** directory**

## 一, initial knowledge

- However, it does not matter if you don't understand the meaning of the function, just remember,
**fftshift(distmatrix) generated Is the distance from each coordinate to the center coordinate**can be

```
[M,N] = size(tif);
D = distmatrix(M,N);
Dist = fftshift(D); % distance matrix (from center)
Figure
Subplot(1,2,1),mesh(D),title('distmatrix');
Subplot(1,2,2),mesh(fftshift(D)),title('fftshift(distmatrix)');
```

- About the Fourier transform, knowing the frequency domain filtering knows that the Fourier transform is Time domain (space domain) to frequency domain transition, for 2D Fourier transform, coordinates (1,1) % (0,0)% in Python is a DC signal with a frequency of 0, coordinates (u, v) are in The signal with the frequency in the x direction is u, and the frequency in the y direction is v

## 二, the ideal LPF

, due to the excessive bluntness, the image will produce ringing artifacts.

```
% idea LPF
H1 = zeros(M,N);
radius = 35;
ind = dist <= radius;
H1(ind) = 1;
Hd1 = double(H1);
```

## 三,Gauss LPF

```
% Gaussion LPF
sigma = 30;
H2 = exp(-dist.^2/2/sigma^2);
Hd2 = double(H2);
```

## 四, Butterworth (LPT

```
% Butterworth LPF
D0 = 30;
n = 3;
H3 = 1./(1+(dist/D0).^(2*n));
Hd3 = double(H3);
```