Introduction to Random Processes

 ELEC 533, Fall 1999

 Rice University

This course covers the basic concepts of probability theory and random processes
at a fairly rigorous level and discusses applications such as to Digital Communication Systems.

Instructor

Dr. Rudolf Riedi
Duncan Hall 2025, 527 8750 x 3020,
Office Hours: Wednesday 2-3 pm, or by appointment
Assistant
Ramesh Neelamani
Duncan Hall 2121, 527 8750 x 3230
Office Hours: Monday 2-3 pm, or by appointment

Tarik Muharemovic
Duncan Hall 2045, 527 8750 x 2371
Office Hours: Friday 9 - 10 am, or by appointment


Time and Place

TTH  10:50 - 12:05, Duncan Hall 1042

[Outline]  [Textbooks]  [Grading]  [Reading assignment]  [Homework problems and solutions]  [Tests] 

Outline
 

Review of Basic Probability Theory (incl. conditional probability)
QUIZ (one sheet or two pages of personal notes)
Random Vectors and Sequences (joint distributions, limiting laws)
Random Processes (wide sense stationarity, Poisson, Markov, Wiener processes)
Midterm EXAM (open-notes, closed-books)
Signal Detection and Parameter Estimation (spectral properties, KLT)
Final EXAM (open-notes)

Textbook

  • H. Stark and J. Woods, `Probability, Random Processes, and Estimation Theory for Engineers'
    • Further suggested reading Standard references on Probability Theory


    Stark & Woods, Wond & Hayek, and Papoulis are on reserve at Fondren Library

    Grading

    15%  QUIZ
    30%  Midterm EXAM
    30%  Last EXAM
    15%  Homework
    10%  Notes and participation in class


    Late Homework Policy
     

    Homework is due at the beginning of class on the due date. After the due date, but before solutions are handed out, homework can be turned in for 50% credit. In this case, please slip your homework under the door of DH 2025, or DH 2121, or bring it to class. After solutions are handed out, 0% credit will be issued. You are encouraged to work in groups for homeworks but you will hand in your own solution which you are expected to understand.

    Classes
     
    Covered material Reading: Stark&Woods (1986)
    August 31 Orientation, history
    September 2 Probability space pp 1-10
    September 7 Conditional Probability pp 11-12, 15-17
    September 9 Bayes, Independence (Binomial law:) pp 18-25
    September 14 Random variables, CDF, pdf pp 37-51, (69-80)
    September 16 Expectation, variance pp 111-116
    September 21 Joint distributions pp 62-67
    September 23 Functions of random variables pp 73-87
    Up to here: Material for Quiz
    September 28 Conditional expectation, discrete
    September 30 Cond expect, continuous pp 67-73, 117-123
    October 5 Cond expect=projection pp 380-392
    October 7 Characteristic function pp 139-146
    October 12 Multivariate Gaussian pp 156-158, 170-173
    October 14 Covariance, Inequalities pp 132-135
    October 19 Fall break
    October 21 Convergence (as, ms, ip, D) pp 245-253
    October 26 ...and relations. Martingales pp 254-256
    October 28 Limit theorems (MCT, LLN) pp 135, 253, 257
    November 2 CLT, LDP, finite dimens. distr. pp 143-146, 264-266
    November 4 stationarity, Renewals pp 285-290
    November 9 Poisson Process pp 267-273
    November 11 Wiener, Markov Processes pp 273-281
    From Quiz to here: Material for Test 1
    November 16 Spectral density pp 337-342
    November 18 Mean square calculus pp 296-307
    November 23 M.S. deriv, integral pp 308-310
    November 30 Linear systems, Gauss-Markov pp 287f,345f,280f
    From Fallbreak to here: Material for Test 2
    December 2 White Noise, KL pp 343f
    December 7 KL pp 322-326

    Homework (Access restricted: graders only)
     
    Homework sheet Due date (in class) Solutions
    Problem Set 1 Sept 14, 1999 Set 1
    Problem Set 2 Sept 21, 1999 Set 2
    Problem Set 3 Sept 28, 1999 Set 3
    Problem Set 4 Oct 12, 1999 Set 4
    Problem Set 5 Oct 21, 1999 handed out in hard copy
    Problem Set 6 Oct 26, 1999 Set 6
    Problem Set 7 Nov 2, 1999 handed out in hard copy
    Problem Set 8 Nov 9, 1999 Set 8
    Problem Set 9 Nov 16, 1999 handed out in hard copy
    Problem Set 10 Dec 2, 1999 Set 10

    Tests
     
    Quiz (15% towards the grade) Friday, October 1, 1999 4-4:45 pm, Abercrombie A 126
    Midterm (30%) Friday, Nov 19, 1999 2:50-6 pm, A 126 (open notes)
    Last Test (30%) due: December 10, 1999 take home, 7 days, 3 hours (open books)

    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.
    August 30, 1999.  Dr. Rudolf Riedi