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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 Cross-spectrum ： ウィキペディア英語版 Cross-spectrum In time series analysis, the cross-spectrum is used as part of a frequency domain analysis of the cross-correlation or cross-covariance between two time series. == Definition == Let $(X\_t,Y\_t)$ represent a pair of stochastic processes that are jointly wide sense stationary with autocovariance functions $\backslash gamma\_$ and $\backslash gamma\_$ and cross-covariance function $\backslash gamma\_$. Then the cross-spectrum $\backslash Gamma\_$ is defined as the Fourier transform of $\backslash gamma\_$ : $$ \Gamma_(f)= \mathcal\(f) = \sum_^\infty \,\gamma_(\tau) \,e^ , where : $\backslash gamma\_(\backslash tau)\; =\; \backslash operatorname(-\; \backslash mu\_x)(Y\_\; -\; \backslash mu\_y))$ . The cross-spectrum has representations as a decomposition into (i) its real part (co-spectrum) and its imaginary part (quadrature spectrum) : $$ \Gamma_(f)= \Lambda_(f) + i \Psi_(f) , and (ii) in polar coordinates : $$ \Gamma_(f)= A_(f) \,e^ . Here, the amplitude spectrum $A\_$ is given by : $A\_(f)=\; (\backslash Lambda\_(f)^2\; +\; \backslash Psi\_(f)^2)^\backslash frac\; ,$ and the phase spectrum $\backslash Phi\_$ is given by : $\backslash begin$ \tan^ ( \Psi_(f) / \Lambda_(f) ) & \text \Psi_(f) \ne 0 \wedge \Lambda_(f) \ne 0 \\ 0 & \text \Psi_(f) = 0 \text \Lambda_(f) > 0 \\ \pm \pi & \text \Psi_(f) = 0 \text \Lambda_(f) < 0 \\ \pi/2 & \text \Psi_(f) > 0 \text \Lambda_(f) = 0 \\ -\pi/2 & \text \Psi_(f) < 0 \text \Lambda_(f) = 0 \\ \end 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「Cross-spectrum」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.