Table Of ContentNonuniform 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
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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
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No pari of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by
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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
