%二值圖象的傅里葉變換
f=zeros(30,30);
f(5:24,13:17)=1;
figure,imshow(f,'notruesize')
F=fft2(f);
figure,mesh(fftshift(abs(F)));%繪制頻譜圖(量化表現(xiàn))(此處有問題)fftshift把零頻率部分搬移到頻譜中間
F2=fftshift(log(abs(F)));%未填充
figure,imshow(F2,[-1 5],'notruesize');%顯示頻譜圖像（顏色表現(xiàn)）
F=fft2(f,256,256);%填充
figure,imshow(fftshift(log(abs(F))),[-1 5]);
colormap(jet);colorbar


%平移特性
f=zeros(1000,1000);
f(350:649,475:524)=1;
subplot(221);%數(shù)據(jù)之間要么用逗號(hào)，要么什么也不用
imshow(f,'notruesize');
title('原始圖象');
subplot(222);
F=fftshift(abs(fft2(f)));
imshow(F,[-1,5],'notruesize');
title('原始圖象的傅里葉變換頻譜');
subplot(223);
f=zeros(1000,1000);
f(350:649,800:849)=1;
imshow(f,'notruesize');
title('x軸方向移動(dòng)后的圖象')
subplot(224);
F=fftshift(abs(fft2(f)));
imshow(F,[-1 5],'notruesize');
title('x軸方向移動(dòng)后的傅里葉變換頻譜');


f=zeros(1000,1000);
f(350:649,475:524)=1;
subplot(221);
imshow(f,'notruesize');
title('原始圖象');
subplot(222);
F=fftshift(abs(fft2(f)));
imshow(F,[-1,5],'notruesize');
title('原始圖象的傅里葉變換頻譜');
subplot(223);
f=zeros(1000,1000);
f(50:349,475:524)=1;
imshow(f,'notruesize');
title('y軸方向移動(dòng)后的圖象')
subplot(224);
F=fftshift(abs(fft2(f)));
imshow(F,[-1 5],'notruesize');
title('x軸方向移動(dòng)后的傅里葉變換頻譜');


%旋轉(zhuǎn)特性
f=zeros(1000,1000);
f(350:649,475:524)=1;
subplot(221);
imshow(f,'notruesize');
title('原始圖象');
subplot(222);
F=fftshift(abs(fft2(f)));
imshow(F,[-1,5],'notruesize');
title('原始圖象的傅里葉變換頻譜');
subplot(223);
f=zeros(1000,1000);
f(50:349,475:524)=1;
f=imrotate(f,45,'bilinear','crop');%以圖象中心為原點(diǎn)旋轉(zhuǎn)45度,(好像有問題)
imshow(f,'notruesize');
title('圖象正向旋轉(zhuǎn)45^{0}');
subplot(224);
F=fftshift(abs(fft2(f)));
imshow(F,[-1 5],'notruesize');
title('圖象旋轉(zhuǎn)45^{0}后的傅里葉變換頻譜')