Topics in Applied Physics Volume 34

Transcription

1 Topics in Applied Physics Volume 34

2 Topics in Applied Physics Founded by Helmut K. V. Lotsch Dye Lasers 2nd Ed. Editor: F. P. Schăfer 2 Laser Spectroscopy of Atoms and Molecules. Editor: H. Walther 3 Numerical and Asymptotic Tecbniques in Electromagnetics Editor: R. Mittra 4 IDteractions on Metal Surfaces Editor: R. Gomer 5 Miissbauer Spectroscopy Editor: U. Gonser 6 Picture Processing and Digital Filtering 2nd Edition. Editor: T. S. Huang 7 lntegrated Optics 2nd Ed. Editor: T. Tamir 8 Ligbt Scattering in Solids 2nd Edition Editor: M. Cardona 9 Laser Speckle and Related Phenomena Editor: J. C. Dainty 1 O Transient Electromagnetic Fields Editor: L. B. Felsen Il Digital Picture Analysis Editor: A. Rosenfeld 12 Turbulence 2nd Ed. Editor: P. Bradshaw 13 Higb-Resolution Laser Spectroscopy Editor: K. Shimoda 14 Laser Monitoriug of the Atmosphere Editor: E. D. Hinkley 15 Radiationless Processes in Molecules and Condensed Phases. Editor: F. K. Fong 16 Nonlinear IDfrared Generation Editor: Y.-R. Shen 17 Electroluminescence Editor: J. 1. Pankove 18 Ultrashort Ligbt Pulses Picosecond Techniques and Applications Editor: S. L. Shapiro 19 Optica! aud Infrared Detectors 2nd Ed. Editor: R. J. Keyes 20 Holographic Recording Materials Editor: H. M. Smith 21 Solid Electrolytes Editor: S. Geller 22 X-Ray Optics. Applications to Solids Editor: H.-J. Queisser 23 Optica! Data Processiog. Applications Editor: D. Casasent 24 Acoustic Surface Waves Editor: A. A. Oliner 25 Laser Beam Propagation in the Atmospbere Editor: J. W. Strohbehn 26 Photoemission in Solids 1. General Principles Editors: M. Cardona and L. Ley 27 Pbotoemission in Solids Il. Case Studies Editors: L. Ley and M. Cardona 28 Hydrogen in Metals 1. Basic Properties Editors: G. Alefeld and J. Viilkl 29 Hydrogen in Metals II Application-Oriented Properties Editors: G. Alefeld and J. Viilkl 30 Excimer Lasers Editor: Ch. K. Rhodes 31 Solar Energy Conversion. Solid State Physics Aspects. Editor: B. O. Seraphin 32 Image Reconstruction from Projections Implementation and Applications Editor: G. T. Herman 33 Electrets Editor: G. M. Sessler 34 Nonlinear Metbods of Spectral Analysis 2nd Edition. Editor: S. Haykin 35 Uranium Enricbment Editor: S. Villani 36 Amorphous Semiconductors Editor: M. H. Brodsky 3 7 Thermally Stimulated Relaxation in Solids Editor: P. Brăun!ich 38 Charge-Coupled Devices Editor: D. F. Barbe 39 Semiconductor Devices for Optica! Communication. 2nd Ed. Editor: H. Kressel 40 Display Devices Editor: J. 1. Pankove 41 The Computer in Optica! Researcb Methods and Applications. Editor: B. R. Frieden 42 Two-Dimensional Digital Signal Processing 1 Linear Filters. Editor: T. S. Huang 43 Two-Dimensional Digital Signal Processing II Transforms and Median Filters. Editor: T. S. Huang 44 Turbulent Reacting Flows Editors: P. A. Libby and F. A. Williams 45 Hydrodynamic lnstabilities aud tbe Transition to Turbulence Editors: H. L. Swinney and J. P. Gollub 46 Glassy Metals 1 Editors: H.-J. Giintherodt and H. Beck 47 Sputtering by Partide Bombardment 1 Editor: R. Behrisch 48 Optica! Information Processing Fundamentals. Editor: S. H. Lee 49 Laser Spectroscopy of Solids Editors: W. M. Yen and P. M. Selzer 50 Ligbt Scatteriog in Solids II. Basic Concepts and Instrumentation Editors: M. Cardona and G. Giintherodt 51 Ligbt Scattering in Solids m. Recent Results Editors: M. Cardona and G. Giintherodt 52 Sputtering by Partide Bombardment II Editor: R. Behrisch 53 Glassy Metals II. Electronic, Magnetic, and Mechanical Properties, Structure and Applications Editors: H. J. Giintherodt and H. Beck 54 Ligbt Scatteriog in Solids IV. Electronic Scattering, Spin Effects, SERS, and Morphic Effects Editors: M. Cardona and G. Giintherodt

3 N onlinear Methods of Spectral Analysis Edited by S. Haykin With Contributions by J. Capon S. Haykin S. Kesler R. N. McDonough M. Ooe E. A. Robinson T. J. Ulrych Second Corrected and Updated Edition With 45 Figures Springer-Verlag Berlin Heidelberg GmbH 1983

4 Simon Haykin, Ph. D., D. Se. Communication Research Laboratory. McMaster University, 1280 Main Street West. Hamilton. Ontario L8S 4L7, Canada ISBN ISBN (ebook) DOI / Library of Congress Cataloging in Publication Data. Main entry under title: Nonlinear methods of spectral analysis. {Topics in applied physics; v. 34). Includes bibliographical references and index. 1. Spectral theory {Mathematics) 2. Entropy {lnformation theory) 3. Nonlinear theories. L Haykin, S. S. Il. Capon, J. (Jack) III. Series. QC20.7.S64N ' This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse ofillustrations. broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under ~ 54 of the German Copyright Law, where copies are made for other than private use. a fee is payable to "Verwertungsgesellschaft Wort'', Munich. by Springer-Verlag Berlin Heidelberg 1979 and 1983 Originallypublished by Springer-Verlag Berlin Heidelberg New York in 1983 The use ofregistered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use

5 Preface to the Second Edition In this second edition, corrections have been made in the various chapters of the book. Also, a new chapter (Chap. 7) has been added, highlighting some recent advances in spectral estimation, which have been reported since the appearance of the first edition of the book. Hamilton, Ontario March 1983 Simon Haykin

6 Preface to the First Edition This Topics volume, written by seven active research workers, is the first book to be completely devoted to a detailed treatment of nonlinear methods of spectral analysis. These methods have found increasing application in a variety of disciplines during the last 10 or 15 years. The topics covered in the volume are as follows: 1) Prediction-error filtering (Chap. 2) 2) Maximum-entropy spectral estimation (Chap. 2, 3, 6) 3) Modeling of discrete time series (Chaps. 3, 4) 4) Maximum-likelihood spectral estimation (Chaps. 5, 6) 5) Array signal processing (Chaps. 5, 6). Chapter 1 is included as an introduction to the volume. The discussions presented on the maximum-entropy method in Chaps. 2, 3 are designed to be somewhat of a complementary nature so as to enhance the presentation; similarly, for the discussions on mixed autoregressive-moving average spectra presented in Chaps. 3 and 4, and for the discussions on the maximum-likelihood method presented in Chaps. 5 and 6. Each chapter is essentially self-contained. Wherever it is appropriate, however, cross-references between chapters of the volume have been included in order to help the reader develop a more complete understanding of the pertinent topic. Much of the material included in the volume has not appeared in book form before. It is hoped that the volume will be found useful by research workers in the field of spectral analysis and its applications, as well as newcomers to the field. In conclusion, I would like to express my deep gratitude to my co-contributors of the volume, and to Dr. H. Lotsch, of Springer Verlag for making the publication of this volume possible. Hamilton, Ontario April 1979 Simon Haykin

7 Contents 1. Introduction By S. Haykin (With 3 Figures) Time Series Autocorrelation and Autocovariance Functions Spectral Density Linear Filtering Modeling of Time Series Linear and Nonlinear Methods of Spectral Analysis Organization of the Volume References Prediction-Error Filtering and Maximum-Entropy Spectral Estimation By S. Haykin and S. Kesler (With 16 Figures) Wiener Filters Wiener-Hopf Equation Minimum Error Power Prediction-Error Filter Prediction-Error Filter Equations Maximum-Entropy Spectral Estimator Recursive Formulas for Calculating the Prediction-Error Filter Coefficients and Minimum Error Power Optimum Procedure for Calculating the Reflection Coefficients Lattice Equivalent Model Properties of the Prediction-Error Filter Consequences of the Orthogonality and Decoupling Properties Maximum-Entropy Extension of the Autocorrelation Function Statistical Properties of the Maximum-Entropy Spectral Estimator Choice of Filter Order Experimental Classification of Radar Clutter Modeling of Radar Clutter as an Autoregressive Process Experimental Results Multichannel Maximum-Entropy Spectral Estimation Conclusions

8 X Contents Appendix A : Properties of the Autocorrelation Matrix Appendix B: Entropy of a Gaussian Process Appendix C: Flow Graph for Calculating the Prediction-Error Filter Coefficients References Autoregressive and Mixed Autoregressive-Moving Average Models and Spectra. By T. J. Ulrych and M. Ooe (With 13 Figures) Overview The General Time Series Model The MA Approximation The AR Approximation The ARMA Approximation Remarks Autoregressive Processes AR Spectra and Maximum Entropy Determination of the AR Order Resolution of the AR/ME Spectral Estimate... The Smoothness of the AR/ME Estimator Estimation of the AR Parameters The Eigenvector Decomposition of the Unit PEO... The Toeplitz Method The Yule-Walker Solution The Burg Solution The Least-Squares Method "Remarks Concerning AR Parameter Determination, 3.4 Adaptive AR Processes The Adaptive LMS Algorithm ,4.2 Applications of Adaptive AR Modeling Autoregressive-Moving Average Processes The ARMA Model for Sinusoids Plus White Noise Relationship Between the Pisarenko and the AR/ME Spectral Estimators Remarks Concerning the Pisarenko Estimate Determination of Parameters of the General ARMA Process The Method of Treitel et al The Method of Akaike Remarks Concerning the Computation of ARMA Models AIC, FPE, and Autocovariance Estimators The AIC Criterion AIC and the Normal Distribution The FPE Criterion Autocovariance Estimators

9 Contents XI 3.7 Numerical Example: Application of AR and ARMA Models to Polar Motion The ARMA Model of the Chandler Wobble Numerical Computations Conclusions References Iterative Least-Squares Procedure for ARMA Spectral Estimation By E. A. Robinson (With 12 Figures) Basic Time Series Models Parsimony and the Physical Model Seismic Deconvolution and the Resulting Spectral Estimate Design of Shaping and Spiking Filters Invertibility Spectral Estimates of the Components ofa Noninvertible ARMA System Example Conclusions References Maximum-Likelihood Spectral Estimation By J. Capon (With 1 Figure) Explanatory Remarks Seismic Signals and Noise Statistical Models for Seismic Noise and Signal Optimum Detector for Seismic Arrays Evaluation of the Likelihood Ratio Signal Estimation Procedures Maximum-Likelihood Estimation Minimum-Variance Unbiased Estimation Case When Slowness Vector of Signal is Unknown Frequency Wave Number Power Spectrum Definition Properties Relation to Coherence Estimation of Frequency Wave Number Power Spectrum Spectral Matrix Estimation Procedure Conventional Method High-Resolution Method Estimation of Coherence Conclusions References

10 XII Contents 6. Application of the Maximum-Likelihood Method and the Maximum- Entropy Method to Array Processing. By R. N. McDonough Overview The Wave Number Spectrum and Its Estimation by Linear Processing Spectral Representation of a Stochastic Process Conventional Linear Spectrum Analysis Linear Estimation of the Frequency Wave-Number Spectrum A Word on Sampled Data The Maximum-Likelihood Processor in the Spatial Domain Linear Maximum-Likelihood Processing The (Nonlinear) Maximum-Likelihood Array Processor The Maximum-Likelihood Estimator as a Filter in Wave Number Space The Effect of Signal Mismatch on the Maximum-Likelihood Processor Adaptive Wave Number Filters The Maximum-Entropy Method in Array Processing The Information-Theoretic Basis of Maximum-Entropy Analysis The Principle of Maximum Entropy Maximum-Entropy Spatial Processing Maximum-Entropy Processing for a Uniformly Spaced Line Array Remarks on Nonuniform Sample Spacing Direction Finding with a Line Array Conclusions References Recent Advances in Spectral Estimation By S. Haykin, S. Kesler, and E. A. Robinson Generalized Burg Algorithm Singular Valve Decomposition in Spectral Analysis CDEARMA Algorithm Other Algorithms References Subject Index

11 Contributors Capon, Jack Lincoln Laboratory, MIT, Lexington, MA 02173, USA Haykin, Simon Communications Research Laboratory, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4L7, Canada Kesler, Stanislav Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104, USA McDonough, Robert N. Applied Physics Laboratory; Johns Hopkins University, Laurel, MD 20810, USA Ooe, Masatsugu International Latitude Observatory, Mizusawa-Shi, Iwate-Ken, Japan Robinson, Enders A. Mathematics Department, University of Tulsa, Tulsa, OK 74104, USA Ulrych, Tad J. Department of Geophysics and Astronomy, The University of British Columbia, 2075 Westbrook Place, Vancouver, B.C. V6T 1W5, Canada