I1=imread('Saturn.tif');     
figure,imshow(I1)
I2=imnoise(I1,'salt & pepper');
figure,imshow(I2)
f=double(I2); 
%傅里葉變換
g=fft2(f); 
%轉換數(shù)據(jù)矩陣
g=fftshift(g);
[N1,N2]=size(g);
n=2;
d0=50;
n1=fix(N1/2);
n2=fix(N2/2);
for i=1:N1
   for j=1:N2
      d=sqrt((i-n1)^2+(j-n2)^2);
     %計算Butterworth低通轉換函數(shù)
h=1/(1+0.414*(d/d0)^(2*n)); 
      result(i,j)=h*g(i,j); 
   end
end

result =ifftshift(result); 
X2=ifft2(result);            
X3=uint8(real(X2));
figure,imshow(X3)