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function FI=fft_filt_2(V,FB,sf);
% FI=fft_filt_2(V,FB,sf);
% fft-based filtering
% requires image to be called "V"
% and filters to be in FB
% sf is the subsampling factor
%
% FI is the result
[M1,M2,N3]=size(FB);
% prepare FFT of image for filtering
[N1,N2]=size(V);
I=zeros(size(V)+[M1-1 M2-1]);
I(1:N1,1:N2)=V;
N1s=length(1:sf:N1);
N2s=length(1:sf:N2);
IF=fft2(I);
FI=zeros(N1s,N2s,N3);
% apply filters
for n=1:N3;
f=rot90(FB(:,:,n),2);
fF=fft2(f,N1+M1-1,N2+M2-1);
IfF=IF.*fF;
If=real(ifft2(IfF));
If=If(ceil((M1+1)/2):ceil((M1+1)/2)+N1-1,ceil((M2+1)/2):ceil((M2+1)/2)+N2-1);
FI(:,:,n)=If(1:sf:N1,1:sf:N2);
end
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