Electromagnetic fields interpolation from nonuniform samples over spherical and cylindrical surfaces

Algorithms for the interpolation of electromagnetic fields from nonuniformly spaced samples over a sphere and over a cylinder are presented. They use an iterative technique and are based on optimal sampling expansions of central type. The algorithms have been found to be convergent if the average sample´s density is slightly higher than the Nyquist one and if it is possible to build a one-to-one correspondence between the nonuniform samples and a lattice of the uniform ones, by associating at each uniform sampling point the nearest nonuniform one. Many numerical simulations have assessed the rapid convergence of the method and have shown that the procedure is computationally much more efficient than the optimal linear estimation algorithm. Moreover, the proposed algorithms can be successfully applied to the case of interpolation from power samples and are stable with respect to both absolute and relative errors in the data