Periodic nonuniform sinc-Gauss sampling

Abstract

The periodic nonuniform sampling has attracted considerable attention both in mathematics and engineering although its convergence rate is slow. To improve the convergence rate, some authors incorporated a regularized multiplier into the truncated series. Recently, the authors of [18] have incorporated a Gaussian multiplier into the classical truncated series. This formula is valid for bandlimited functions and the error bound decays exponentially, i.e. ? Ne??N, where ? is a positive number. The bound was established based on Fourier-analytic approach, so the condition that f belongs to L2(R) cannot be considerably relaxed. In this paper, we modify this formula based on localization truncated and with the help of complex-analytic approach. This formula is extended for wider classes of functions, the class of entire functions includes unbounded functions on R and the class of analytic functions in an infinite horizontal strip. The convergence rate is slightly better, of order e??N/? N. Some numerical experiments are presented to confirm the theoretical analysis.