18-751: Applied Stochastic Processes

Course Description

We introduce random processes and their applications. Throughout the course, we mainly take a discrete-time point of view, and discuss the continuous-time case when necessary. We first introduce the basic concepts of random variables, random vectors, stochastic processes, and random fields. We then introduce common random processes including the white noise, Gaussian processes, Markov processes, Poisson processes, and Markov random fields. We address moment analysis (including Karhunen-Loeve transform), the frequency-domain description, and linear systems applied to stochastic processes. We also present elements of estimation theory and optimal filtering including Wiener and Kalman filtering. Advanced topics in modern statistical signal processing such as linear prediction, linear models and spectrum estimation are discussed.

  • Number of Units: 12

  • Pre-requisite: 18-391 and senior or graduate standing

  • Course Area: Signals and Systems, Signal Processing and Communications

  • Tentative Syllabus: Given here

Instructor and Administrative Staff

  • Instructor: Prof. Osman Yağan                        diamond Teaching Assistant: Yingrui Zhang

  • Office Location: Bldg. 23, 221                         diamond Office: Bldg. 19,

  • Email Address: oyagan@ece.cmu.edu           diamond Email: yingruiz@andrew.cmu.edu

  • Office Hours: TBD             diamond Office Hours: TBD

Class Schedule

  • Lecture: Mondays and Wednesdays 9:30 am – 11:20 am

  • Recitation: Fridays 9:30 am - 11:20 am

  • Location: Bldg. 23, Room 212


  • A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed., McGraw-Hill, 2001.

Recommended supplementary readings:

  • Robert Gallager, Stochastic Processes: Theory for Applications, Draft available here.

  • A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed., Prentice Hall, 1993.

  • C.W. Helstrom, Probability and Stochastic Processes for Engineers, 2nd ed., Prentice Hall, 1990.


Homeworks (Best 9 out of 10 sets) 30%
Quizzes (3 sets) 10%
Tests (3 tests, 20% each) 60%