The Fourier transform of linearly varying functions with polygonal support

New formulas for the two-dimensional Fourier transform of functions with polygonal support and linear amplitude variation are derived from the corresponding formula for a constant function. These expressions, valid for all nonzero values of the transform variable k, are superior to those previously reported, which fail when k is perpendicular or parallel to any edge of the polygon. These transforms have applications in diffraction theory and computational electromagnetics.<
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