Abstract
The shape function s(x, y) of a planar aperture \Sigma is defined ashaving value one inside \Sigma and zero outside. The two-dimensional Fourier transform of s(x, y) when \Sigma is an N -sided polygon is considered, and a closed-form exact solution is presented. Applications of these results are described for 1) the calculation of the secondary pattern of a reflector antenna with a noncircular aperture, and 2) high-frequency transmission through a periodic frequency selective surface.
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