Butterworth.txt

close all;
clear all;

f = imread('test4 copy.bmp');
f = mat2gray(f,[0 255]);

[M,N] = size(f);
P = 2*M;
Q = 2*N;
fc = zeros(M,N);

for x = 1:1:M
    for y = 1:1:N
        fc(x,y) = f(x,y) * (-1)^(x+y);
    end
end

F = fft2(fc,P,Q);

H_1 = zeros(P,Q);
H_2 = zeros(P,Q);


for x = (-P/2):1:(P/2)-1
     for y = (-Q/2):1:(Q/2)-1
        D = (x^2 + y^2)^(0.5);
        D_0 = 20;
        H_1(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D/D_0)^2);   
        H_2(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D/D_0)^6);
     end
end
H_3 = 1-H_1;

G_1 = H_1 .* F;
G_2 = H_2 .* F;
G_3 = H_3 .* F;

g_1 = real(ifft2(G_1));
g_1 = g_1(1:1:M,1:1:N);

g_2 = real(ifft2(G_2));
g_2 = g_2(1:1:M,1:1:N);         

g_3 = real(ifft2(G_3));
g_3 = g_3(1:1:M,1:1:N);   

for x = 1:1:M
    for y = 1:1:N
        g_1(x,y) = g_1(x,y) * (-1)^(x+y);
        g_2(x,y) = g_2(x,y) * (-1)^(x+y);
        g_3(x,y) = g_3(x,y) * (-1)^(x+y);
    end
end

figure();
subplot(3,3,1);
imshow(f,[0 1]);
xlabel('a).ԭͼ');

subplot(3,3,2);
pw1=abs(F).^2/128;  
k=0:length(F)-1;
w=2*pi*k/128;
plot(w/pi/2,pw1);
xlabel('b).ԭͼ¹¦ÂÊÆ×');


subplot(3,3,4);
h = mesh(1:20:P,1:20:Q,H_1(1:20:P,1:20:Q));
set(h,'EdgeColor','k');
axis([0 P 0 Q 0 1]);
xlabel('u');ylabel('v');
zlabel('c)Butterworth Lowpass (D_{0}=100,n=1)');


subplot(3,3,5);
imshow(g_1,[0 1]);
xlabel('d).½á¹û');

subplot(3,3,6);
pw2=abs(G_1).^2/128;  
k=0:length(G_1)-1;
w1=2*pi*k/128;
plot(w1/pi/2,pw2);
xlabel('e).¹¦ÂÊÆ×');

subplot(3,3,7);
h = mesh(1:20:P,1:20:Q,H_2(1:20:P,1:20:Q));
set(h,'EdgeColor','k');
axis([0 P 0 Q 0 1]);
xlabel('u');ylabel('v');
zlabel('f).Butterworth Lowpass (D_{0}=100,n=3');


subplot(3,3,8);
imshow(g_2,[0 1]);
xlabel('g).½á¹û');

subplot(3,3,9);
pw3=abs(G_2).^2/128;  
k=0:length(G_2)-1;
w2=2*pi*k/128;
plot(w2/pi/2,pw3);
xlabel('h).¹¦ÂÊÆ×');

figure();
subplot(1,3,1);
h = mesh(1:20:P,1:20:Q,H_3(1:20:P,1:20:Q));
set(h,'EdgeColor','k');
axis([0 P 0 Q 0 1]);
xlabel('u');ylabel('v');
zlabel('a)Butterworth Highpass (D_{0}=20,n=1)');

subplot(1,3,2);
imshow(g_3,[0 1]);
xlabel('b).½á¹û');

subplot(1,3,3);
pw4=abs(G_3).^2/128;  
k=0:length(G_3)-1;
w3=2*pi*k/128;
plot(w3/pi/2,pw4);
xlabel('c).¹¦ÂÊÆ×');