Search results
Results From The WOW.Com Content Network
[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 ...
Cross-covariance may also refer to a "deterministic" cross-covariance between two signals. This consists of summing over all time indices. For example, for discrete-time signals f [ k ] {\displaystyle f[k]} and g [ k ] {\displaystyle g[k]} the cross-covariance is defined as
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 ...
For instance, if the signals are functions of time, the cross-correlation is a measure of the similarity of the two signals as a function of the time lag relative to each other and the autocorrelation is a measure of the similarity of each signal with itself in different instants of time. In this case the coherence is a function of frequency.
The theorem states that the cross-correlation between a Gaussian signal before and after it has passed through a nonlinear operation are equal to the signals auto-correlation up to a constant. It was first published by Julian J. Bussgang in 1952 while he was at the Massachusetts Institute of Technology. [1]
Let (,) represent a pair of stochastic processes that are jointly wide sense stationary with autocovariance functions and and cross-covariance function . Then the cross-spectrum Γ x y {\displaystyle \Gamma _{xy}} is defined as the Fourier transform of γ x y {\displaystyle \gamma _{xy}} [ 1 ]
[A] For complex-valued functions, the cross-correlation operator is the adjoint of the convolution operator. Convolution has applications that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, geophysics, engineering, physics, computer vision and differential equations. [1]
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.