REPRODUCING KERNELS AND THE USE OF ROOT LOCI OF SPECIFIC FUNCTIONS INTHE RECOVERY OF SIGNALS FROM NONUNIFORM SAMPLES

The scope of the sampling expansion and the reproducing kernel approac hes in the recovery of signals from nonuniform samples is extended to transform domains other than the Fourier transform domain. The extensi on is achieved through the direct application of Kramer's generalized sampling theorem. This application produces sampling expansions relate d to reproducing kernels corresponding to signal spaces generated from discrete integral transformations. The coefficients of the sampling e xpansions are samples centered at the roots of specific functions, and , consequently, the root distribution plays a part in the reconstructi on from nonuniform samples, as well as in other applications. The conc ept of a signal with finite support on a discrete set of points is pre sented as the discrete counterpart to the concept of a bandlimited sig nal in the Fourier transform domain.