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Cross-correlation. If each of X and Y is a scalar random variable which is realized repeatedly in temporal sequence (a time series ), then the correlations of the various temporal instances of X are known as autocorrelations of X, and the cross-correlations of X with Y across time are temporal cross-correlations.
Which is an example of the use of signal autocorrelation?
Physically, signal autocorrelation indicates how the signal energy (power) is distributed within the signal, and as such is used to measure the signal power. Typical applications of signal autocorrelation are in radar, sonar, satellite, and wireless communications systems.
How is cross correlation similar to convolution of two functions?
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.
Is the autocorrelation of a periodic function the same?
The autocorrelation of a periodic function is, itself, periodic with the same period. ) is the sum of the autocorrelations of each function separately. Since autocorrelation is a specific type of cross-correlation, it maintains all the properties of cross-correlation.
What is the normalized cross correlation in statistics?
In time series analysis, as applied in statistics, the cross-correlation between two time series is the normalized cross-covariance function.
When does the average converge to the true cross correlation?
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 cross-correlation.
When do you use lagged cross correlation in econometrics?
With complex-valued functions and , taking the conjugate of 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.