%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%傅里叶变换与反变换%%%%%%%%%%%%%%%%%%%%%

clc;clear; close all

I=imread('lena.bmp');

figure(1);

subplot(231);

imshow(I);

title('原图像');

H=fft2(I);

HH=abs(fftshift(H));

subplot(232);

imshow(log(1+HH),[])

title('幅度谱');

ang=angle(H);

subplot(233);

imshow(ang,[]);

title('相位谱');

I_man=imread('cameraman.bmp');

subplot(234);

imshow(I_man);

title('原图像');

H_man=fft2(I_man);

HH_man=abs(fftshift(H_man));

subplot(235);

imshow(log(1+HH_man),[])

title('幅度谱');

ang_man=angle(H_man);

subplot(236);

imshow(ang_man,[]);

title('相位谱');

figure(2);

Hamp=abs(H);

Iamp=real(ifft2(Hamp));

subplot(221);

imshow(log(1+Iamp),[]);

title('由Lena幅度谱重建的结果');

Hang=complex(cos(ang),sin(ang));

Iang=real(ifft2(Hang));

subplot(222);

imshow(Iang,[]);

title('由Lena相位谱重建的结果');

mix = complex(Hamp.*cos(ang_man),Hamp.*sin(ang_man));

Iamp=real(ifft2(mix));

subplot(223);

imshow(Iamp,[]);

title('Lena幅度、Cameraman相位重建的结果');

Hamp_man=abs(H_man);

mix = complex(Hamp_man.*cos(ang),Hamp_man.*sin(ang));

Iang=real(ifft2(mix));

subplot(224);

imshow(Iang,[]);

title('Cameraman幅度、Lena相位重建的结果');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%频域滤波%%%%%%%%%%%%%%%%%%%%%%%

close all;clear

f=imread('texts.bmp');

figure(1);

subplot(1,2,1);imshow(f);title('Original Image');

F=fftshift(fft2(f));

[row,col] = size(f);

H=zeros(row,col);

hr=row/2;

hc=col/2;

D0=80;

for i=1:row

    for j=1:col

        d=((i-hr)^2+(j-hc)^2);

        H(i,j)=exp(-d/(2*D0^2));        

    end

end

G=F.*H;

g=ifft2(ifftshift(G));

subplot(1,2,2); imshow(uint8(real(g)));title('Low-pass filtrated result')

figure(2);

[U,V]=meshgrid(1:col,1:row);

surf(U,V,H);