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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 Bussgang theorem ： ウィキペディア英語版 Bussgang theorem In mathematics, the Bussgang theorem is a theorem of stochastic analysis. The theorem states that the crosscorrelation of a Gaussian signal before and after it has passed through a nonlinear operation are equal up to a constant. It was first published by Julian J. Bussgang in 1952 while he was at the Massachusetts Institute of Technology.〔J.J. Bussgang,"Cross-correlation function of amplitude-distorted Gaussian signals", Res. Lab. Elec., Mas. Inst. Technol., Cambridge MA, Tech. Rep. 216, March 1952.〕 ==Statement of the theorem== Let $\backslash left\backslash$ be a zero-mean stationary Gaussian random process and $\backslash left\; \backslash \; =\; g(X(t))$ where $g(\backslash cdot)$ is a nonlinear amplitude distortion. If $R\_X(\backslash tau)$ is the autocorrelation function of $\backslash left\backslash$, then the cross-correlation function of $\backslash left\backslash$ and $\backslash left\backslash$ is :$R\_(\backslash tau)\; =\; CR\_X(\backslash tau),$ where $C$ is a constant that depends only on $g(\backslash cdot)$. It can be further shown that : $C\; =\; \backslash frac^\backslash infty\; ug(u)e^\}\; \backslash ,\; du.$ 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「Bussgang 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.