ELEC 531: Statistical Signal Processing

Rice University, Fall 2004

Instructor: Clay Scott
Classroom: Sewell 462
Office: Duncan Hall 2117
Campus extension: 3776
Email: cscott at rice dot edu
Office hour: Fri. 11-12

Feedback form

Course assistants:

Name office hour email office number
Wai Lam (William) Chan Tues. 2-3 wailam DH 2046
Jyoti Uppuluri Mon. 1-2 juppu DH 2121

Required text: none

Recommended texts: (on reserve at Fondren)
1) Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory, by Steven Kay, 1993
2) Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory, by Steven Kay, 1998

Another helpful text: (on reserve at Fondren)
1) Statistical Signal Processing, Louis Scharf, 1991

Prerequisites

If you feel underprepared, talk with me.

Final Grade

Homework: 50%
Class participation 5%
Midterm exam: 10%
Final project: 15%
Final exam: 20%

Homework Policy

There will be in the range of 10-12 homeworks, about one per week. If you need to turn an assignment in late, please contact me in advance. Unexcused late homeworks will not be accepted.

I consider homeworks to be the most important part of the class. When writing up your problem sets, you are expected to

Topics to be covered

The Linear Model
  • Linear least squares
  • Polynomial signals
  • Sinusoidal signals
  • Linear signal subspaces

Estimation Theory

  • Maximum likelihood and the EM algorithm
  • Minimum variance unbiased estimators (Rao-Blackwell theorem, Cramer Rao lower bound, BLUE)
  • Bayesian estimators (MAP, MMSE)
  • Linear Bayesian estimators (Wiener filter, Kalman filter)
Detection Theory
  • Detection criteria (Bayes risk, Prob. of error, Neyman-Pearson)
  • The likelihood ratio test (LRT)
  • Key examples: signal constellations and the matched filter, binary symmetric channel
  • Detection with unknown signal parameters (UMP tests, Karlin-Rubin theorem, GLRT, Bayes factor)

Adaptive Filtering (time permitting)

  • LMS algorithm
  • Particle filters
  • The El Farol problem

Collaboration and the Honor Code

You may work together on homeworks, but you are required to write up/code your solutions by yourself. You may not refer to material from previous offerings of this course, including problem sets and solution sets. If you find a problem worked in a book or on the web, resist the temptation to copy it.

Students with Disabilities

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disabled Student Services in the Ley Student Center.

Problem sets and related files

Description Problems Solutions
HW 1 hw1.pdf sol1.pdf
HW 2 hw2.pdf sol2.pdf
HW 3 hw3.pdf sol3.pdf
HW 4 hw4.pdf sol4.pdf
HW 5 hw5.pdf sol5.pdf
HW 6 hw6.pdf sol6.pdf
HW 7 hw7.pdf sol7.pdf
HW 8 hw8.pdf sol8.pdf
HW 9 hw9.pdf sol9.pdf
HW 10 hw10.pdf sol10.pdf
HW 10 hw11.pdf sol11.pdf

q.m (Q-function)

qinv.m (Inverse Q-function)

Final Project

Project description

Files: fmri.mat, ref.mat, fmri.m.

A paper that may stimulate your thinking (note: this paper is more sophisticated that what I would expect you to do): Generalized likelihood ratio detection for fMRI using complex data , Nan, F.Y.; Nowak, R.D., IEEE Transactions on Medical Imaging, Volume: 18 Issue: 4 , April 1999 Page(s): 320 -329

2003 project description

 

Additional resources

Last summer Prashant made a nice applet for viewing and understanding different probability density and mass functions. This is a good resource for those of you who might be less familiar with certain distributions we'll be using. It allows you to play with the different parameter settings of a density/mass function and see how the shape of the function changes. The instructions for viewing the applet are listed below. You need a special program called LabVIEW, which you can download, in order to view the applet.

To run the applet, you first need to install the LabVIEW Run-Time Engine and the Connexions VI Runner (just one installer for the pair). Download and install setup_plus_rte.exe from http://cnx-246-91.ece.rice.edu/~prash/installers and you should be ready to go. If you're on a computer that's already got LabVIEW, you should install setup_minus_rte.exe. Once that's installed, go to http://cnx-246-91.ece.rice.edu/~prash/apps.html and click on the Common Probability Distributions link. If all goes well, the VI Runner should download and run the VI for you. The installation information is also posted at http://cnx.rice.edu/content/m11550/latest/