EE 632: Random Processes

Tuesdays –Thursdays, 3:00 pm – 4:30 pm, Spring 2003

Prerequisite:

EE 530 or equivalent or permission from the instructor

Textbook:

“Probability and Random Processes with Applications to Signal Processing,” by Henry Stark and John Woods, Prentice Hall, Third Edition, 2002.

Reference Textbooks:

• “Probability and Random Processes,” by Grimmett and Stirzaker, Oxford University Press, Third Edition, 2001.

• “Stochastic Processes,” by Sheldon Ross, Wiley and Sons, Second Edition, 1996.

Course description:

This is a graduate level course on random processes that builds on a first level graduate probability course (EE 530). It covers the basic concepts of random processes and its application to communication and control systems. A brief and tentative outline of the course is given below:
 

• Sequences of Random variables
• Convergence Notions
• Almost sure convergence
• Convergence in probability
• Convergence in mean
• Convergence in distribution
• Limit theorems
• Random Processes
• Continuous and discrete time processes
• Stationarity and Wide-sense stationarity
• Correlation function and power spectral densities
• Different types of Random processes
• Markov processes
• Gaussian processes
• Poisson Processes
• Wiener processes
• Renewal theory (if time permits)
• Calculus for Stochastic Processes
• Continuity, Differentiation and Integration
• Karhunen-Loeve Expansions
• Ergodicity
• Spectral Analysis of Random Processes
• Random processes through linear systems
• Spectral representation of random processes
• MMSE Estimation
• MMSE estimation and linear MMSE estimation for random vector
• Discrete and Continuous time Kalman filter (if time permits)
• Weiner filter and spectral factorization (if time permits)