Periodic nonuniform Sinc-gauss sampling

Rashad M Asharabi

Filomat, Tome 37 (2023) no. 1, p. 279

Résumé

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 −βN , where β is a positive number. The bound was established based on Fourier-analytic approach, so the condition that f belongs to L 2 (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 −βN / √ N. Some numerical experiments are presented to confirm the theoretical analysis.

Détail

DOI : 10.2298/FIL2301279A

Classification : 30E10, 30D15, 41A25, 94A20, 41A80, 65B10
Keywords: Nonuniform sampling, Sinc approximation, Gaussian regularization, Entire functions of exponential type, Error bounds