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