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Online Course

# Statistical Signal Processing

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## Overview

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 UG PRE- REQUISITES : A Basic Course in Probability SUPPORT INDUSTRY : Nil

## Syllabus

COURSE LAYOUT 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.

#### Taught by

Prof. Prabin Kumar Bora

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