Images and sound can be thought of as superpositions of signals (waves), which can be used for compression and noise reduction.
The basis for this is the fact that functions can be decomposed into waves, and this is called Fourier analysis after Fourier,
who studied this.

In this class, students learn the main tools in Fourier analysis: Fourier series, Fourier transform, wavelet transform, and their applications.

In this class, students learn the main tools in Fourier analysis: Fourier series, Fourier transform, wavelet transform, and their applications.

The purpose of this class is to understand the concepts of Fourier series, Fourier transform, and wavelet transform, and to
be able to perform calculations. In addition, students understand how they are used in signal processing and other applications.

- To be able to understand the definition of Fourier series expansion and be able to calculate it.
- To be able to understand the definition of wavelet series expansion and be able to calculate it.
- To be able to understand the definition of Fourier transform and be able to perform basic calculations.
- To be able to understand the definition of wavelet transform and be able to perform basic calculations.
- To be able to understand the following applications of Fourier analysis.

*Differential equation solving using Fourier transform

*Definition of multiresolution representation and its calculation method

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1. | Periodic signal and Fourier series expansion 1 | Read through the handouts, and solve the exercises before class. Review after class. | 190minutes |

2. | Fourier series expansion 2, orthogonal expansion and orthogonal projection | Read through the handouts, and solve the exercises before class. Review after class. | 190minutes |

3. | Fourier Transform | Read through the handouts, and solve the exercises before class. Review after class. | 190minutes |

4. | Fast Fourier Transform and wavelet Transform | Read through the handouts, and solve the exercises before class. Review after class. | 190minutes |

5. | Wavelet transform and its properties | Read through the handouts, and solve the exercises before class. Review after class. | 190minutes |

6. | Engineering applications (multi-resolution representation) and applications to differential equations | Read through the handouts, and solve the exercises before class. Review after class. | 190minutes |

7. | Final examination and its explanation | Preparation of final examination. | 190minutes |

Total. | - | - | 1330minutes |

Final examination | Reports and little examinations | Total. | |
---|---|---|---|

1. | 11% | 11% | 22% |

2. | 11% | 11% | 22% |

3. | 11% | 11% | 22% |

4. | 11% | 11% | 22% |

5. | 6% | 6% | 12% |

Total. | 50% | 50% | - |

Final examination(50%), Reports and little examinations(50%)

60% if students can understand and solve exercises in the handouts

Reports and little examinations will include problems similar to the example problems and the exercises in the handouts.

60% if students can understand and solve exercises in the handouts

Reports and little examinations will include problems similar to the example problems and the exercises in the handouts.

Reference materials:

フーリエ解析、井町昌弘、内田伏一、裳華房

信号処理入門、雨宮好文、佐藤幸男、佐波孝彦、オーム社

よくわかる信号処理、和田成夫、森北出版

フーリエ解析、井町昌弘、内田伏一、裳華房

信号処理入門、雨宮好文、佐藤幸男、佐波孝彦、オーム社

よくわかる信号処理、和田成夫、森北出版

Review Differential and Integral Calculus 1, Differential and Integral Calculus 1, and Mathematical Modeling

- 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 |

Last modified : Wed Mar 23 04:32:09 JST 2022