2020 Faculty Courses School of Engineering Undergraduate major in Systems and Control Engineering

Random Signal Processing

Academic unit or major: Undergraduate major in Systems and Control Engineering
Instructor(s): Masayuki Tanaka
Class Format: Lecture (Zoom)
Media-enhanced courses: -
Day of week/Period (Classrooms): 5-6 Tue (S516) / 5-6 Fri (S516)
Class: -
Course Code: SCE.I202
Number of credits: 200
Course offered: 2020
Offered quarter: 3Q
Syllabus updated: Jul 10, 2025
Language: Japanese

Syllabus

Course overview and goals

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.

Course description and aims

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

Student learning outcomes

実務経験と講義内容との関連 (又は実践的教育内容)

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

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/Objectives

	Course schedule	Objectives
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

Study advice (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.

Textbook(s)

Slides

Reference books, course materials, etc.

Books in Japanese

Evaluation methods and criteria

Assignments, excersises, final exams.

Related courses

SCE.I201 ： Introduction to Measurement Engineering

Prerequisites

Basics of statistics