Course Details

Subject {L-T-P / C} : EC6606 : Statistical Signal Processing { 3-0-0 / 3}

Subject Nature : Theory

Coordinator : Prof. Lakshi Prosad Roy

Syllabus

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

Course Objectives

Course Outcomes

CO 1:Able to remember, understand and apply the theory, the basic methodologies and algorithms of statistical signal processing <br /> <br /> CO2: Masters the most important estimation principles such as minimum variance, maximum likelihood, least squares and minimum mean square error estimators <br /> <br />CO3: Understands the basics of detection and classification theory: hypothesis testing, receiver operating characteristics (ROC), the Neyman-Pearson and Bayesian detectors <br /> <br />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 <br /> <br />CO5:Possess fundamental grounding and sophistication needed to apply statistical signal processing to real world problems.

Essential Reading

Supplementary Reading