Course

Unit 1

Review of random variables Distribution and density functions, moments, independent, uncorrelated and orthogonal random variables; Vector-space representation of Random variables, Schwarz Inequality Orthogonalit principle in estimation, Central Limit theorem, Random processes, wide-sense stationary processes, autocorrelation and autocovariance functions, Spectral representation of random signals, Wiener Khinchin theorem Properties of power spectral density, Gaussian Process and White noise process. Random signal modelling: MA(q), AR(p) , ARMA(p,q) models.

Unit 2

Parameter Estimation Theory Principle of estimation and applications, Properties of estimates, unbiased and consistent estimators, Minimum Variance Unbiased Estimates (MVUE), Cramer Rao bound, Efficient estimators; Criteria of estimation: the methods of maximum likelihood and its properties; Baysean estimation: Mean square error and MMSE, Mean Absolute error, Hit and Miss cost function and MAP estimation. Estimation of signal in presence of white Gaussian Noise Linear Minimum Mean-Square Error (LMMSE) Filtering: Wiener Hoff Equation, FIR Wiener filter, Causal IIR Wiener filter, Noncausal IIR Wiener filter, Linear Prediction of Signals, Forward and Backward Predictions, Levinson Durbin Algorithm, Lattice filter realization of prediction error filters.

Unit 3

Adaptive Filtering: Principle and Application, Steepest Descent Algorithm Convergence characteristics; LMS algorithm, convergence, excess mean square error, Leaky LMS algorithm; Application of Adaptive filters;RLS algorithm, derivation, Matrix inversion Lemma, Intialization, tracking of nonstationarity. Kalman filtering: State-space model and the optimal state estimation problem, discrete Kalman filter, continuous-time Kalman filter, extended Kalman filter. Spectral analysis: Estimated autocorrelation function, periodogram, Averaging the periodogram (Bartlett Method), Welch modification, Blackman and Tukey method of smoothing periodogram, Prametric method, AR(p) spectral estimation and detection of Harmonic signals, MUSIC algorithm.

Pre-Requisite(s): A Basic Course in Probability

Course Objectives

• To understand the qualitative problems of Signal Detection and Estimation in the framework of statistical inference.
• To write down hypothesis tests and estimation schemes for typical problems of interests
• To gain an understanding of Signal Detection and Estimation of signals in white and non-white Gaussian noise

Course Outcomes

• CO1: Understand the qualitative problems of Signal Detection and Estimation in the framework of statistical inference.
• CO2: Understand different hypotheses in Signal Detection and Estimation problems
• CO3: Write down hypothesis tests and estimation schemes for typical problems of interest.
• CO4: Gain an understanding of Signal Detection and Estimation of signals in white and non-white Gaussian noise
• CO5: Understand the detection of random signals.

CO – PO Mapping

Text Book(s)

1. Discrete Random Signals and Statistical Signal Processing, By Charles W. Therrien, Prentice Hall Signal Processing
2. M. H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley & Sons, Inc.,

Reference(s)

1. D.G. Manolakis, V.K. Ingle and S.M. Kogon: Statistical and Adaptive Signal Processing, McGraw Hill, 2000.
2. Monson H. Hayes, ‘Statistical Digital Signal Processing and Modeling”, John Wiley and Sons, Inc, Singapore,