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Dirichlet characters, Gauss sums and arithmetic Fourier transforms

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Jing Gao

  2. School of Mathematics, Northwest University, Xi’an, 710127, China

    Hua-ning Liu

Authors
  1. Jing Gao
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  2. Hua-ning Liu
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Correspondence to Jing Gao.

Additional information

Supported by National Natural Science Foundation of China (11201370), the Science and Technology Program of Shaanxi Province of China (2013JM1017, 2014JM1007, 2014KJXX-61), and the Natural Science Foundation of the Education Department of Shaanxi Province of China (2013JK0558).

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Gao, J., Liu, Hn. Dirichlet characters, Gauss sums and arithmetic Fourier transforms. Appl. Math. J. Chin. Univ. 29, 307–316 (2014). https://doi.org/10.1007/s11766-014-2777-2

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  • DOI: https://doi.org/10.1007/s11766-014-2777-2

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