一. 內容:I. Probability and Random Variablesa) Transformations and Operations on Random Variablesb) Vector Random Variables and Sequence of Random Variables.c) Minimum Mean-Square Estimation, the Orthogonality Principlesd) The Multivariate Distribution. II. Random Processes and Spectral Analysisa) Stationary Concepts, Correlation Functions.b) Time Averages, Ergodicity.c) Correlation Functions and Power Spectrum of Stationary Processes.d) Noise Mechanisms, the Gaussian and Poisson Processes.e) Representations of Random Processes, Orthogonal Expansions. III. Transformations and Operations on Random Processesa) Linear Systems with Random Inputs.b) Representation and Processing of Narrowband Random Processes.c) Finite-State Linear Systems Driven by White Noise. IV. Optimum Linear Systemsa) The Formulation of Optimum Systems.b) Optimum Linear Systems that Maximize Signal-to-Noise Ratio.c) The Orthogonality Principles in Linear Mean-Square Estimation.d) Least Mean-Square Error Filtering, Estimation, Prediction, and the Wiener Filter Theory.二.教科書Peyton Z. Peebles, Jr., PROBABILITY, RANDOM VARIABLES AND RANDOM SIGNAL PRINCIPLES , Fourth Edition, McGraw-Hill, 2001.三.成績評定: Homeworks (10%), Midterm Exam. (45%), and Final Exam (45%).四.預修課程: Probability and Linear Systems are the requisitions for taking the course.