翻訳と辞書 Words near each other ・ Poisson formula ・ Poisson games ・ Poisson hidden Markov model ・ Poisson Hill ・ Poisson image editing ・ Poisson kernel ・ Poisson limit theorem ・ Poisson manifold ・ Poisson number ・ Poisson point process ・ Poisson random measure ・ Poisson regression ・ Poisson ring ・ Poisson sampling ・ Poisson scatter theorem ・ Poisson summation formula ・ Poisson superalgebra ・ Poisson supermanifold ・ Poisson Volant ・ Poisson wavelet ・ Poisson's equation ・ Poisson's ratio ・ Poisson, Saône-et-Loire ・ Poissonia ・ Poissonnière (Paris Métro) ・ Poissons ・ Poisson–Boltzmann equation ・ Poisson–Lie group ・ Poissy ・ Poisvilliers Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Poisson summation formula ： ウィキペディア英語版 Poisson summation formula In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original function's Fourier transform. And conversely, the periodic summation of a function's Fourier transform is completely defined by discrete samples of the original function. The Poisson summation formula was discovered by Siméon Denis Poisson and is sometimes called Poisson resummation. ==Forms of the equation== For appropriate functions $f,\backslash ,$  the Poisson summation formula may be stated as: \int_^ f(x)\ e^\, dx.〕 of $f\backslash ,$;  that is   $\backslash hat\; f(\backslash nu)\; =\; \backslash mathcal\backslash .$ |}} With the substitution, $g(xP)\backslash \; \backslash stackrel\backslash \; f(x),\backslash ,$  and the Fourier transform property,  $\backslash mathcal\backslash \backslash \; =\; \backslash frac\; \backslash cdot\; \backslash hat\; g\backslash left(\backslash frac\backslash right)$  (for ''P'' > 0),   becomes: With another definition,  $s(t+x)\backslash \; \backslash stackrel\backslash \; g(x),\backslash ,$  and the transform property  $\backslash mathcal\backslash \backslash \; =\; \backslash hat\; s(\backslash nu)\backslash cdot\; e^,$  becomes a periodic summation (with period ''P'') and its equivalent Fourier series: Similarly, the periodic summation of a function's Fourier transform has this Fourier series equivalent: where T represents the time interval at which a function s(t) is sampled, and 1/T is the rate of samples/sec. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Poisson summation formula」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.