Interpolation of electromagnetic radiated fields over a plane by nonuniform samples

An iterative algorithm is developed which allows the interpolation of two-dimensional band-limited functions from nonuniformly distributed samples. Such a scheme is based on optimal sampling expansions of central type and is applied to the interpolation of electromagnetic fields over a plane. The algorithm can be applied whenever the “average” sample´s density is higher than the Nyquist one and there is a one-to-one correspondence between the nonuniform samples and a lattice of the uniform ones, which associates at each uniform sampling point the nearest nonuniform sampling point. As compared with the optimal linear estimation algorithm, the procedure is computationally much more efficient. Many numerical simulations have assessed the rapid convergence of the method as well as its stability with respect to both absolute and relative errors in the data