A Double Exponential Formula for the Fourier Transforms

@article{Ooura2005ADE,
  title={A Double Exponential Formula for the Fourier Transforms},
  author={Takuya Ooura},
  journal={Publications of The Research Institute for Mathematical Sciences},
  year={2005},
  volume={41},
  pages={971-977}
}
  • T. Ooura
  • Published 31 December 2005
  • Mathematics
  • Publications of The Research Institute for Mathematical Sciences
In this paper, we propose a new and efficient method that is applicable for the computation of the Fourier transform of a function which may possess a singular point or slowly converge at infinity. The proposed method is based on a generalization of the method of the double exponential (DE) formula; the DE formula is a powerful numerical quadrature proposed by H. Takahasi and M. Mori in 1974 [1]. Although it is a widely applicable formula, it is not effective in computing the Fourier transform… 

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