y2fft.m

自己手写的图像的FFT变换和DCT变换的MATLAB代码

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

%%%%%%%   二维的Lena图像的傅立叶变换，并显示出变换后的Lena图像     %%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Y2FFT()
f=imread('Lena.bmp');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%       显示初始的图像   %%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
imshow(f);
title '原始的Lena图像';
[wideth,height]=size(f);
  y=zeros(wideth,height);
    q=zeros(wideth,height);
    for i=1:wideth
        for j=1:height
            y(i,j)=f(i,j);
        end;
    end;
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    %%%%%%%%%  进行行的傅立叶变换  %%%%%%%%%%%%%%%
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    temp=zeros(1,height);
    for i=1:wideth
        for j=1:height
            temp(j)=y(i,j);            
        end;
        temp=Y1FFT(temp,height);
        for j=1:height
            y(i,j)=temp(j);
        end;
    end;
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    %%%%%%%%%  进行列的傅立叶变换  %%%%%%%%%%%%%%%
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    temp=zeros(1,height);
    for j=1:height
        for i=1:wideth
            temp(i)=y(i,j);            
        end;
        temp=Y1FFT(temp,wideth);
        for i=1:wideth
            y(i,j)=temp(i);
        end;
    end;
    % % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % 

%%%%%%%%%%%%%%%%%%            将进行完傅立叶变换后的数值求其模，进行实数的转换       %%%%%%%%%%%%%%%%%%%%%%%

% % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % % % % %% % % % 
 [wideth,height]=size(f);
for i=1:1:wideth
    for j=1:1:height
        q(i,j)=abs((sqrt(real(y(i,j))*real(y(i,j))+imag(y(i,j))*imag(y(i,j))))/100);
        if q(i,j)>255
            q(i,j)=255;
        end;
    end;
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%        调整图像的显示的中心    %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:1:height
    for j=1:1:wideth
       if(i>height/2)
            i1=i-height/2;
        else 
            i1=i+height/2;
       end;
        if(j>wideth/2)
             j1=j-wideth/2;
        else
             j1=j+wideth/2;
        end;
         y1(i1,j1)=uint8(q(i,j)); %%%%%取整操作
    end;
end;
    figure,imshow(y1);
    title '傅立叶变换后的Lena图像';
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%                   傅立叶反变换                 %%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  for i=1:wideth
        for j=1:height
            uu(i,j)=conj(y(i,j));
        end;
  end;
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    %%%%%%%%%  进行行的傅立叶反变换  %%%%%%%%%%%%%%%
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    temp2=zeros(1,height);
    for i=1:wideth
        for j=1:height
            temp2(j)=uu(i,j);            
        end;
        temp2=Y1FFT(temp2,height)/height;
        for j=1:height
            uu(i,j)=temp2(j);
        end;
    end;
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    %%%%%%%%%  进行列的傅立叶反变换  %%%%%%%%%%%%%%%
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    temp2=zeros(1,height);
    for j=1:height
        for i=1:wideth
            temp2(i)=uu(i,j);            
        end;
        temp2=Y1FFT(temp2,wideth)/wideth;
        for i=1:wideth
            uu(i,j)=conj(temp2(i));
        end;
    end;      
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     for i=1:1:wideth
%     for j=1:1:height
%         uu(i,j)=abs((sqrt(real(uu(i,j))*real(uu(i,j))+imag(uu(i,j))*imag(uu(i,j))))/100);
%         if uu(i,j)>255
%             uu(i,j)=255;
%         end;
%     end;
% end;
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    figure, imshow(real(uint8(uu)));
    title '进行反变换后的图像';
end