Module 1- Introduction: [2 hrs]
Problem Formulation and Objective of Signal Detection and Signal Parameter Estimation in Discrete-Time Domain, classification of estimation and detection problems, Applications: Radar, image processing, speech, communications.

Module 2-Review on mathematical preliminary: [6 hrs]
Recap of calculus, linear algebra, Probability and stochastic processes, Review of Gaussian Variables and Processes spectral characteristics of signals and noise

Module 3-Estimation of Signal Parameters: [ 16 hrs]
Bias, Minimum Variance Unbiased Estimation(MVUE), Fisher Information Matrix, Cramer-Rao Lower Bound, Linear Models,Finding MVU estimators via linear models Generalized Minimum Variance Unbiased Estimation,Rao Blackwell Lehman Sheffe theorem, Best Linear Unbiased Estimators (BLUE), Maximum Likelihood Estimation(MLE), Bayesian: Minimum mean square error (MMSE), Linear MMSE, Minimum absolute error, Minimum probability of error (MAP), Least SquaresBasic ideas, adaptive techniques, Recursive LS ,Kalman filtering, Applications: image, radar, processing, speech, communications

Module 4-Statistical Decision Theory [16 hrs]
Hypothesis Test, Likelihood Ratio TestNeyman-Pearson Theorem, Receiver Operating Characteristics, Minimum Probability of Error, Bayes Risk, Multiple Hypothesis Testing, Detection of Deterministic Signals: Matched Filter Detector and Its Performance, Generalized Matched Filter Multiple Signals.
Detection of Random Signals: Estimator-Correlator, Linear Model, General Gaussian Detection Statistical Decision Theory II: Composite Hypothesis Testing and its approaches, Locally Most Powerful Detectors, Multiple Hypothesis Testing. Applications

Introduce the fundamental statistical signal processing concepts and trends in modern applications

Develop statistical parameter estimation methods to extract information from signals in noise and application of statistical hypothesis testing to the detection of signals in noise..

Introduce the mathematical tools that engineers and statisticians use to draw inference from imperfect or incomplete measurements.

Make Students well equipped for research or cutting edge development in Radar, image processing, speech, communications.

CO 1:Able to remember, understand and apply the theory, the basic methodologies and algorithms of statistical signal processing

CO2: Masters the most important estimation principles such as minimum variance, maximum likelihood, least squares and minimum mean square error estimators

CO3: Understands the basics of detection and classification theory: hypothesis testing, receiver operating characteristics (ROC), the Neyman-Pearson and Bayesian detectors

CO4: Equipped to analyze, evaluate and create concepts, algorithms, and systems for the statistical estimation and detection of deterministic and random parameters applied to Radar, SONAR, Image processing, Acoustic Signal Processing, information and communication systems

CO5:Possess fundamental grounding and sophistication needed to apply statistical signal processing to real world problems.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Vol-I, Prentice Hall PTR , 2009

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Vol-II, Prentice Hall PTR , 2009

H. V. Poor, An Introduction to Signal Detection and Estimation, Springer, 2/e , 1998

Harry L. Van Trees, Detection, Estimation and Modulation Theory” (Detection, Estimation and Modulation Theory, Part-I, John Wiley & Sons , 2002