Statistical Signal Processing

Many practical signals are random in nature or modelled as random processes. Statistical Signal Processing involves processing these signals and forms the backbone of modern communication and signal processing systems.This course will the three broad components of statistical signal processing: random signal modelling, estimation theory and detection theory.INTENDED AUDIENCE : PG and senior UGPRE- REQUISITES : A Basic Course in ProbabilitySUPPORT INDUSTRY : Nil<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->

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 factorizationWeek 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) estimationWeek 5 : Signal estimation in white Gaussian noise– MMSE, conditional expectation; Linear minimum mean-square error( LMMSE ) estimation-–, orthogonality principle and Wiener Hoff equationWeek 6 : FIR Wiener filter, linear prediction-forward and backward predictions, Levinson-Durbin Algorithm, application –linear prediction of speechWeek 7 : Non-causal IIR wiener filter, Causal IIR Wiener filteringWeek 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 networkWeek 10 & 11: Kalman filters: Gauss -Markov state variable models; innovation and Kalman recursion, steady-state behaviour of Kalman filtersWeek 12: Review; Conclusions.