Statistical Signal Processing

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.