Application of Sampling Theorem to the Synthesis of Transmission Line Tapers and Antenna Radiation Patterns (Correspondence)

In this note it is demonstrated how the sampling theorem may be used to reduce the problems of transmission line taper synthesis and antenna aperture field synthesis to that of optimizing a polynomial. In both cases the problem may be stated mathematically in the following form: find the function g(x) which is zero outside the domain - π≤x≤π that will yield a desired f(u) where f(u) is given by the fourier transform of g(x).