18-751 Applied Stochastic Processes

(12 Units, taught every Fall, next offering Fall 2004, graduate course, satisfies ECE coverage requirements) We introduce random processes and their applications. Throughout the course, we emphasize the discrete-time point of view, although we also discuss the continuous-time case from time to time. Topics covered include: basic concepts of random variables, random vectors, random sequences, stochastic processes, and random fields; expectation and conditional expectation, moments, and characteristic functions; most common classes of random sequences and processes including white noise, Gaussian processes, Markov processes, Poisson processes, and Markov random fields; second order descriptions for random sequences and random processes: mean, auto and cross correlation, auto and crosscovariance; 2nd order Fourier analysis, energy and power spectral and crossspectral densities, and random processes and linear systems. We also present elements of estimation theory and optimal filtering including Wiener and Kalman-Bucy filtering. Advanced topics in modern statistical signal processing such as linear prediction, linear models and spectrum estimation are discussed. 4 hrs. lec. Prerequisites: 36-217 and 18-396 is required for undergraduates, or permission of the instructor.