ELEC 531: Statistical Signal Processing: Course Outline

ELEC 531: Statistical Signal Processing
Fall 2007

The Basics

Instructor: Michael Lexa
Lectures: Tuesday, Thursday 1:00-2:20 p.m., Herzstein 118
Office hours: Mondays 2-4 p.m. DH 2031 or by appointment
Graders: Debashi Dash, Mona Sheikh

Description

Introductory graduate level course in statistical signal processing. This course focuses on the roles---good and bad---that stochastic signals play. Some interesting signals, e.g. communication and neural signals, are by their very nature stochastic. Deterministic signals, when measured in the presence of random noise, can also be modeled as stochastic signals. Statistical signal processing develops optimal algorithms to extract information from or in the presence of stochastic signals. All of these algorithms hinge on fundamental results in estimation and detection.
Prerequisites: Knowledge of stochastic processes and probability.

Course Outline

Review
Probability, stochastic processes.
Estimation Theory

Terminology
Minimum mean-Squared error estimation (MMSE): conditional mean estimators, orthogonality principle
Linear MMSE: parameter estimation, FIR Weiner filtering
Maximum-likelihood estimates (MLE): properties, Cramer-Rao bound, Expectation-Maximization (EM) algorithm
Maximum a posterior (MAP) estimators
IIR Wiener filters, Kalman filters
Least mean-squared (LMS) adaptive filters

Discrete-Time Detection Theory
- Statistical hypothesis testing: optimality criteria, likelihood ratio test (simple binary tests, composite tests, multiple hypothesis tests)
- Detection of signals in additive Gaussian noise
- Detection in the presence of certainties: unknown signal and noise parameters, unknown signal waveforms. CFAR detection.
- Stein's lemma
- Sequential tests
- Distributed test
- Continuous-time detection

Resources

D.H. Johnson. Estimation & Detection Theory. Available as a coursepak at the Rice Campus Store and online here.
L. Scharf. Statistical Signal Processing: Detection, Estimation, and Time Series Analysis. Addison-Wesley Publishing Co., 1991.
M. Hayes. Statistical Digital Signal Processing and Modeling. John Wiley & Sons, Inc., 1996.
G. Casella and R. Berger. Statistical Inference. Duxbury, 2002.
S. Kay.Fundamentals of Statistical Signal Processing: Vol. I Estimation Theory, Vol II. Detection Theory. Prentice Hall, Inc., 1993.
A. Papoulis. Probability, Random Variables, and Stochastic Processes. 3rd Edition. McGraw-Hill, Inc., 1991.
R. Gray. and L. Davisson. Random Processes: A Mathematical Approach for Engineers. Prentice-Hall, Inc., 1986.

Grading

Problem Sets: 50%
Quizzes: 15% each
Final Exam: 20%