Exponential Approximation of Band-limited Signals from Nonuniform Sampling

Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A simple Gaussian or hyper-Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling. In this paper, we prove that exponential approximation can also be attained for general nonuniform sampling. The analysis is based on the the residue theorem to represent the truncated error by a contour integral. Several concrete examples of nonuniform sampling with exponential convergence will be presented.