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[ELEC5300]不那么隨機过的隨機過程

課程時間:2019年F季
授課教授:MOW, Wai Ho

我覺得教授:挺不错的,讲课挺清楚
評分標準:assignment 15%  + midterm 35% + final 50% 这个sem没有参考价值

這門課的Grade:Grade神/較好 同上

内容:就是接著elec2600的内容繼續講。這門課雖然標題叫隨機過程,不過内容上我覺得更像是統計信號處理,和math那邊的隨機過程差別還挺大的。math3425主要是講各種隨機過程的model,而這門課講的是如何利用各種統計學上的性質來預測信號。下面我附了syllabus的。這門課主要就是教了你一些隨機過程的性質,重點是如何運用。主要就是各種filter來回用,對於communication還是比較重要的,signal processing上的用處也還是蠻大的。這門課講了wiener filter之後,可以推導一下2D情況下的,對於image processing中的相關部分理解有一定幫助。

我覺得難度不大,這門課以前也是4000level的。根據我上課的經驗,pre-requisite應該是elec2100和elec2600,畢竟拉普拉斯變換和Z變換用的飛起,上課也都默認你很熟悉信號與系統那些東西了。elec3100有部分内容有涉及到,不過我覺得問題不大,遇見了再自學即可。根據phd們的表述,這門課算是比較簡單的pg課,而且課堂上我也看見了不少認識的ug來上,多半是ee和cpeg的。總體來説我覺得,如果想稍微多學一些概率,又不想直接去上math版,可以先來這邊過度一下。

這門課最大的問題就是,6點鐘到9點鈡,3個小時,我從來沒有清醒地完整聽完過。所以下來還是得自己多看看,因爲上課多半是昏昏欲睡的。

至於grade,又是elec又是pg課,還用說嗎。

有用又好龟,而且不算難。

syllabus:

Lecture 1: Review of Probability Theory and Random Variables

·       Review of Basic Probability

o   Random Experiments

o   Axioms of Probability

o   Conditional Probability and Independence

·       Single Random Variables (RVs)

o   Definition and equivalent events

o   Specifying a RV (CDF, PDF, PMF, Characteristic Function)

o   Expectation of a RV and functions of a RV, Moments

o   Mean as the minimum mean squared error estimate

·       Multiple RVs

o   Joint distribution and density functions

o   Conditional density and independence

o   Expectation and joint moments

o   Correlation and Covariance

Lecture 2: Transformations, Random processes, Convergence

·       Affine Functions of RVs

o   Density

o   Mean and variance

·       Jointly Gaussian RVs

o   Definition

o   Properties

·       Random Processes and Sequences

o   Definitions and intepretations

o   Convergence of random sequences

o   Specifying RPs by joint distributions/densities

o   Mean, autocorrelation and covariance functions

o   Examples: IID and Gaussian RPs

Lecture 3: Stationary random processes, Power spectral density

·       Stationary and Wide-Sense Stationary RPs

o   Properties of the autocorrelation of WSS RPs

·       Ergodicity

·       Multiple Random Processes

o   Cross correlation function

·       Power Spectral Density

o   Cross Power Spectral Density

·       Important Random Processes

o   Continuous Time White Noise

o   Bandlimited White Noise

o   Gauss-Markov Process

o   Random Telegraph Signal

o   Wiener Process

Lecture 4: Response of Linear Systems to Random Inputs

·       Continuous time linear systems: a review

·       Filtering WSS Random Processes

o   Mean, Cross and Autocorrelations, Power Spectral Density

o   Generating the Gauss-Markov Process

o   Filtering the Gauss-Markov and Bandlimited White Noise Processes

o   Regular Processes

o   Spectral Factorization

o   Noise equivalent bandwidth

·       Transient analysis of linear systems

o   Response to initial conditions and input

o   Weiner process

Lecture 5: Estimation and optimal filtering

·       Minimum mean squared estimation

o   Linear estimation from single variable data

o   Orthogonality principle

o   Estimation from multiple variable data

o   Whitening viewpoint

o   Optimal nonlinear estimator

o   Generalized orthogonality principle

o   Estimating Gaussian Random Variables

·       Optimal linear filtering

o   Parameter optimization

o   Continuous-time Weiner filtering

o   Orthogonality principle

§  Non-causal filter

§  Causal filter for white data

§  Causal filter for colored data

Lecture 6: Discrete-time Wiener Filtering

·       Discrete-time linear filtering of random processes

·       Discrete-time regular processes

·       Discrete-time Wiener filtering

·       Comparison of estimation from N random variables with continuous/discrete-time Weiner filtering

Lecture 7: Parameter Estimation

·       Maximum-likelihood estimation

o   Introduction

o   Single parameters

o   Multiple parameters

·       Properties of Estimates

o   Biasedness and convergence

o   Cramer-Rao bound

§  Proof

§  Alternative form and example

Lecture 8: Parameter Estimation (cont)

·       Estimating the autocorrelation

·       Estimating the power spectral density

·       Bayesian Estimation

o   Motivation and the Conjugate Prior

o   Bernoulli distribution

o   Mean of the Gaussian

o   Mean and Variance of the Gaussian

·       Exponential family of distributions

Lecture 9: Principal Component Analysis and Deterministic Least Squares (Outside Exam Scope)

·       Principal Component Analysis 

o   Motivation

o   Maximum variance formulation

§  Constrained Optimization

o   Minimum error formulation

o   Applications

·       Deterministic Least Squares 

o   Problem formulation and solution

o   Properties of solution

o   Dealing with correlated noise

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