New rigorous solution of some antenna synthesis problems according to prescribed amplitude radiation pattern

The problem of the least-square minimization of the difference between the prescribed and obtained amplitude patterns is solved for the linear antenna in the closed form with a limited number of complex parameters which are calculated from the set of transcendental equations. The number of parameters depends on the electrical length of the antenna. Numerical results are presented. The method is extended to equidistant linear antenna arrays. The results may be applied to other problems described by the continuous or discrete Fourier transformation.