### 2023　Theory of Linear System E

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Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s)
Ohashi Takumi
Class Format
Lecture / Exercise    (Blended)
Media-enhanced courses
Courses specified
Day/Period(Room No.)
Mon3-4(S3-207(S322))  Thr3-4(S3-207(S322))
Group
E
Course number
TSE.M203
Credits
2
2023
Offered quarter
2Q
Syllabus updated
2023/3/24
Lecture notes updated
-
Language used
English
Access Index

### Course description and aims

The purpose is to learn how to handle complex numbers and their functions, the concept of frequency, and the theory of linear systems necessary for analyzing these systems, which are important in the study of engineering.

### Student learning outcomes

To learn the basics of linear algebra, the function of complex numbers, Fourier transform, Laplace transform, z-transform, theory to model systems and to understand linear circuits and the basis of control theory.

### Keywords

Determinant, eigenvalue, eigenvector, function of complex numbers, Cauchy-Riemann equations, Taylor series, Laurant series, pole, Fourier expansion, Fourier transform, Laplace transform, discrete time Fourier transform, discrete Fourier transform, z-transform, continuous time system, discrete time system, controllability, observability, and stability.

### Competencies that will be developed

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

### Class flow

Lecture and Practice as follows;

Lecture: The first class (guidance) will be conducted via Zoom. All other classes will be conducted in an on-demand format (i.e., uploaded videos).
Assignments: Submit weekly reports through T2SCHOLA by the deadline specified separately. After the due date, the sample answer and individual feedback to each student will be provided.
Tool: All announcements will be made using Slack, and instructions on how to register for the Slack workspace will be provided on T2SCHOLA.
Q&A: Questions will be accepted via Slack. Office hours via Zoom will be held upon request by students (reservation required via Slack).
Language: English

### Course schedule/Required learning

Course schedule Required learning
Class 1 Guidance (via Zoom), Introduction, Review of Basic Operations (1) To understand the course flow and how to learn in this on-demand style classes effectively. To understand the overview and objectives of the course. Review matrix operations. Be able to solve for minor of matrices, and cofactors.
Class 2 Review of Basic Operations (2) Review matrix operations. Be able to solve for minor of matrices, and cofactors.
Class 3 Complex sine waves To understand the notion of “complex sine wave” and to apply it to AC (alternating-current) electrical circuit
Class 4 Bode plot To understand how to draw Bode plot and its application.
Class 5 Fourier series expansion To be able to decompose periodic function into sine waves of different frequency (Fourier series expansion).
Class 6 Fourier transform To be able to transfer aperiodic function in time domain to function in frequency domain (Fourier transform).
Class 7 Convolution To understand the notion of convolution and relationship with Fourier transform.
Class 8 Laplace transform To be able to handle transient signals by Laplace transform.
Class 9 Control System To understand the notion of “control” and to be able to stabilize unstable system by feedback control.
Class 10 State-space representation To understand “state-space representation” and to be able to handle multiple inputs/outputs for the LTI system.
Class 11 Analysis of continuous-time LTI system To be able to analyze the system in the qualitative and quantitative manners.
Class 12 Discrete-time signal To understand the notion of discrete-time signal and prepare for the z-transform.
Class 13 z-transform To understand z-transform and be able to analyze discrete-time signal.
Class 14 Discrete-time LTI system To solve discrete-time state-space representation by z-transform and analyze the discrete-time LTI system.

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

To enhance effective learning, students are encouraged to spend approximately 200 minutes watching the on-demand videos while note-taking each week. Plus, 200 minutes reviewing class content afterward (including assignments) for each week.
They should refer to textbooks and other course material (videos).

### Textbook(s)

None in particular.

### Reference books, course materials, etc.

Hwei P. Hsu, "Signals and Systems"
(for Japanese speaker) 山下幸彦「線形システム論」朝倉書店, 2013.

### Assessment criteria and methods

Evaluated based on the weekly reports and the face-to-face final examination.
The active participation in the Slack workspace is also evaluated.

### Related courses

• TSE.M201 ： Ordinary Differential Equations and Physical Phenomena

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

None in particular

### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

ohashi.t.af (at) m.titech.ac.jp

### Office hours

An appointment through e-mail is required. After registration to Slack, you can reserve the office hour via Slack.

### Other

The syllabus will be changed as needed.