ECE 534
Random Processes

Section Type Times Days Location Instructor
F DIS 1100 - 1220 T R   245 Everitt Lab  Olgica Milenkovic
Web Page http://courses.engr.illinois.edu/ece534/
Official Description Basic concepts of random processes; linear systems with random inputs; Markov processes; spectral analysis; Wiener and Kalman filtering; applications to systems engineering. Course Information: Prerequisite: One of ECE 313, MATH 461, STAT 400.
Subject Area General Sciences
Course Prerequisites Credit in ECE 313 or MATH 461 or STAT 400 or STAT 410
Course Directors Bruce Hajek
Detailed Description and Outline

Topics:

  • Review of basic probability: probability spaces, random variables, distribution and density functions, expectation, characteristic functions, conditional probability, conditional expectation
  • Sequences of random variables: convergence concepts, laws of large numbers, central limit theorem, large deviations
  • Random vectors and estimation: random vectors, covariance characterization, jointly Gaussian random variables, orthogonality principle, minimum mean squared error estimation, Kalman filtering
  • Basic concepts of random processes: definition and classification, stationarity and ergodicity, correlation functions, continuity, differentiation, and integration of random processes
  • Representations of random processes: sampling theorem, Karhunen-Loeve expansion, envelope representationadn simulation of narrowband processes Special processes: Markov processes, Martingales, Wiener process, Poisson processes, shot noise, thermal noise, random walk
  • Random processes in linear systems and Wiener filtering: spectral analysis of random processes in linear systems, the orthogonality principle, non-casual and casual Wiener filtering
Texts
H. Stark and J.W. Woods, Probability, Random Processes and Estimation Theory for Engineers, Prentice-Hall, 1994.
Last updated: 2/13/2013