課程資訊
課程名稱
 隨機訊號分析
Random Signal Analysis 
開課學期
 104-2 
授課對象
 共同教育中心  統計碩士學位學程  
授課教師
 周呈霙 
課號
 BME7402 
課程識別碼
 631 M3140 
班次
  
學分
 3 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期一7,8,9(14:20~17:20) 
上課地點
 知203 
備註
 本課程為學程乙組(工程環境組)選修課程之一。
總人數上限：30人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1042BME7402_random 
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課程概述

Course objectives: To become familiar with the theory of random sequences and stochastic processes. To learn the mathematical tools available for the analysis and estimation of random phenomena. To see how stochastic modeling is used in practice. 

課程目標
 1. Review of basic probability: probability spaces, sample description spaces, events, probability measure, random variable, PDFs, PMFs, and pdfs, function of one, two, N random variables, expectations and moments, correlation coefficient, characteristic functions.
2. Random sequences: The meaning of a random sequence, stationary sequences, auto- and cross-correlation functions. Wide-sense stationary sequences; Power spectral density (psd); The Wiener – Khinchin Theorem.
3. Continuous-time random processes: The meaning of a random process; sample functions and sequences of random variables; the random telegraph signal; the binary switching sequence; the Markov random process; white noise; the independent-increment process; power spectrum and correlation functions; Input/output computations; power-spectral estimation.
4. Signal processing: The orthogonality principle; optimum interpolation; hidden Markov process; applications to speech processing; Wiener and Kalman filter.
 
課程要求
 預修科目：工數、信號處理 
預期每週課後學習時數
  
Office Hours
  
指定閱讀
 待補 
參考書目
 Athanasios Papoulis, S. Unnikrishna Pillai, Probability, random variables, and stochastic processes, 4th Edition, McGraw-Hill, c2002.
H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing 3rd Edition, Prentice-Hall, 2002. 
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
第1週
 2/22  Introduction 
第2週
 2/29  No class 
第3週
 3/07  Random variables and probability theory 
第4週
 3/14  Function of a random variable 
第5週
 3/21  Functions of two random variables 
第6週
 3/28  Expected values and characteristic functions 
第7週
 4/04  Spring break -- no class 
第8週
 4/11  Two random functions of two random variables  
第9週
 4/18  Random vectors and processes 
第10週
 4/25  Midterm exam 
第11週
 5/02  Stochastic process 
第12週
 5/09  Power spectral density 
第13週
 5/16  White noise and match filter 
第14週
 5/23  Estimation theory 
第15週
 5/30  MAP and Mean square estimation 
第16週
 6/06  Decision theory 
第17週
 6/13  Decision theory and practice