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Error control of a numerical formula for the Fourier transform by Ooura's continuous Euler transform and fractional FFT
http://hdl.handle.net/10445/7721
http://hdl.handle.net/10445/772132a11c3e-a685-4804-adbe-1fd9ad602081
| Item type | 学術雑誌論文 / Journal Article(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2014-09-03 | |||||
| タイトル | ||||||
| タイトル | Error control of a numerical formula for the Fourier transform by Ooura's continuous Euler transform and fractional FFT | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | journal article | |||||
| アクセス権 | ||||||
| アクセス権 | metadata only access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
| 著者 |
田中, 健一郎
× 田中, 健一郎 |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in a given range of the frequency. Recently, some useful formulas for the Fourier transform have been proposed to resolve the difficulty of the computation caused by the slow decay and the oscillation of the integrand. In particular, Ooura proposed formulas with continuous Euler transformation and showed their effectiveness. It has, however, also been reported that their errors become large outside some ranges of the frequency. Then, for an illustrative representative of the formulas, in order to compute the Fourier transform with given accuracy in a given frequency range, we choose the parameters in the formula based on its error analysis. Furthermore, by combining the formula and fractional FFT, a generalization of the fast Fourier transform (FFT), we execute the computation in the same order of computation time as that of the FFT. | |||||
| 書誌情報 |
Journal of Computational and Applied Mathematics 巻 266, p. 73-86, 発行日 2014 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 03770427 | |||||
| 査読有無 | ||||||
| 値 | あり/yes | |||||
| 研究業績種別 | ||||||
| 値 | 原著論文/Original Paper | |||||
| 単著共著 | ||||||
| 値 | 共著/joint | |||||
| 出版者 | ||||||
| 出版者 | Elsevier | |||||
