Statistical Signal Analysis

Review of probability theory and random variables. Transformation (function) of random variables. Conditional expectation. sequence of random variables, convergence of sequence of random variables. stochastic processes : wide sense stationary process, orthogonal increment process, Wiener process, and the Poisson process, KL expansion, ergodicity. Mean square continuity, mean square derivative and mean square integral of stochastic processes. Stochastic systems : response of linear dynamic systems (e.g. state space or ARMA systems) to stochastic inputs, Lyapunov equations, correlational function, power spectral density function, introduction to linear least square estimation, Wiener filtering and Kalman filtering.