Generalized Gaussian quadrature applied to an inverse problem in antenna theory: II. The two-dimensional case with circular symmetry

Abstract

We investigate the linear inverse problem of determining the weighting function for a disc source antenna from its directivity pattern. The relationship between the two is a finite two-dimensional Fourier transform and we use its singular functions to expand the directivity pattern and the weighting function. These singular functions are closely related to the generalized prolate spheroidal functions. The inverse problem is regularized by controlling the superdirective ratio.