This course deals with Fourier series and Fourier transform, which are part of the mathematics that form the basis of information
and communication engineering.
The Fourier series expansion and Fourier transform that you will learn in this course are calculated using the trigonometric functions you have learned so far, such as integrals, partial integrals, and matrices.
These calculations form the basis for time domain and frequency domain analysis in signal processing, which you will use in future courses.
The Fourier series expansion and Fourier transform that you will learn in this course are calculated using the trigonometric functions you have learned so far, such as integrals, partial integrals, and matrices.
These calculations form the basis for time domain and frequency domain analysis in signal processing, which you will use in future courses.
The purpose of this class is to acquire basic mathematical knowledge and be able to apply it to the information and communications
field.
- To calculate the integration of basic trigonometric functions and the Fourier series expansion of periodic functions.
- To perform Fourier transforms and understand the correlation between the time domain and the frequency domain.
- To understand how the Fourier transform is used in the information and communications field.
| 中間試験等 | 期末試験 | Total. | |
|---|---|---|---|
| 1. | 20% | 20% | 40% |
| 2. | 20% | 25% | 45% |
| 3. | 0% | 15% | 15% |
| Total. | 40% | 60% | - |
The midterm exam, exercises, reports, and quizzes will be rated at 40%, and the final exam will be rated at 60%.
A total score of at least 60% will be considered a pass.
Scoring guideline: You can earn 60 points or more if you thoroughly review the content covered in each lesson and are able to derive the answers to the examples and exercises covered in class, as well as similar problems.
A total score of at least 60% will be considered a pass.
Scoring guideline: You can earn 60 points or more if you thoroughly review the content covered in each lesson and are able to derive the answers to the examples and exercises covered in class, as well as similar problems.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | - Introduction - What is Fourier analysis? - Applications of Fourier analysis - Properties and integration of trigonometric functions - Integration of trigonometric functions including elementary functions - Integration of even and odd functions |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 2. | - Integrals of trigonometric functions including exponential functions - Integrals of complex functions - Imperfect integrals and infinite integrals |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 3. | - Fourier series expansion - Fourier coefficients |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 4. | - Gibbs's theorem - Fourier cosine series - Fourier sine series - Fourier series for general periodic functions |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 5. | - Fourier series of general periodic functions - Complex Fourier series |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 6. | - Parseval's equation - Properties of Parseval's equation |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 7. | - Midterm exam [Exam scope] Integration of trigonometric functions, Fourier series expansion, complex Fourier series (assessment of achievement goal 1) - Answer explanation after the exam. |
Review all previous handouts. | 190minutes |
| 8. | - Term-wise differentiation - Term-wise integration |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 9. | - Fourier integral and Fourier transform - Inverse Fourier transform |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 10. | - Fourier sine transform - Fourier cosine transform - Properties of Fourier transform (1) - Inverse transform - Linear law - Differential law - Translation, expansion, and contraction |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 11. | - Properties of the Fourier transform (2) - Convolution - Plancherel's equation - Fourier transform of the delta function |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 12. | - Discrete Fourier transform - Inverse discrete Fourier transform |
Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 13. | - Fast Fourier transform | Download lecture handouts from ScombZ and read it in advance. | 70minutes |
| Confirm the contents of the lecture by solving problems specified in the lecture handouts. | 120minutes | ||
| 14. | - Final exam [Exam scope] Complex Fourier series, Fourier transform, discrete Fourier transform (assessment of achievement goals 2 and 3) - Answer explanation after the exam. |
Review all previous handouts. | 190minutes |
| Total. | - | - | 2660minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
Textbook: "Engineering Basics: Fourier Transform and Its Applications [Revised Edition] (in Japanese)" by Hatagami Itaru,
published by Mathematical Engineering Publishing Co., Ltd. (published by Science Publishing Co., Ltd.)
ISBN978-4-86481-016-6
ISBN978-4-86481-016-6
This course assumes knowledge of "Differential and Integral Calculus 1" and "Differential and Integral Calculus 2," and it
is recommended that students also take "Fourier Analysis."
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | 該当しない |
- 4.QUALITY EDUCATION
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Wed Mar 19 04:08:23 JST 2025