Frequency Filtered Random Noise

Frequency Filtered Random Noise : another variation of frequency filtered random noise.
(* runtime: 20 seconds *)
n = 275; SeedRandom[1]; fourier = Fourier[Table[Random[], {n}, {n}]];
filter = Table[fourier[[i, j]]/((j/n - 0.5)^2 + (i/n - 0.5)^2), {i, 1, n}, {j, 1, n}];
ListDensityPlot[Map[Abs, InverseFourier[filter], {2}], Mesh -> False, Frame -> False, ColorFunction -> (Hue[# + 0.5] &)];


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