### 2020　Random Signal Processing

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Undergraduate major in Systems and Control Engineering
Instructor(s)
Tanaka Masayuki
Class Format
Lecture    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
Tue5-6(S516)  Fri5-6(S516)
Group
-
Course number
SCE.I202
Credits
2
2020
Offered quarter
3Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

The real-world signal can be considered as a random signal. The random signal processing is a technique to estimate parameters from the random signal. For that purpose, typical probability distributions will introduced. Then, statistical estimators will be discussed. The course will demonstrate how to use the statistical estimators for real-world problems.

This course will provide a comprehensive overview of the probability distributions and the statistical estimators. The derivations of Gaussian and Poisson distributions will be presented. Law of large numbers and central limit theorem will be proven. Maximum likelihood and maximum a priori will be introduced. The course will conclude by discussing how to apply those estimators to the real-world problem.

### Student learning outcomes

By the end of this course, students will be able to:
1. Explain and derive Gaussian and Poisson distributions
2. Prove and use the law of large numbers and the central limit theorem
3. Explain and apply the maximum likelihood and the maximum a posteriori estimators

### Course taught by instructors with work experience

How instructors' work experience benefits the course ✔ Applicable A faculty who has a private company experience give a lecture.

### Keywords

Gaussian distribution, Poisson distribution, the law of large numbers, the central limit theorem, the maximum likelihood estimator, and a posteriori estimator

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

Assignment is checked and reviewed. Then, main points are discussed in detailed. Student are asked to provide the solution of quick expiries during class.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction of the course Understand importance
Class 2 Definition of probability, mean, variance and moment Compute mean, variance and moment
Class 3 Various types of distributions Know various types of distribution
Class 4 Derivation of Poisson distribution Derive Poisson distribution
Class 5 Moment generating function Understand moment generating function
Class 6 the law of large numbers Understand the law of large number
Class 7 the central limit theorem Proove the central limit theorem
Class 8 application of the central limit theorem Apply the central limit theorem
Class 9 Least square Understand the least squre
Class 10 Conditional probability, posterior, Bayes’ theorem Understand Conditional probability, posterior, Bayes’ theorem
Class 11 Maximum likelihood estimator Understand Maximum likelihood estimator
Class 12 maximum a posteriori estimator Understand maximum a posteriori estimator
Class 13 Natural prior Understand Natural prior
Class 14 stochastic process, filter Understand stochastic process, filter
Class 15 MCMC, Gibbs sampling Understand MCMC, Gibbs sampling

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Slides

### Reference books, course materials, etc.

Books in Japanese

### Assessment criteria and methods

Assignments, excersises, final exams.

### Related courses

• SCE.I201 ： Introduction to Measurement Engineering

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Basics of statistics 