Info
Home
Problem sets
Lecture notes
Statements

ECE 534 - Random Processes (Spring 2025)

Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Instructor: Ilan Shomorony (he/him), ilans@illinois.edu.
Office hours: Monday, 1:00PM - 2:00PM, via Zoom.

Lectures: Monday and Wednesday at 11:00AM - 12:20PM in ECEB 1015
Lectures will be recorded and videos will be available on mediaspace

TAs:

  • Moulik Choraria, moulikc2@illinois.edu. Office hours: Thursday, 2:30 PM - 4:00 PM in room ECEB 2036
  • Yashaswini Murthy, ymurthy2@illinois.edu. Office hours: Tuesday, 3:00 PM - 4:00 PM in ECEB 3034

Recitations: 

  • Friday (Bi-weekly; Next on 3/28), 4:00 PM - 5:00 PM in room ECEB 4070 (Problem-solving, Recordings on mediaspace)

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

  • Midterm 1 was graded. Mean: 42 (out of 65), Standard deviation: 13.2 (solutions)
  • Midterm 1 will be on Monday, 03/10 from 7pm to 9pm CT.
    • Location: ECEB 2015 and ECEB 2017
    • The exam will cover everything until lecture 13.
    • One cheat sheet (two-sided) of handwritten formulas will be allowed.
    • Calculators will not be allowed.
  • The Probability Quiz was graded. Mean: 51.5 (out of 70), Standard deviation: 13
  • The Probability Quiz will be on Monday, 02/10 from 7pm to 9:00pm CT.
    • Location: ECEB 2015 (Last names A-K) and ECEB 2017 (Last names L-Z)
    • A list of topics can be found here.
    • One double-sided sheet of handwritten formulas will be allowed.
    • Calculators are not allowed.
  • There will be no in-person lecture on Monday, 01/27. The lecture has been recorded and is posted on mediaspace.
  • The Piazza for the course can be accessed here. See syllabus for access code.
  • You can access the Gradescope page for the course here. See syllabus for entry code.
  • Full course syllabus available here

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%
    • First midterm exam - 20%
    • Second midterm exam - 20%
    • Final Exam - 35% (May 9, 8am)