Quantitative Estimates: How Well Does the Discrete Fourier Transform Approximate the Fourier Transform on [math]

IF 6.1 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2026-02-09 DOI:10.1137/24m1650399

Martin Ehler, Karlheinz Gröchenig, Andreas Klotz

引用次数: 0

Abstract

SIAM Review, Volume 68, Issue 1, Page 93-123, February 2026.
Abstract. In order to compute the Fourier transform of a function [math] on the real line numerically, one samples [math] on a grid and then takes the discrete Fourier transform. We derive exact error estimates for this procedure in terms of the decay and smoothness of [math]. The analysis provides an asymptotically optimal recipe for how to relate the number of samples, the sampling interval, and the grid size.

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定量估计：离散傅立叶变换在数学上近似傅立叶变换有多好

SIAM评论，第68卷，第1期，第93-123页，2026年2月。摘要。为了在实数线上数值计算函数的傅里叶变换，在网格上采样，然后进行离散傅里叶变换。我们根据[数学]的衰减和平滑度推导出这个过程的精确误差估计。该分析为如何将样本数量、采样间隔和网格大小联系起来提供了一个渐近最优配方。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.