ECE 534 - Random Processes

TitleRubricSectionCRNTypeTimesDaysLocationInstructor
Random ProcessesECE534F33989DIS1100 - 1220 M W  1015 ECE Building Rayadurgam Srikant

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.

Prerequisites

Credit in ECE 313 or MATH 461 or STAT 400 or STAT 410

Subject Area

General Sciences

Course Directors

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.

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

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