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Many electronic and acoustic signals can be modeled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterize the periodicity or near-periodicity of a signal and consequently to identify its source. Quinn and Hannan present and analyze several practical techniques used for such estimation. The problem of tracking slow frequency changes of a very noisy sinusoid over time is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large.
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The Estimation and Tracking of Frequency
CAMBRIDGE SERIES IN STATISTICAL AND PROBABILISTIC MATHEMATICS Editorial Board R. Gill, Department of Mathematics, Utrecht University B.D. Ripley, Department of Statistics, University of Oxford S. Ross, Department of Industrial Engineering, University of California, Berkeley M. Stein, Department of Statistics, University of Chicago D. Williams, School of Mathematical Sciences, University of Bath
This series of high quality upper-division textbooks and expository monographs covers all aspects of stochastic applicable mathematics. The topics range from pure and applied statistics to probability theory, operations research, optimization and mathematical programming. The books contain clear presentations of new developments in the field and also of the state of the art in classical methods. While emphasizing rigorous treatment of theoretical methods, the books also contain applications and discussions of new techniques made possible by advances in computational practice. Already published 1. Bootstrap Methods and Their Application, by A. C. Davison and D. V. Hinkley 2. Markov Chains, by J. Norris 3. Asymptotic Statistics, by A. W. van der Vaart 4. Wavelet Methods for Time Series Analysis, by Donald B. Percival and Andrew T. Walden 5. Baye.sian Methods: An Analysis for Statisticians and Interdisciplinary Researchers, by Thomas Leonard and John S. J. Hsu 6. Empirical Processes in M-Estimation, by Sara van de Geer 7. Numerical Methods of Statistics, by John Monahan 8. A User's Guide to Measure-Theoretic Probability, by David Pollard
The Estimation and Tracking of Frequency B. G. Quinn University of Manchester Institute of Science and Technology
E. J. Hannan Late, Australian National University
CAMBRIDGE UNIVERSITY PRESS
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS
The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011 -4211, US A 10 Stamford Road, Oakleigh, VIC 3166, Australia Ruiz de Alarc6n 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Cambridge University Press 2001 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2001 Printed in the United States of America Typeface Computer Modern 11/13 pt.
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A catalog record for this book is available from the British Library. Library of Congress Cataloging in Publication data Quinn, Barry G. The estimation and tracking of frequency / B.G. Quinn, E.J. Hannan. p. cm. — (Cambridge series in statistical and probabilistic mathematics) Includes bibliographical references and indexes. ISBN 0-521-80446-9 1. Signal processing—Mathematics. 2. Signal processing—Data processing. 3. Modulation (Electronics)—Mathematical models. 4. Time-series ana