Interpolation of electromagnetic fields from nonuniform samples

A nonuniform sampling algorithm for practical applications must be computationally manageable, stable, and accurate from the point of view of truncation errors. It is more advisable to recover the uniform samples from the irregularly spaced ones than to resort to a direct interpolation formula. Accordingly, once the uniform samples have been determined, the function values can be efficiently recovered by means of the optimal sampling expansions of central type, which minimize the truncation error for a given number of retained samples. Therefore, the main problem is the development of an efficient and stable algorithm to reconstruct the uniform sample values from the irregularly spaced ones. An algorithm is developed for the 1D case; it can be extended to any 2D case for which a uniform sampling representation is available. To test the algorithm performance, a set of numerical experiments has been carried out relevant to the reconstruction of the electric field radiated by a nonfocusing planar circular array symmetric with respect to the x axis.<>