function, as consisting merely of a collection of discrete samples, that is, values taken by the function at some countable set of sample points. When this can be done one is saying effectively that the information contained in the function's samples is equivalent to, or at least approximately equivalent to, that present in the whole function. In order to reach such a desirable position one needs to ask whether the set of sample points is a set of uniqueness for some class of functions, and if so, how a member of the class could be reconstructed from data which would often consist of samples of the function, or perhaps of pre-processed versions of it. Going beyond the finite case to that of infinitely many sample points, the simplest, indeed the "classical", case involves uniformly distributed sample points along the real line and is embodied in the famous sampling theorem associated with the names of E. T. Whittaker, V. A. Kotel'nikov and C. E. Shannon (and others); a theorem that can be found in many places throughout this book. It is from such basic ideas that sampling developed, ever more rapidly, throughout the last century and into the present. Indeed, sampling is now a multi disciplinary activity, and is often found where some or all of: harmonic analysis including classical Fourier analysis, function theory, approximation theory, prediction theory, stochastic processes, information theory and practical consid erations of signal processing are seen to overlap (and that is just a short list!). ix x Foreword Movements of scientific thought develop continuously, and are indeed intelligible to us as continuity. The past informs the present, which in turn will inevitably inform the future. However, we live in an era when these developments are, more often than not, accompanied by changes that are huge and rapid. We are forced, therefore, to ask the question: how do we cope with this change; how are we to deal with the new? I believe that books such as the present one have an important role to play here (and it will surely be a sad day for the human race when there is no role for books to play any more). We can pause with them; we can gain breathing space, a time to ponder, a time to sift foreground from background before the tidal waves of change press us forward once again. On a more day-to-day level, the usefulness of a book such as this will depend in part on its selection from the masses of material available in· the literature and in the minds of its contributors; in part on how it improves access to the subject, and in part on whether its contributions contain careful analysis, informative bibliographies and a high quality of elucidation. I confidently predict that this book will not be found wanting in any of these attributes. It seems that there is no shortage of new and interesting problems in non uniform sampling, and I am sure that the present volume will help to maintain that interest. Happy sampling! J. R. Higgins, Cambridge, UK Preface Shannon never claimed any credit for originating The Sampling Theorem, he simply realized as part of his original development of a mathematical Theory of Communication that a band-limited signal could (in theory) be reconstructed from uniformly spaced values provided the samples were closer than a critical amount. In my first encounters with The Sampling Theorem, it was called the "Shannon-Whittaker-Kotel'nikov Sampling Theorem", with honors shared by Shannon with the radar pioneer and originator of Signal Detection Theory. Regardless of the origins of the result-which are considered in this book-these three, and Shannon in particular, had a profound effect on the rapid spread of both understanding and applications of sampling to communications and signal processing theory and practice. On the theoretical side, sampling provided the means of converting contin uous time signals to discrete-time signals without loss of information. This permitted tools for discrete time signals such as linear algebra and time-series analysis to be applied to the evaluation of channel capacities and source rates of continuous time processes. When sampling, the discretization of time, was combined with quantization, the discretization of amplitude, the result was analog-to-digital conversion and the true beginnings of the modem digital revolution, as embodied in the first digital communication technique for contin uous waveforms-pulse coded modulation (PCM), as popularized by Oliver, Pierce, and Shannon. The descendants of this technique are ubiquitous in the Internet and modem wireless communication. Sampling has grown in many directions, especially nonuniform sampling and generalization incorporating transforms such as Fourier, Karhunen-Loeve, wavelets, and filter-banks. For all of these extensions, however, the basic issue for an engineer remains the discretization of time or space, whether the goal be to prove a theorem or transmit speech or video. Along with quantization, sampling resides at the border between the analog world of nature, and the digital world of communication, signal processing and computing. This book provides a thorough and varied tour of that border. Prof Robert M. Gray Department of Electrical and Computer Engineering Stanford University Stanford, California xi
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