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[12] [13] [clarification needed] After calculating the cross-correlation between the two signals, the maximum (or minimum if the signals are negatively correlated) of the cross-correlation function indicates the point in time where the signals are best aligned; i.e., the time delay between the two signals is determined by the argument of the ...
The samples included in the average can be an arbitrary subset of all the samples in the signal (e.g., samples within a finite time window or a sub-sampling of one of the signals). For a large number of samples, the average converges to the true covariance. Cross-covariance may also refer to a "deterministic" cross-covariance between two signals.
In signal processing, the coherence is a statistic that can be used to examine the relation between two signals or data sets. It is commonly used to estimate the power transfer between input and output of a linear system. If the signals are ergodic, and the system function is linear, it can be used to estimate the causality between the input ...
Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric [ 19 ] is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images.
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them.
The r* cross-correlation metric is based on the variance metrics of SSIM. It's defined as r*(x, y) = σ xy / σ x σ y when σ x σ y ≠ 0, 1 when both standard deviations are zero, and 0 when only one is zero. It has found use in analyzing human response to contrast-detail phantoms. [18] SSIM has also been used on the gradient of ...
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1] If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an ...
The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The cross-correlation matrix is used in various digital signal processing algorithms.