Fourier series and Fourier transform that is the most important mathematics in the field of information and communication
engineering are explained from a technological point of view.
Fourier series and Fourier transform are carried out by the operation using (already learned) integration of the trigonometrical function, partial integration and matrices. These operation is the basics of time-domain and frequency-domain analysis for the signal processing that will be learned later.
Fourier series and Fourier transform are carried out by the operation using (already learned) integration of the trigonometrical function, partial integration and matrices. These operation is the basics of time-domain and frequency-domain analysis for the signal processing that will be learned later.
To acquire basic knowledge of mathematics, and to apply these knowledge to the field of information and communication technology.
- The students who succeeded in this course will be able to to operate basic integration of the trigonometrical function and Fourie series expansion of periodic functions.
- They also will be able to operate Fourier transform, and understand the relation between time-domain and frequency-domain.
- They also will be able to understand the application of Fourier transform to the field of information and communication engineering.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | - Introduction - What is Fourier analysis? - Application example of Fourier analysis - Property and integration of trigonometrical functions - Integration of trigonometrical function including elementary functions - Integration of odd and even functions |
Prepare the material of 1st class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 2. | - Integration of trigonometrical function including exponential functions - Integration which includes complex function - Improper integration - Infinite integration |
Prepare the material of 2nd class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 3. | - Fourier series expansion - Fourier coefficient |
Prepare the material of 3rd class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 4. | - Gibbs' theorem - Fourier cosine series - Fourier sine series - Fourier series of general periodic function |
Prepare the material of 4th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 5. | - Fourier series of more general periodic function - Complex Fourier series - Characteristics of Fourier series (1) - Parseval's identity |
Prepare the material of 5th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 6. | - Characteristics of Fourier series (2) - Meanings of Parseval's identity - Term-by-term integration |
Prepare the material of 6th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 7. | - Midterm exam | Review all materials so far. | 190minutes |
| 8. | - Characteristics of Fourier series (3) - Term-by-term differentiation - Fourier integration and Fourier transform - Fourier inverse transform |
Prepare the material of 8th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 9. | - Fourier cosine transform - Fourier sine transform - Characteristics of Fourier transform (1) - Inverse transform - Linear rule - Differential rule - Shift and Scaling |
Prepare the material of 9th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 10. | - Characteristics of Fourier transform (2) - Convolution - Plancherel's identity |
Prepare the material of 10th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 11. | - Fourier transform of delta function | Prepare the material of 11th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 12. | - Discrete Fourier transform - Inverse discrete Fourier transform |
Prepare the material of 12th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 13. | - Fast Fourier transform | Prepare the material of 13th class which can be downloaded from scomb. | 70minutes |
| Review the material of complete version which can be downloaded from scomb. | 120minutes | ||
| 14. | - Final exam. | Review all materials. | 190minutes |
| Total. | - | - | 2660minutes |
| Midterm examination | Final examination | Total. | |
|---|---|---|---|
| 1. | 16% | 24% | 40% |
| 2. | 12% | 18% | 30% |
| 3. | 12% | 18% | 30% |
| Total. | 40% | 60% | - |
-Grade is judged by the midterm exam (40%), by the final exam (60%).
-Passing standard is over 60%.
-Passing standard is over 60%.
Lecture materials with blanks can be downloaded from scomb
by the 2day before each class. When you miss or could not understand
sufficiently, full version of materials are delivered using scomb
in the next day of the class. So it's desirable to review using these materials.
by the 2day before each class. When you miss or could not understand
sufficiently, full version of materials are delivered using scomb
in the next day of the class. So it's desirable to review using these materials.
Knowledge derived from the class "Differential and Integral Calculus 1 and 2" is supposed to have, and it's desirable to take
the class "Exercise in Differential and Integral Calculus 1 and 2",and "Fourier transformation".
- Before the class (10:40-10:50) and after the class (12:30-13:10).
- E-mail can be received anytime.
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicatable |
|---|---|
| N/A | N/A |
Last modified : Thu Mar 21 15:09:05 JST 2019