ECE 534 - Random Processes

Summer 2009 | Fall 2009 | Spring 2010 | Summer 2010
Section Type Times Days Location Instructor
C DIS 1400 - 1520 T R   165 Everitt Lab  Venugopal Veeravalli

Web Page http://courses.ece.uiuc.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. Prerequisite: One of ECE 313, MATH 461, STAT 400.
Hours 4 hours.
Subject Area General Sciences
Course Prerequisites Credit in ECE 313 or MATH 461 or STAT 400
Course Directors Bruce Hajek
Description Basic concepts of random processes; epectral analysis; linear systems with random inputs; Markov chains and Markov processes; spectral analysis, Wiener and Kalman filtering; applications to systems engineering.
Credit 4 hours
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
Course Prerequisites One of ECE 313, MATH 461, STAT 400.
Texts H. Stark and J.W. Woods, Probability, Random Processes and Estimation Theory for Engineers, Prentice-Hall, 1994.