翻訳と辞書 Words near each other ・ Cross-border region ・ Cross-border town naming ・ Cross-boundary subsidy ・ Cross-browser ・ Cross-Canada Hit Parade ・ Cross-cap ・ Cross-Channel guns in the Second World War ・ Cross-check ・ Cross-checking ・ Cross-City Line ・ Cross-city route ・ Cross-class alliance ・ Cross-collateralization ・ Cross-community vote ・ Cross-conjugation ・ Cross-correlation ・ Cross-Correspondences ・ Cross-counter ・ Cross-Country (G.I. Joe) ・ Cross-Country Crime ・ Cross-country cycling ・ Cross-country eliminator ・ Cross-country equestrianism ・ Cross-country flying ・ Cross-country jump ・ Cross-country lines of the Glasgow and South Western Railway ・ Cross-Country Romance ・ Cross-country skiing ・ Cross-country skiing (sport) ・ Cross-country skiing at the 1924 Winter Olympics Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Cross-correlation ： ウィキペディア英語版 Cross-correlation In signal processing, cross-correlation is a measure of similarity of two series as a function of the lag of one relative to the other. This is also known as a ''sliding dot product'' or ''sliding inner-product''. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. For continuous functions ''f'' and ''g'', the cross-correlation is defined as: : $(f\; \backslash star\; g)(\backslash tau)\backslash \; \backslash stackrel\; \backslash int\_^\; f^$ *(t)\ g(t+\tau)\,dt, where $f^$ * denotes the complex conjugate of $f$ and $\backslash tau$ is the lag. Similarly, for discrete functions, the cross-correlation is defined as: : $(f\; \backslash star\; g)()\backslash \; \backslash stackrel\; \backslash sum\_^\; f^$ *()\ g(). The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal power. In probability and statistics, the term cross-correlations is used for referring to the correlations between the entries of two random vectors ''X'' and ''Y'', while the ''autocorrelations'' of a random vector ''X'' are considered to be the correlations between the entries of ''X'' itself, those forming the correlation matrix (matrix of correlations) of ''X''. This is analogous to the distinction between autocovariance of a random vector and cross-covariance of two random vectors. One more distinction to point out is that in probability and statistics the definition of ''correlation'' always includes a standardising factor in such a way that correlations have values between −1 and +1. If $X$ and $Y$ are two independent random variables with probability density functions ''f'' and ''g'', respectively, then the probability density of the difference $Y\; -\; X$ is formally given by the cross-correlation (in the signal-processing sense) $f\; \backslash star\; g$; however this terminology is not used in probability and statistics. In contrast, the convolution $f$ * g (equivalent to the cross-correlation of ''f''(''t'') and ''g''(−''t'') ) gives the probability density function of the sum $X\; +\; Y$. ==Explanation== As an example, consider two real valued functions $f$ and $g$ differing only by an unknown shift along the x-axis. One can use the cross-correlation to find how much $g$ must be shifted along the x-axis to make it identical to $f$. The formula essentially slides the $g$ function along the x-axis, calculating the integral of their product at each position. When the functions match, the value of $(f\backslash star\; g)$ is maximized. This is because when peaks (positive areas) are aligned, they make a large contribution to the integral. Similarly, when troughs (negative areas) align, they also make a positive contribution to the integral because the product of two negative numbers is positive. With complex-valued functions $f$ and $g$, taking the conjugate of $f$ ensures that aligned peaks (or aligned troughs) with imaginary components will contribute positively to the integral. In econometrics, lagged cross-correlation is sometimes referred to as cross-autocorrelation. 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-correlation」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.