Statistical Signal Processing

Modern information systems must handle huge amounts of data having varied natural or technological origins. Automated processing of these increasing loads of signals requires training specialists capable of formalising the problems encountered. This book aims at supplying a formalised, concise presentation of the basis of statistical signal processing. Similar interest is directed to aspects related to signal modelling and to signal estimation. So, in order to supply the reader with the desirable theoretical bases and to allow him to make progress in the discipline, most of the results presented here are carefully justified.

From the reviews:

"This book is a formal introduction to signal image processing, and a rather complete one too. a good reference book to have if you are a research student, a practitioner interested in fundamentals of signal processing and their implementation, a teacher of signal processing. It comes with code, a clear formal style, a number of concisely stated facts and results." (Emmanuel Trucco, IEE Proceedings Vision, Image and Signal Processing, September, 2003)

"This book presents an introduction to statistical signal processing. It mainly deals with the modelling and spectral estimation of wide sense stationary processes, and their filtering. This book is intended for graduate students, especially for students both in telecommunications and applied statistics. It can also serve as an excellent reference book for engineers, researchers and professors interested in statistical signal processing. I have found that the book is very helpful." (Yuehua Wu, Zentralblatt MATH, Vol. 1003 (3), 2003)

Zusammenfassung
The only book on the subject at this level, this is a well written formalised and concise presentation of the basis of statistical signal processing. It teaches a wide variety of techniques, demonstrating how they can be applied to many different situations.

Inhalt

1. Introduction.- 2. Random Processes.- 3. Power Spectrum of WSS Processes.- 4. Spectral Representation of WSS Processes.- 5. Filtering of WSS Processes.- 6. Important Particular Processes.- 7. Non-linear Transforms of Processes.- 8. Linear Prediction of WSS Processes.- 9. Particular Filtering Techniques.- 10. Rational Spectral Densities.- 11. Spectral Identification of WSS Processes.- 12. Non-parametric Spectral Estimation.- 13. Parametric Spectral Estimation.- 14. Higher Order Statistics.- 15. Bayesian Methods and Simulation Techniques.- 16. Adaptive Estimation.- A. Elements of Measure Theory.- C. Extension of a Linear Operator.- D. Kolmogorov's Isomorphism and Spectral Representation...- E. Wold's Decomposition.- F. Dirichlet's Criterion.- G. Viterbi Algorithm.- H. Minimum-phase Spectral Factorisation of Rational.- I. Compatibility of a Given Data Set with an Autocovariance Set.- 1.1 Elements of Convex Analysis.- 1.2 A Necessary and Sufficient Condition.- J. Levinson's Algorithm.- K. Maximum Principle.- L. One Step Extension of an Autocovariance Sequence.- N. General Solution to the Trigonometric Moment Problem ..- O. A Central Limit Theorem for the Empirical Mean.- P. Covariance of the Empirical Autocovariance Coefficients ...- Q. A Central Limit Theorem for Empirical Autocovariances ..- R. Distribution of the Periodogram for a White Noise.- S. Periodogram of a Linear Process.- T. Variance of the Periodogram.- U. A Strong Law of Large Numbers (I).- V. A Strong Law of Large Numbers (II).- W. Phase-amplitude Relationship for Minimum-phase Causal Filters.- X. Convergence of the Metropolis-Hastings Algorithm.- Y. Convergence of the Gibbs Algorithm.- Z. Asymptotic Variance of the LMS Algorithm.- References.