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.

Formal mathematical treatment of an advanced area of signal processing including many specially-written end-of-chapter excercises Teaches a wide variety of techniques necessary for modern applications of signal processing and demonstrates how the techniques can be applied to a wide variety of situations by the student himself without recourse to an exhaustive list of when to use which technique The only book on this subject at this level for students specialising in this area

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.