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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 Choi–Williams distribution function ： ウィキペディア英語版 Choi–Williams distribution function Choi–Williams distribution function is one of the members of Cohen's class distribution function.〔E. Sejdić, I. Djurović, J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” ''Digital Signal Processing'', vol. 19, no. 1, pp. 153-183, January 2009.〕 It was first proposed by Hyung-Ill Choi and William J. Williams in 1989. This distribution function adopts exponential kernel to suppress the cross-term. However, the kernel gain does not decrease along the $\backslash eta,\; \backslash tau$ axes in the ambiguity domain. Consequently, the kernel function of Choi–Williams distribution function can only filter out the cross-terms that result from the components that differ in both time and frequency center. == Mathematical definition == The definition of the cone-shape distribution function is shown as follows: :$C\_x(t,\; f)\; =\; \backslash int\_^\backslash infty\; \backslash int\_^\backslash infty\; A\_x(\backslash eta,\backslash tau)\; \backslash Phi(\backslash eta,\backslash tau)\; \backslash exp\; (j2\backslash pi(\backslash eta\; t-\backslash tau\; f))\backslash ,\; d\backslash eta\backslash ,\; d\backslash tau,$ where :$A\_x(\backslash eta,\backslash tau)\; =\; \backslash int\_^\backslash infty\; x(t+\backslash tau\; /2)x^$ *(t-\tau /2) e^\, dt, and the kernel function is: :$\backslash Phi\; \backslash left(\backslash eta,\backslash tau\; \backslash right)\; =\; \backslash exp\; \backslash left(\backslash left(\backslash eta\; \backslash tau\; \backslash right)^2\; \backslash right).$ Following are the magnitude distribution of the kernel function in $\backslash eta,\; \backslash tau$ domain with different $\backslash alpha$ values. As we can see from the figure above, the kernel function indeed suppress the interference which is away from the origin, but for the cross-term locates on the $\backslash eta$ and $\backslash tau$ axes, this kernel function can do nothing about it. 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「Choi–Williams distribution function」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.