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%¶þάDFT 
clear 
 
%Filename='Lena256_gaussian.bmp' 
     
P=imread('Lena256_gaussian.bmp'); 
imshow(P) 
P=double(P)/255; 
 
PP=Colortogray(P); 
 
figure 
subplot(2, 3, 1) 
imshow(PP) 
 
%¼ÆËãPPµÄDFT 
[M,N]=size(PP); 
 
FPP=FFT2(PP); 
subplot(2, 3, 2) 
imshow(abs(FPP)/max(max(abs(FPP)))) 
 
FPPs=FFTSHIFT(FPP); 
subplot(2, 3, 3) 
imshow(abs(FPPs)/max(max(abs(FPPs)))) 
  
IFPP=IFFT2(FPP); 
subplot(2, 3, 4) 
imshow(IFPP) 
 
delta=1; 
L=4; 
w0=pi; 
 
for gama=3:4 
     
    LL=floor(6.6*2^gama*delta+1);   
    m0=(2^gama*delta)^2/2; 
    MM=M+LL-1; 
    NN=N+LL-1; 
     
    PPP(MM,NN)=0; 
     
    for i=1:M 
        for j=1:N 
            PPP(i,j)=PP(i,j); 
        end 
    end 
     
    subplot(2, 3, 5) 
    imshow(PPP) 
     
    FPPP=FFT2(PPP);    
         
    for l=2:L-1 
        sita=l*pi/L; 
         
        for u=1:MM 
            for v=1:NN 
                FPPPP(u,v)=FPPP(u,v)*exp(-m0*((2*pi*u/MM-2^(-gama)*w0*cos(sita))^2+(2*pi*v/NN-2^(-gama)*w0*sin(sita))^2)); 
            end 
        end 
         
        IFPPPP=IFFT2(FPPPP); 
        figure 
        imshow(real(IFPPPP)) 
    end 
end