# Statistical Signal Processing

## EE262 - Introduction to Statistical Signal Processing

Covers fundamental approaches to designing optimal estimators and detectors of deterministic and random parameters and processes in noise, and includes analysis of their performance. Binary hypothesis testing: the Neyman-Pearson Theorem. Receiver operating characteristics. Deterministic versus random signals. Detection with unknown parameters. Optimal estimation of the unknown parameters: least square, maximum likelihood, Bayesian estimation. Will review the fundamental mathematical and statistical techniques employed. Many applications of the techniques are presented throughout the course. Note: While a review of probability and statistics is provided, this is not a basic course on this material.

### General

• Instructor:  Alyson Fletcher, Assistant Professor, Electrical Engineering
• Phone:  831-459-3877
• Email: afletcher@soe.ucsc.edu
• Text:  Fundamentals of Statistical Signal Processing: Vols. 1, 2:  Detection and Estimation, by Steven M. Kay
• Grading:  Homeworks 25%, Midterm 30%, Final 45%
• Some homework will involve MATLAB
• Office Hours: 12-1:30 Tuesday or by emal appointment
• See course website for more information (will require soe.ucsc.edu email or permission of instructor)

### Tentative syllabus

• Lect 1 (Vol. 2: Ch 1, Appendix A1.1) Introduction, overview of history and applications of detection and estimation. Review of the requisite mathematical concepts, including concepts in matrix, probability, and statistical analysis.
• Lect 11-12 (Vol. 2: Ch 3): Binary hypothesis testing. Neyman-Pearson Theorem. Minimum Probability of Error. Bayes Risk.
• Lect 13-16 (Vol. 2: Ch 4) Detection of deterministic signals. Matched filters, Linear model, performance.
• Lect 17-19 (Vol 2: Ch 5, 6.4-7, Ch 7) Detection of deterministic signals with unknown parameters. The Generalized Likelihood Ratio Test (GLRT).
• Lect 10 Midterm (Feb 12)
• Lect 2 (Vol. 1: Ch 2), Introduction to estimation, minimum variance unbiased estimation.
• Lect 3-5 (Vol.1: Ch 3.1-3.6, Ch 4) The Cramer-Rao bound, the linear model.
• Lect 6-7 (Vol 1: Ch 7, Ch. 11.5) Maximum Likelihood and MAP estimation
• Lect 8-9 (Vol 1: Ch. 8) Least Squares
• Lect 20 (Vol 1: Ch 10) MMSE Detection and Estimation.