Affiliation:
1. Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia
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.
Publisher
National Library of Serbia
Cited by
1 articles.
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