Course Objectives
Learn the basics and applications of the Fourier transformation. Create program codes to perform the discrete Fourier transformation of various data.
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
| Achievement 1 | Able to solve the standard problems of the Fourier transformation. | Able to solve the basic problems of the Fourier transformation. | Unable to solve the basic problems of the Fourier transformation. |
| Achievement 2 | Able to understand the application examples of the Fourier transformation. | Able to understand the application examples of the Fourier transformation, to some extent. | Unable to understand the application examples of the Fourier transformation. |
| Achievement 3 | Able to create the programming codes that perform the discrete Fourier transformation on data. | Able to create the programming codes that perform the discrete Fourier transformation on data, with the help of teachers. | Unable to create the programming codes that perform the discrete Fourier transformation on data. |
Assigned Department Objectives
Teaching Method
Outline:
Overview of engineering applications of Fourier transform and learn Fourier series expansion, Fourier transformation, and discrete Fourier transformation. We will also learn how to compute discrete Fourier transform of the real data using the discrete Fourier transformation libraries in the various programming languages. The first semester is mainly devoted to learning theory. In particular, we will solidify the understanding of the delta function and prepare for applying the theory. In the second half, we will practice programming for the discrete Fourier transformation using the programming language Python. In the exercises, we will perform the numerical calculations of the discrete Fourier transformation, the power spectrum, and the noise removal using a low-pass filter.
Style:
This course will consist of the lectures and exercises. We expect you to actively participate in this class, including the lectures, the exercises, and the submission of the assignments.
Notice:
The mathematics will be explained as needed. In the first and second classes, we will see the application examples of the Fourier analysis (signal analysis, image compression, CT scanning, etc.). After that, the first semester will be devoted to learning the mathematics. In the second half, each group will create the codes for the discrete Fourier transformation. We welcome students who have the programing experiences with the computer languages (C/C++, BASIC, Python, Fortran, etc.), or those who are motivated even if they have no experience. In the second semester, you will be using a PC for the programing, so bring your own PC for the class.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 2nd Semester |
| 3rd Quarter |
| 1st |
Other generalized functions |
Unit step function, window function, signum function. Convolution theorem.
|
| 2nd |
Discrete Fourier transformation 1 |
The derivation of the discrete Fourier transformation(DFT).
|
| 3rd |
Discrete Fourier transformation 2 |
Same as above.
|
| 4th |
Discrete Fourier transformation 3 |
The non-dimensionalized DFT. The matrix expression for the DFT. The fast Fourier transformation.
|
| 5th |
Powere spectral density and signal analysis |
The power spectral density for the DFT, and its symetrisity.
|
| 6th |
Programing for the DFT 1 |
Python programing for the DFT.
|
| 7th |
Programing for the DFT 2 |
Same as above.
|
| 8th |
Programing for the DFT 3 |
Same as above.
|
| 4th Quarter |
| 9th |
Programing for the DFT 4 |
Same as above.
|
| 10th |
Presentation |
Presentation about the midterm achievement.
|
| 11th |
Programing for the DFT 5 |
Python programing for the DFT.
|
| 12th |
Programing for the DFT 6 |
Same as above.
|
| 13th |
Programing for the DFT 7 |
Same as above.
|
| 14th |
Programing for the DFT 8 |
Same as above.
|
| 15th |
Presentation |
Presentation about the final achievement.
|
| 16th |
|
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 0 | 25 | 15 | 0 | 60 | 0 | 100 |
| Basic Proficiency | 0 | 10 | 5 | 0 | 20 | 0 | 35 |
| Specialized Proficiency | 0 | 5 | 5 | 0 | 20 | 0 | 30 |
| Cross Area Proficiency | 0 | 10 | 5 | 0 | 20 | 0 | 35 |