A Sharp Error Estimate for Numerical Fourier Transform of Band-Limited Functions Based on Windowed Samples

被引：1
作者：
Goebbels, Steffen J. [1 ]
机构：
[1] Niederrhein Univ Appl Sci, Fac Elect Engn & Comp Sci, D-47805 Krefeld, Germany
来源：
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2013年 / 32卷 / 04期
关键词：
Sharp error bounds; resonance principle; aliasing; window functions; Fourier transform; CONNECTION; APPROXIMATION; SMOOTHNESS; PRINCIPLE; MODULI; TERMS; RATES;
D O I：
10.4171/ZAA/1490
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
W. Dickmeis and R. J. Nessel published their first version of a quantitative extension of the classical uniform boundedness principle in [J. Approx. Theory 31 (1981), 161-174]. It is a general approach to finding counterexamples that prove sharpness of error estimates. So far applications of this principle include error bounds for approximation processes, cubature rules, ordinary and partial differential equations, and reconstruction from samples. Here we discuss the error of discrete approximations of the Fourier transform based on windowed samples for band-limited functions. The results can be applied to the Hann- and Blackmann-Harris-window but also to window-functions that enable higher orders of convergence. We describe a class of such windows.
引用
收藏
页码：371 / 387
页数：17
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