| Course title | |||||
| フーリエ解析および演習 [Fourier Analysis & Practices] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 3 | |
| Department | Year | 2～4 | Semester | Spring | |
| Course type | Spring | Course code | 022704 | ||
| Instructor(s) | |||||
| 西舘 泉, 岩井 俊昭 [NISHIDATE Izumi, IWAI Toshiaki] | |||||
| Facility affiliation | Graduate School of Bio-Applications and Systems Engineering | Office | BASE614 | Email address | |
| Course description |
| This course provides students with the mathematical foundations of Fourier analysis. Also, it will address the applications of Fourier analysis to solutions of problems in electric circuit, communication, coding, encryption, and wave analysis. |
| Expected Learning |
| Learners who successfully complete this course will be able to understand the mathematical foundations of Fourier analysis as well as the applications of Fourier analysis to solutions of problems in electric circuit, communication, coding, encryption, and wave analysis. |
| Course schedule |
|
1. Introduction 1.1 Periodic functions 1.2 Complex number and complex plane 1.3 Even and odd functions 2. Fourier series 2.1 Fourier trigonometric series 2.2 Exponential Fourier series 2.3 Circuit equation 2.4 Circuit equation with electromotive force of sine wave alternating current 2.5 Circuit equation with electromotive force of non-sine wave alternating current 3. Fourier transform 3.1 Fourier integral representation 3.2 Properties of Fourier transform 3.3 Circuit equation with electromotive force of non-periodic alternating current 4. Hyperfunction 4.1 Dirac delta function 4.2 Fourier transform of Dirac delta function 4.3 Fourier transform of Dirac delta function periodic function 4.4 Fourier transform of Heaviside step function 5. Convolution and correlation function 5.1 Convolution theorem 5.2 Convolution theorem and Parseval’s theorem 5.3 Sampling theorem 5.4 Correlation function 5.5 Fourier transform of correlation function 6. Application of Fourier transform to liner system 6.1 Solution of linear differential equation 6.2 Linear system 7. Laplace transform 7.1 What is Laplace transform? 7.2 Properties of Laplace transform 7.3 Inverse Laplace transform 7.4 Application of Laplace transform to Solution of linear differential equation 7.5 Relationship between Laplace transform and Fourier transform |
| Prerequisites |
| Required Text(s) and Materials |
| 黒川・小畑著：演習で身につくフーリエ解析（共立出版） |
| References |
| H.P.スウ著、佐藤訳「フーリエ解析」森北出版、松尾著「やさしいフーリエ変換」森北出版、小暮著「なっとくするフーリエ変換」講談社 |
| Assessment/Grading |
| Assessment depends on the total score of short test in every class and final exam. |
| Message from instructor(s) |
| Course keywords |
| Office hours |
| Anytime |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/3/2017 10:15:00 PM |