clear;
close all;
P = peaks(20);
X = repmat(P,[5 10]);
subplot(3,1,1); imshow(X);
title('Default image');

F=fft2(X);
S=abs(F);
subplot(3,1,2); imshow(S, []);
title('Fourier spectrum');

Fc=fftshift(F);
subplot(3,1,3);imshow(abs(Fc), [])
title('Fourier spectrum shifted to center');

figure()
w=fspecial('sobel');
freqz2(w', [200 100]);
title('Sobel filter');
H = freqz2(w', [200 100]);

figure()
L = imfilter(X, w);
subplot(3,1,1); imshow(L);
title('Spatial filtering');

G1 = F*H;
g1 = real(ifft2(G1));
gc1 = g1(1 : 20, 1 : 20);
gs1 = imfilter(X, gc1);
subplot(3,2,3); imshow(gs1);
title('Frequency filtering');
subplot(3,2,4); imshow (abs(gs1) >0.2*abs(max(gs1(:))), [ ]);
title('Frequency filtering adjusted');

G2 = Fc*H;
g2 = real(ifft2(G2));
gc2 = g2(1 : 10, 1 : 10);
gs2 = imfilter(X, gc2);
subplot(3,2,5); imshow(gs2);
title('Frequency filtering centred');
subplot(3,2,6); imshow (abs(gs2) >0.2*abs(max(gs2(:))), [ ]);
title('Frequency filtering centred adjusted');

dif1 = norm(X-L)
dif2 = norm(X-gs1)
dif3 = norm(X-gs2)