Preprint
On the Computation of Fourier Coefficients
Abstract
In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f'(t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f'(t) are known, and vice
versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases.
versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases.
Citation
@article{urn:nbn:de:hebis:34-2006111615737,
author={Koepf, Wolfram and Nana Chiadjeu, Etienne},
title={On the Computation of Fourier Coefficients},
year={2006}
}
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<resource xsi:schemaLocation="http://datacite.org/schema/kernel-2.2 http://schema.datacite.org/meta/kernel-2.2/metadata.xsd"> 2006-11-16T11:00:18Z 2006-11-16T11:00:18Z 2006-11-16T11:00:18Z urn:nbn:de:hebis:34-2006111615737 http://hdl.handle.net/123456789/2006111615737 229838 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Fourier Series 510 On the Computation of Fourier Coefficients Preprint In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f'(t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f'(t) are known, and vice versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases. open access Koepf, Wolfram Nana Chiadjeu, Etienne 68W30 33F10 Fourier-Reihe </resource>
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