English: 160_by_160_thumbnail_of_'Green_Sea_Shell' - 1.1. fourier filtered image for downsampling to 40 x 40 in fourier domain.

In R channel in fourierdomain, logarithmic. Zero frequency in the center.

matlab Code: filt=zeros(160,160); filt(1:20,1:20)=1; filt(end-19:end,1:20)=1; filt(1:20,end-19:end)=1; filt(end-19:end,end-19:end)=1; x160_f(:,:,1)=ifft2(fft2(double(x160(:,:,1))).*filt); x160_f(:,:,2)=ifft2(fft2(double(x160(:,:,2))).*filt); x160_f(:,:,3)=ifft2(fft2(double(x160(:,:,3))).*filt);

figure; imagesc(fftshift(log(abs(fft2(x160_f(:,:,1))))));

% information content of the R channel

sum(sum(abs(fft2(x160_f(:,:,1)))))./sum(sum(abs(fft2(x160(:,:,1)))))

% 32.99% of the relevant effective infromation is retained instead of the expected 6.25% (1/16) -> 5.28x more information as expected, ultimately due to the low frequency character and fourier domain sparsity of the image