1. Fourier Series 2014. 9. 15 Prof. Woonchul Ham
Chonbuk National University, South Korea

2. 1 2 3 4 5 Contents Approximation of vector Approximation of function
Periodic function 4
General formula 5
etc

3. Vector Approximation 1 Quiz: Linear combination problem
Where y1 = (1 2 3) , x1 = (1 0 0) and x2 = ( 0 1 0)
Answer : y1
(1 2 3)
y1 – y1e orthogonal to x1
orthogonal to x2 y z
y1e=(1 2 0) x

4. Vector Approximation 2 Quiz: Linear combination problem
Where y1 = (1 2 3) , x1 = (1 1 0) and x2 = ( 0 1 1)
Answer : y1
(1 2 3)
y1 – y1e orthogonal to x1
orthogonal to x2 y z
y1e x

5. Vector Approximation 2

6. Function Approximation 1/4
Quiz: Linear combination problem

7. Function Approximation 2/4
Quiz: Linear combination problem

8. Function Approximation 3/4
Quiz: Linear combination problem
Let us define inner product of function as follows.

9. Function Approximation 4/4
Quiz: Linear combination problem
We choose orthogonal functions for easiness of calculation!!!

10. Fourier Series 1/6
Quiz: Linear combination problem

11. Fourier Series 2/6
Quiz: Linear combination problem

12. Fourier Series 3/6
Quiz: Linear combination problem

13. Fourier Series 4/6
Quiz: Linear combination problem

14. Fourier Series 5/6
Quiz: Linear combination problem

15. Fourier Series 6/6
Quiz: Linear combination problem