frequency-domain filtering (low-pass and high-pass)

A low-pass filter keeps only frequency bins within a cutoff radius r_0 of the origin (r=\sqrt{f_u^2+f_v^2}\le r_0), removing fine detail and noise while preserving smooth content; a high-pass filter keeps the exact complement (r>r_0), preserving edges and fine texture while discarding the image's own DC average. Both are built by multiplying the DFT by a 0/1 mask, then inverse-transforming (the convolution theorem's filtering application).