ECE 534 - Random Processes (Fall 2019)

Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Lectures: Tuesdays and Thursdays at 11:00AM - 12:20PM in Room 2017, ECE Building.
Instructor: Ilan Shomorony, ilans@illinois.edu, 324 CSL. Office hours: Tuesday 1:30-3:00pm

TAs: Parisa Karimi, parisa2@illinois.edu. Office hours: TBD
         Leda Sari, lsari2@illinois.edu. Office hours: TBD

Recitations: TBD

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

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 Markov Chains
  • Continuous-Time Markov Chains and Poisson Processes
  • Stationarity, WSS and Ergodicity
  • Martingales and the Azuma-Hoeffding Inequality
  • Random Processes Through Linear Systems
  • Kalman and Wiener Filtering
  • Other topics as time permits

Grading

  • Homework 15%
  • Probability Review Quiz - 10%
  • First midterm exam - 20%
  • Second midterm exam - 20%
  • Final Exam - 35%