Fourier Series Prof. Woonchul Ham

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Presentation transcript:

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

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

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

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

Vector Approximation 2

Function Approximation 1/4 Quiz: Linear combination problem

Function Approximation 2/4 Quiz: Linear combination problem

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

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

Fourier Series 1/6 Quiz: Linear combination problem

Fourier Series 2/6 Quiz: Linear combination problem

Fourier Series 3/6 Quiz: Linear combination problem

Fourier Series 4/6 Quiz: Linear combination problem

Fourier Series 5/6 Quiz: Linear combination problem

Fourier Series 6/6 Quiz: Linear combination problem