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ECE 534 - Random Processes (Spring 2024)

Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Instructor: Ilan Shomorony (he/him), ilans@illinois.edu.
Office hours: Monday 2-3pm over Zoom (info)

Lectures: Monday and Wednesday at 11:00AM - 12:20PM
Lecture videos will be available on mediaspace

TAs:

  • Kayvon Mazooji, mazooji2@illinois.edu. Office hours: Friday at 1:00PM - 2:30PM in room ECEB 2036
  • Taha Ameen, tahaa3@illinois.edu. Office hours: Thursday at 1:00 PM - 2:00 PM in room ECEB 2036

Recitations: every other Friday at 11:00AM - 12:00PM in room ECEB 2015 (next session: 4/19/2024)


Prerequisites: ECE 313 (Undergraduate Probability); Knowledge of linear systems and undergraduate real analysis will be helpful
Text: B. Hajek, Random Processes for Engineers. Available at http://hajek.ece.illinois.edu/ECE534Notes.html

Statements on diversity, inclusion, and academic integrity.

 

Announcements

  • Final exam was graded: mean = 65/90, stdev = 11.6 (Solutions)
  • Midterm 2 was graded: mean = 60.8/75, stdev = 7.6 (Solutions)
  • Midterm 2 will be on Monday, 04/15 from 7pm to 9pm CT.
    • Location: ECEB 1013 and ECEB 1015
    • The exam will cover everything until discrete-time and continuous-time Markov Processes.
    • The material since Midterm 1 roughly corresponds to sections 3.4, 3.5, 3.6, Chapter 4, and sections 6.1, 6.2, 6.3 (but our discussion on Markov processes diverged a bit from that in the book).
    • One cheat sheet (two-sided) of handwritten formulas will be allowed in the quiz.
    • Calculators will not be allowed.
  • Midterm 1 was graded: mean = 40.5/60, stdev = 10.5 (Solutions)
  • Midterm 1 will be on Monday, 03/04 from 7pm to 9pm CT.
    • Location: ECEB 1013 and ECEB 1015
    • The exam will cover everything until lecture 12.
    • One cheat sheet (two-sided) of handwritten formulas will be allowed in the quiz.
    • Calculators will not be allowed.
  • Probability Quiz was graded: mean = 42/55, stdev = 8.5 (Solutions)
  • A Piazza for the course was created and can be accessed here. This will mainly be used for discussions between students.
  • Pre-Course Anonymous Survey
  • Full course syllabus available here
  • You can access the Gradescope page for the course here. The code entry code is 4GWP82.

Topics

  • Probability Review
  • Convergence of a Sequence of Random Variables
  • Minimum Mean Squared Error Estimation
  • Jointly Gaussian random variables and vectors
  • Random Walks and Brownian Motion
  • Discrete-Time and Continuous-Time Markov Processes
  • Poisson Process
  • Stationarity and WSS
  • Martingales and the Azuma-Hoeffding Inequality
  • Random Processes Through Linear Systems
  • Kalman and Wiener Filtering
  • PCA and the Karhunen-Loève Expansion

Grading

  • The grading will be distributed as follows:
    • Homework 15%
    • Probability Review Quiz - 10% (Feb 5, in class)
    • First midterm exam - 20% (Mar 4, 7-9pm)
    • Second midterm exam - 20% (Apr 15, 7-9pm)
    • Final Exam - 35% (Thursday, May 9, 8-11am)