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. The Fourier-transform pair can readily be generalized to two dimensions, whereupon1+00-00F(kx, ky)e¯i(kxx+kyy) dk dkyf(x, y) =(2π)+00andF(kx, kyKy) = [Sf(x, y) e¹(kxx+kyy) dx dy108Suppose we were looking at the image of a tiled floor made up alternately of black and whitesquares aligned with their edges parallel to the x- and y-directions. If the floor were infinite inextent, 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 eitheraxis would be 2e, and the associated fundamental angular spatial frequencies wouldequal л/l. These and their harmonics would certainly be needed to construct afunctiondescribing the scene.Calculate the Fourier transform (FT) of the 2-dimensionnal square function for this tiled flor.

Question

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. The Fourier-transform pair can readily be generalized to two dimensions, whereupon1+00-00F(kx, ky)e¯i(kxx+kyy) dk dkyf(x, y) =(2π)+00andF(kx, kyKy) = [Sf(x, y) e¹(kxx+kyy) dx dy108Suppose we were looking at the image of a tiled floor made up alternately of black and whitesquares aligned with their edges parallel to the x- and y-directions. If the floor were infinite inextent, 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 eitheraxis would be 2e, and the associated fundamental angular spatial frequencies wouldequal л/l. These and their harmonics would certainly be needed to construct afunctiondescribing the scene.Calculate the Fourier transform (FT) of the 2-dimensionnal square function for this tiled flor.

Accepted Answer

Answered: Image /qna-images/answer/5814747e-5239-4af5-a047-3a931061d00d.jpg