COM 5110-0

Brief

This course will cover the fundamental theory of random processes with emphasis on applications to signal processing and communications. This is a basic yet important course for students pursuing studies in these fields. The course will include basic concepts, stationarity, convergence of random sequences, law of large numbers, important examples of random processes, and applications to communications and signal processing.

Description

Course keywords: probability, random process, stationary, Markov chain, Gaussian, signal processing 一、課程說明(Course Description) This course will cover the fundamental theory of random processes with emphasis on applications to signal processing and communications. This is a basic yet important course for students pursuing studies in these fields. The course will include basic concepts, stationarity, convergence of random sequences, law of large numbers, important examples of random processes, and applications to communications and signal processing. 二、指定用書(Text Books) Athanasios Papoulis and S. Unnikrishna Pillai, "Probability, Random Variables, and Stochastic Processes," McGraw Hill, 2002 Robert G. Gallager, Stochastic Processes: Theory for Applications, Cambridge University Press, 2017 三、參考書籍(References) TBD 四、教學方式(Teaching Method) 3 hours of weekly lectures plus reading assignments and homework 五、教學進度(Syllabus) 1.Brief Review on Random Variables and Random Vectors. 2.Random Sequences and Random Processes Basic concepts; basic principles of discrete-time linear systems; Random sequences and linear systems; Wide-sense stationary (WSS) random sequences; Markov random sequences; Vector Random sequences and state equations; Convergence of Random sequences; Law of large numbers 3.Random Processes Basic definitions; Some important random processes; Continuous-time linear systems with random inputs; Wide-sense stationary processes and LSI systems; Periodic and cyclostationary processes; Vector processes and state equations. Midterm 4.Advanced Topics in Random Processes Markov Chains; Ergodicity; Karhunen-Loeve expansion; Representation of bandlimited and periodic processes. 5.Applications to Statistical Signal Processing Estimation of random variables; innovation sequences and Kalman Filtering; Wiener filters for random processes; Spectral Estimation. Final Exam 六、成績考核(Evaluation) 30% Homework 35% Midterm 35% Final Exam. 七、可連結之網頁位址 To be announced

Timetable

Scores

Average Percentage 80.65

Std. Deviation 17.2

Remarks

16週課程，本課程每週上課150分鐘，其餘時間由教授彈性運用。

Restrictions

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization