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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 Final value theorem ： ウィキペディア英語版 Final value theorem In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain behavior as time approaches infinity. A final value theorem allows the time domain behavior to be directly calculated by taking a limit of a frequency domain expression, as opposed to converting to a time domain expression and taking its limit. Mathematically, if :$\backslash lim\_f(t)$ has a finite limit, then :$\backslash lim\_f(t)\; =\; \backslash lim\_$ where $F(s)$ is the (unilateral) Laplace transform of $f(t)$. Likewise, in discrete time :$\backslash lim\_f()\; =\; \backslash lim\_$ where $F(z)$ is the (unilateral) Z-transform of $f()$. == Proof == By integrating from the definition of Laplace transform of a derivative we have: :$\backslash lim\_\backslash int\_^\backslash frace^dt=\backslash lim\_()$ ''If'' the infinite integral on LHS exists, then the limit of integral can be written as integral of limit, therefore: :$\backslash int\_^\backslash lim\_\backslash frace^dt=\backslash int\_^df(t)=f(\backslash infty)-f(0)$ By equating RHSs of previous equations and canceling f(0) on both sides: :$f(\backslash infty)=\backslash lim\_()$ 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「Final value theorem」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.