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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 ...
Barker codes of length N equal to 11 and 13 are used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties (the sidelobe level of amplitude of the Barker codes is 1/N that of the peak signal). [15]
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.
The highest absolute cross-correlation in this set of codes is 2 (n+2)/2 + 1 for even n and 2 (n+1)/2 + 1 for odd n. The exclusive or of two different Gold codes from the same set is another Gold code in some phase. Within a set of Gold codes about half of the codes are balanced – the number of ones and zeros differs by only one. [5]
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 ...
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
MUSIC (MUltiple SIgnal Classification) is an algorithm used for frequency estimation [1] [2] [3] ... is traditionally estimated using sample correlation matrix
One common correlation function is the radial distribution function which is seen often in statistical mechanics and fluid mechanics. The correlation function can be calculated in exactly solvable models (one-dimensional Bose gas, spin chains, Hubbard model) by means of Quantum inverse scattering method and Bethe ansatz. In an isotropic XY ...