We introduce random processes and their applications. Throughout the course, we mainly take a discrete-time point of view, and discuss the continuous-time case when necessary. We first introduce the basic concepts of random variables, random vectors, stochastic processes, and random fields. We then introduce common random processes including the white noise, Gaussian processes, Markov processes, Poisson processes, and Markov random fields. We address moment analysis (including Karhunen-Loeve transform), the frequency-domain description, and linear systems applied to stochastic processes. We also present elements of estimation theory and optimal filtering including Wiener and Kalman filtering. Advanced topics in modern statistical signal processing such as linear prediction, linear models and spectrum estimation are discussed.
4 hrs. lec.