On regularized Shannon sampling formulas with localized sampling

TL;DR

This paper introduces new regularized Shannon sampling formulas that utilize localized window functions, offering exponential decay and robustness to noise, supported by numerical experiments.

Contribution

It presents novel regularized Shannon sampling formulas with localized windows like Gaussian, B-spline, and sinh-type functions, improving stability and decay properties over classical methods.

Findings

Formulas exhibit exponential decay.

Enhanced robustness to noise.

Numerical experiments confirm theoretical advantages.

Abstract

In this paper we present new regularized Shannon sampling formulas which use localized sampling with special window functions, namely Gaussian, B-spline, and sinh-type window functions. In contrast to the classical Shannon sampling series, the regularized Shannon sampling formulas possess an exponential decay and are numerically robust in the presence of noise. Several numerical experiments illustrate the theoretical results.