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Zeitschrift für Analysis und ihre Anwendungen


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Volume 32, Issue 4, 2013, pp. 371–387
DOI: 10.4171/ZAA/1490

Published online: 2013-09-19

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

Steffen J. Goebbels[1]

(1) Niederrhein University of Applied Sciences, Krefeld, Germany

W. Dickmeis and R. J. Nessel published their rst 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 nding counterexamples that prove sharpness of error estimates. So far applications of this principle include error bounds for approximation processes, cubature rules, ordinary and partial di erential 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.

Keywords: Sharp error bounds, resonance principle, aliasing, window functions, Fourier transform

Goebbels Steffen: A Sharp Error Estimate for Numerical Fourier Fransform of Band-Limited Functions Based on Windowed Samples. Z. Anal. Anwend. 32 (2013), 371-387. doi: 10.4171/ZAA/1490