Fourier transform (FT) of the 2-dimensional square function
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uppose we were looking at the image of a tiled floor made up alternately of black and white squares aligned with their edges parallel to the x- and y-directions. If the floor were infinite in extent, the mathematical distribution of reflected light could be regarded in terms of a two-dimensional Fourier series. With each tile having a length l, the spatial period along either axis would be 2l, and the associated fundamental angular spatial frequencies would equal pi/l. These and their harmonics would certainly be needed to construct a functiondescribing the scene. Calculate the Fourier transform (FT) of the 2-dimensional square function for this tiled floor.
Transcribed Image Text:The Fourier-transform pair can readily be generalized to two dimensions, whereupon
1
+00
-00
F(kx, ky)e¯i(kxx+kyy) dk dky
f(x, y) =
(2π)
+00
and
F(kx, ky
Ky) = [S
f(x, y) e¹(kxx+kyy) dx dy
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Suppose we were looking at the image of a tiled floor made up alternately of black and white
squares aligned with their edges parallel to the x- and y-directions. If the floor were infinite in
extent, the mathematical distribution of reflected light could be regarded in terms of a two-
dimensional Fourier series. With each tile having a length (, the spatial period along either
axis would be 2e, and the associated fundamental angular spatial frequencies would
equal л/l. These and their harmonics would certainly be needed to construct a
functiondescribing the scene.
Calculate the Fourier transform (FT) of the 2-dimensionnal square function for this tiled flor.
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