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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sampling function ： ウィキペディア英語版 Dirac comb In mathematics, a Dirac comb (also known as an impulse train and sampling function in electrical engineering) is a periodic tempered distribution constructed from Dirac delta functions :$\backslash operatorname\_T(t)\; \backslash \; \backslash stackrel\backslash \; \backslash sum\_^\; \backslash delta(t\; -\; k\; T)\; =\; \backslash frac\backslash operatorname\backslash left(\backslash frac\backslash right)$ for some given period ''T''. The symbol $\backslash operatorname(t)$, where the period is omitted, represents a Dirac comb of unit period. Some authors, notably Bracewell as well as some textbook authors in electrical engineering and circuit theory, refer to it as the Shah function (possibly because its graph resembles the shape of the Cyrillic letter sha Ш). Because the Dirac comb function is periodic, it can be represented as a Fourier series: :$\backslash operatorname\_T(t)\; =\; \backslash frac\backslash sum\_^\; e^\}.$ The Dirac comb function allows one to represent both continuous and discrete phenomena, such as sampling and aliasing, in a single framework of continuous Fourier analysis on Schwartz distributions, without any reference to Fourier series. Owing to the Poisson summation formula, in signal processing, the Dirac comb allows modelling sampling via ''multiplication'' with it, but it also allows modelling periodization via ''convolution'' with it.〔; 1st ed. 1965, 2nd ed. 1978.〕 == Dirac Comb Identity == The Dirac comb can be constructed in two ways, either by using the ''comb'' operator (performing sampling) applied to the function that is constantly $1$, or, alternatively, by using the ''rep'' operator (performing periodization) applied to the Dirac delta $\backslash delta$. Formally, this yields :$\backslash operatorname\_T\; \backslash left\; \backslash \; \backslash ,=\backslash ,\; \backslash operatorname\_T\; \backslash ,=\backslash ,\; \backslash operatorname\_T\; \backslash left\; \backslash$ where :$$ \operatorname_T \left \ \,\stackrel\, \sum_^\infty \, f(kT) \, \delta(t-kT)     and     $$ \operatorname_T \left \ \,\stackrel\, \sum_^\infty \, g(t-kT)       ,   . In signal processing, this property on one hand allows sampling a function $f(t)$ via ''multiplication'' with $\backslash operatorname\_T$, and on the other hand it also allows the periodization of $f(t)$ via ''convolution'' with $\backslash operatorname\_T$ (). 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「Dirac comb」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.