The Grainger College of Engineering
Electrical & Computer Engineering

ECE 534

ECE 534 - Random Processes

Fall 2024

TitleRubricSectionCRNTypeHoursTimesDaysLocationInstructor
Random ProcessesECE534C29989DIS41000 - 1120 W F  1015 Electrical & Computer Eng Bldg Dimitrios Katselis

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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 Director

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.

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