Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?
Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.
Concept
Corrélation croisée
Résumé
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement 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. 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 energy.
In probability and statistics, the term cross-correlations refers to the correlations between the entries of two random vectors and , while the correlations of a random vector are the correlations between the entries of itself, those forming the correlation matrix of . If each of and is a scalar random variable which is realized repeatedly in a time series, then the correlations of the various temporal instances of are known as autocorrelations of , and the cross-correlations of with across time are temporal cross-correlations. 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 and are two independent random variables with probability density functions and , respectively, then the probability density of the difference is formally given by the cross-correlation (in the signal-processing sense) ; however, this terminology is not used in probability and statistics. In contrast, the convolution (equivalent to the cross-correlation of and ) gives the probability density function of the sum .
For continuous functions and , the cross-correlation is defined as:which is equivalent towhere denotes the complex conjugate of , and is called displacement or lag. For highly-correlated and which have a maximum cross-correlation at a particular , a feature in at also occurs later in at , hence could be described to lag by .
Source officielle
À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.