Reconstructing a Band-limited function Using Empirical Orthogonal Functions

A reconstruction procedure for a band-limited function from its samples taken in a finite segment is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited basis function set and then to generate a set of empirical orthogonal functions (EOF´s) adaptively from the sample values of the band-limited function set. Simulation results indicate that, in addition to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, thus suggesting the robustness of the proposed procedure