Fourier Transformation

Euler’s formula

$$e^{i\varphi }=cos\varphi +isin\varphi$$

Amplitude

$$A=\pm \sqrt{Re(\varphi {)}^2+Im(\varphi {)}^2}$$

Phase

$$\mathrm{\Phi }=ta{n}^{-1}\frac{Im(\varphi )}{Re(\varphi )}$$

1 D Fourier Transformation

$$F(u)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}f(x)e^{-i2\pi ux}dx$$

2 D Fourier Transformation

$$F(u,v)=\sum _{x=0}^{M-1}\sum _{y=0}^{N-1}f(x,y)e^{-2\pi i(\frac{ux}{M}+\frac{vy}{N})}$$