Course Websites
ECE 534 - Random Processes
Last offered Fall 2024
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.
Related Faculty
Subject Area
- General Sciences
Course Director
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.
| Title | Section | CRN | Type | Hours | Times | Days | Location | Instructor |
|---|---|---|---|---|---|---|---|---|
| Random Processes | C | 29989 | DIS | 4 | 1000 - 1120 | W F | 1015 Electrical & Computer Eng Bldg | Dimitrios Katselis |