dftfilt(x)

%Question No: 6
%Take a sample image of size 256 by 256. Write a MATLAB function for
%implementing DFT filtering with (a)padding and (b)without padding.
%Compare the results.

function dftfilt(x)
F=imread(x);
F=im2double(F);
[r c]=size(F);
%without padding
sig=10;
DF=DFT(F);
H=gaussfilt(r,c,sig);
R=H.*DF;
G=real(IDFT(R));
%with padding
p=r*2;
q=c*2;
DFP=fft2(F,p,q);
HP=gaussfilt(p,q,2*sig);
RP=HP.*DFP;
GP=real(ifft2(RP));
GPC=GP(1:r,1:c);
figure,imshow(F),title('Original Image');
figure,imshow(G),title('DFT Filtering - Without Padding');
figure,imshow(GPC),title('DFT Filtering - With Padding');
end
function H=gaussfilt(r,c,sig)
u=0:(r-1);
v=0:(c-1);
id=find(u>r/2);
u(id)=u(id)-r;
id=find(v>c/2);
v(id)=v(id)-c;
[V,U]=meshgrid(v,u);
D=sqrt(U.^2+V.^2);
H=exp(-(D.^2)./(2*(sig^2)));
end

function DF=DFT(F)
[r c]=size(F);
F=im2double(F);
N=r;
for m=1:N
    for n=1:N
        W(m,n)=exp((-j*2*pi*(m-1)*(n-1))/N);
    end
end
DF=W*F*W;
end
function DF=IDFT(F)
[r c]=size(F);
F=im2double(F);
N=r;
for m=1:N
    for n=1:N
        W(m,n)=exp((j*2*pi*(m-1)*(n-1))/N);
    end
end
DF=W*F*W;
DF=DF/N^2;
end