Statistical Signal Processing

Week 1 & 2 : Introduction; Stationary processes: Strict sense and wide sense stationarity; Correlation and spectral analysis of discrete-time wide sense stationary processes, white noise, response of linear systems to wide-sense stationary inputs, spectral factorization

Week 2, 3 & 4 : Parameter estimation: Properties of estimators, Minimum Variance Unbiased Estimator (MVUE Cramer Rao bound, MVUE through Sufficient Statistics, Maximum likelihood estimation- properties. Bayseaen estimation-Minimum Mean-square error(MMSE) and Maximum a Posteriori(MAP) estimation

Week 5 : Signal estimation in white Gaussian noise– MMSE, conditional expectation; Linear minimum mean-square error( LMMSE ) estimation-–, orthogonality principle and Wiener Hoff equation

Week 6 : FIR Wiener filter, linear prediction-forward and backward predictions, Levinson-Durbin Algorithm, application –linear prediction of speech

Week 7 : Non-causal IIR wiener filter, Causal IIR Wiener filtering

Week 8, 9 & 10: Iterative and adaptive implementation of FIR Wiener filter: Steepest descent algorithm, LMS adptive filters, convergence analysis, least-squres(LS) method, Recursive LS (RLS) adaptive filter, complexity analysis, application- neural network

Week 10 & 11: Kalman filters: Gauss -Markov state variable models; innovation and Kalman recursion, steady-state behaviour of Kalman filters

Week 12: Review; Conclusions.