ECE534 Spring 2009

Random Processes

2:00-3:30 TuTh, 163 EL

 


Prerequisites: ECE 413 or equivalent. (Knowledge of basic linear systems, such as Fourier transforms, and basic real analysis would also be useful.)
Instructor: Prof. R. Srikant, 107 CSL, rsrikant@uiuc.edu , Office Hours: 3:00-4:00 Mondays

TAs: Yu (Robin) Ru, Office Hours: 4-5 Tuesdays, Room 361EL, yuru2@illinois.edu

        Xiaolan (Joy) Zhang, Office Hours: 3-4 Wednesdays, Room 368EL, xzhang29@illinois.edu

Credit: 4 hours

Homepage: http://www.ifp.uiuc.edu/~srikant/ECE534_spring09.html

Text: B. Hajek, An Exploration of Random Processes for Engineers. (Also see notes below on Discrete Time Markov Chains)

Available at http://www.ifp.uiuc.edu/~hajek/Papers/randomprocesses.html

Copies for purchase are available in 243EL.

Spring Break, No Class: March 24, 26

Other class cancellations (may be updated): Feb. 3, Feb. 5, April 21

Last Day of Class: May 6

 

 

Topics

  • Probability Review
  • Convergence of a Sequence of Random Variables
  • Minimum Mean Squared Error Estimation
  • Random Processes
  • Inference for Markov Models
  • Markov Chains (Countable State-Space Markov Processes)
  • Basic Calculus of Random Processes
  • Random Process in Linear Systems
  • Wiener Filtering
  • More on Discrete-time Markov Chains

 

 

Grading

  • 10% Homework
  • 10% Probability Review Quiz, Date: Feb. 10 (Tuesday), 7:00-8:30 pm, Room 269EL. No notes will be allowed. No calculators or any other electronic devices will be allowed. Solutions.
  • 20% each, Two midterm exams:
    • First Midterm, Date: March 12 (Thursday), 7:00-8:30 pm, Room 269EL. You will be allowed one 8.5x11” sheet (two pages) of handwritten notes. No calculators or any other electronic devices will be allowed. Topics: Chapters 2 and 3 of Hajek. You should also be very familiar with the material in Chapter 1. Detailed list of topics. Solutions.
    • Second Midterm, Date: April 16 (Thursday), 7:00-8:30 pm, Room 269EL. You will be allowed one 8.5x11” sheet (two pages) of handwritten notes. No calculators or any other electronic devices will be allowed. Topics: Chapters 4 and 7 (only sections 7.1-7.4 in chapter 7). As always, familiarity with the topics covered in the quiz and midterm exam I will be useful. Detailed list of topics. Solutions.
  • 40% Final Exam. 8:00-11:00 Friday, May 15, Room 135 MEB. You will be allowed three 8.5x11” sheets (six pages) of handwritten notes. No calculators or any other electronic devices will be allowed. Detailed list of topics.

 

 

Important Information

  • Collaboration on the homework is permitted, however each student must write and submit independent solutions.
  • Homework is due within the first 5 minutes of the class period on the due date.
  • No late homework will be accepted.
  • Usually, I will not give hard copy handouts (such as homework assignments, solutions, information on exams, etc.) in the class. I will email this information to your illinois.edu accounts. It is important to ensure that there is enough space in your mailbox to receive email. If not, emails will bounce and you may not receive important information. If you are not registered for the course, you will not receive this email.

 

 

Problem Sets

 

 

 

References

  • R.G. Gallager, Discrete Stochastic Processes, Kluwer, 1996.
  • H. Stark and J. W. Woods, Probability and Random Processes, and Estimation Theory for Engineers, third edition, Prentice Hall, 2002.
  • W.B. Davenport, Jr. and W.L. Root, An Introduction to the Theory of Random Signals and Noise, McGraw Hill, 1987 edition.
  • E. Wong and B. Hajek, Stochastic Processes in Engineering Systems, Springer Verlag, 1985.
  • A. Papoulis, Probability, Random Variables and Stochastic Processes, 2nd edt., McGraw Hill, 1984.
  • E. Wong, Introduction to Random Processes, Springer Verlag, 1983.
  • B.D.O. Anderson and J.B. Moore, Optimal Filtering, Prentice Hall, 1979.
  • W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill, New York, 1976.
  • R.B. Ash, Basic Probability Theory, Academic Press, 1972.
  • L. Breiman, Probability, Addison-Wesley, 1968.
  • H. Cramer and M.R. Leadbetter, Stationary and Related Stochastic Processes, Wiley, 1967.
  • E. Parzen, Stochastic Processes, Holden Day, 1962.
  • G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes, Cambridge University Press.