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Dirichlet characters, Gauss sums and arithmetic Fourier transforms

Dirichlet characters, Gauss sums and arithmetic Fourier transforms In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic (continuous) functions is developed based on Dirichlet characters, Gauss sums and the generalized Möbius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

Dirichlet characters, Gauss sums and arithmetic Fourier transforms

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-014-2777-2
Publisher site
See Article on Publisher Site

Abstract

In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic (continuous) functions is developed based on Dirichlet characters, Gauss sums and the generalized Möbius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given.

Journal

Applied Mathematics-A Journal of Chinese Universities – Springer Journals

Published: Sep 17, 2014

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