The course objectives are to provide the understanding of: 1. Stochastic signal models and their use in signal processing applications 2. Optimal linear-time invariant (LTI) filtering of stochastic processes 3. Estimation theory using classical and Bayesian approaches.

Random processes. Power spectral density. Auto-regressive processes. Moving-average processes. Periodic processes. Spectral decomposition. Whitening filter. Innovations. Stochastic signal models. Yule-Walker equations. Linear-time invariant filtering of random processes. Estimation. Linear Estimators. Linear minimum mean square error estimator. Wiener filter. Optimal FIR filters. Optimal IIR filters. Filtering, prediction, smoothing applications. Reduced dimension stochastic signal representation. Karhunen-Loeve transform.