Sinh regularized Lagrangian nonuniform sampling series

TL;DR

This paper introduces a sinh-type regularization to nonuniform sampling series, significantly improving convergence rates over existing Gaussian-based methods, supported by theoretical analysis and numerical experiments.

Contribution

It proposes a novel sinh regularization method for nonuniform sampling series, enhancing convergence speed beyond current Gaussian regularized approaches.

Findings

Sinh regularization outperforms Gaussian regularization in convergence rate.

Theoretical error estimates confirm improved convergence.

Numerical experiments validate the superiority of the sinh regularized series.

Abstract

Recently, some window functions have been introduced into the nonuniform fast Fourier transform and the regularized Shannon sampling. Inspired by these works, we utilize a sinh-type function to accelerate the convergence of the Lagrangian nonuniform sampling series. Our theoretical error estimates and numerical experiments demonstrate that the sinh regularized nonuniform sampling series achieves a superior convergence rate compared to the fastest existing Gaussian regularized nonuniform sampling series.