In the field of signal processing, circuit theory, control theory etc., Fourier transformation and Laplace transformation
are very important and powerful tools. This course provides some basic knowledge on Fourier series, Fourier transformation
and Laplace transformation. This leads to "Control Engineering" and "Fundamentals of Linear Systems" in later.
Topics include examples, definitions and exercise of Fourier series, Fourier transformation and Laplace transformation. Also
sampling theorem that is very important key tool for data acquisition is derived based on Fourier series expansion.
- -understanding of physical interpretation of Fourier series and its convergence
-derivation of complex form of Fourier series
-drawing of spectrum of Fourier series - -understanding of physical interpretation of Fourier transformation and its basic properties
-calculation of Fourier transformation for non-periodic functions and its spectrum - -applying sampling theorem to examine sampling period
- -understanding of basic properties of Laplace transformation
-calculation of Laplace transformation of elementary functions
-solution of ordinary differential equation applying above - -calculation of impulse/step responses for 1st/2nd order systems
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | -introduction of Fourier series -experiment: element of audio signal -preliminaries |
Euler's forulae, odd/even functions, l'Hospital's rule | 60minutes |
| definite integration, orthogonal functions | 60minutes | ||
| definition of Fourier series expansion | 60minutes | ||
| 2. | -Examples of Fourier series expansion -convergence of Fourier series expansion -Gibbs phenomena |
norm, convergence (uniform convergence, pointwise convergence) | 100minutes |
| Gibbs phenomena | 100minutes | ||
| 3. | -complex form of Fourier series expansion -Fourier transformation |
complex form | 100minutes |
| discrete spectrum | 50minutes | ||
| Fourier transformation | 50minutes | ||
| 4. | -properties of Fourier transformation -decoding of time function |
sinc function and its inverse transformation | 150minutes |
| continuous spectrum | 30minutes | ||
| 5. | -Laplace transformation -properties of Laplace transformation 1 |
linearity, differential/integral formula in Laplace transformation | 200minutes |
| 6. | -properties of Laplace transformation 2 | exponential function | 200minutes |
| 7. | -convolution integral and its Laplace transformation | change of order in integral | 200minutes |
| 8. | -application for solving ordinary differential equation | initial-value problem splution | 100minutes |
| Heaviside's expansion formula | 100minutes | ||
| 9. | -midterm exam -solution and comment |
misunderstanding and pitfall | 360minutes |
| 10. | -discrete Fourier transformation | spectrum | 200minutes |
| 11. | -sampling theorem | Nyquist frequency | 100minutes |
| aliasing phenomenon | 100minutes | ||
| 12. | -response of linear system: 1st order system | linear system, impulse/step responses | 100minutes |
| convolution integral | 100minutes | ||
| 13. | -response of linear system: 2nd order system | spring-mass-damper system | 30minutes |
| poles, zeros, natural angular frequency, damping coefficient | 150minutes | ||
| 14. | -final exam -solution and comment |
misunderstanding and pitfall | 360minutes |
| Total. | - | - | 3060minutes |
| assignment | midterm exam | final exam | Total. | |
|---|---|---|---|---|
| 1. | 10% | 10% | 5% | 25% |
| 2. | 10% | 10% | 10% | 30% |
| 3. | 0% | 0% | 5% | 5% |
| 4. | 5% | 5% | 10% | 20% |
| 5. | 5% | 5% | 10% | 20% |
| Total. | 30% | 30% | 40% | - |
-assignment(30%)
-midterm exam(30%)
-final exam(40%)
The necessary conditions for accreditation are:
1) All assignments should be submitted, and
2) Midterm and fimal exams have been sat
Accreditation criteria is to be able to solve and explain problems in assignments.
-midterm exam(30%)
-final exam(40%)
The necessary conditions for accreditation are:
1) All assignments should be submitted, and
2) Midterm and fimal exams have been sat
Accreditation criteria is to be able to solve and explain problems in assignments.
- Come to listen to the lecture before or after it starts.
- Course that cultivates a basic problem-solving skills
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| Applicable | Applying linear system theory and Laplace/Fourier transformation, lecturer designed practical controller. In lecture, some comments are made for practical image. |
- 4.QUALITY EDUCATION
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Mon Feb 12 04:04:19 JST 2024