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. $\sqrt{N}\mathrm{e}^{-\beta N}$, where $\beta$ is a positive number.
The bound was established based on Fourier-analytic approach, so the condition that $f$ belongs to $L^{2}(\mathbb{R})$ 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 $\mathbb{R}$ and the class of analytic functions in an infinite horizontal strip. The convergence rate is slightly better, of order $\mathrm{e}^{-\beta N}/\sqrt{N}$. Some numerical experiments are presented to confirm the theoretical analysis.
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. $\sqrt{N}\mathrm{e}^{-\beta N}$, where $\beta$ is a positive number.
The bound was established based on Fourier-analytic approach, so the condition that $f$ belongs to $L^{2}(\mathbb{R})$ 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 $\mathbb{R}$ and the class of analytic functions in an infinite horizontal strip. The convergence rate is slightly better, of order $\mathrm{e}^{-\beta N}/\sqrt{N}$. Some numerical experiments are presented to confirm the theoretical analysis.
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