Basic concepts of random processes; spectral analysis; linear systems with random inputs; Markov chains and Markov processes; spectral analysis, Wiener and Kalman  filtering; and applications to communications control systems engineering.

• 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 representation and 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-causal and casual Wiener filtering

H. Stark and J.W. Woods, Probability, Random Processes and Estimation Theory for Engineers, Prentice-Hall, 1994.

• MATH 361 or ECE 313 or STAT 310 or consent of instructor.
• Concurrent registration in MATH 344 or MATH 347 is helpful.

This Course is a Prerequisite For:

ECE 455, ECE 461, and ECE 467

Course Credit:

1 unit.

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