When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the "'autocorrelation coefficient "'. or autocovariance function.
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The correlation coefficient " ? ", expressed as an autocorrelation function or cross-correlation function, depends on the lag-time between the times being considered.
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The value of the autocorrelation function at lag 0 is the power of x ( n ), or its variance if the mean value of x ( n ) is zero:
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*For real-valued functions, the symmetric autocorrelation function has a real symmetric transform, so the Wiener Khinchin theorem can be re-expressed in terms of real cosines only:
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The autocorrelation function, more properly called the autocovariance function unless it is normalized in some appropriate fashion, measures the strength of the correlation between the values of separated by a time lag.
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So we can say that the sum of autocorrelation functions of complementary sequences is a delta function, which is an ideal autocorrelation for many applications like radar pulse compression and spread spectrum telecommunications.
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The motivation for the Wigner function is that it reduces to the spectral density function at all times t for stationary processes, yet it is fully equivalent to the non-stationary autocorrelation function.
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Since this cross-correlation is equal ( save for the K attenuation factor ), to the autocorrelation function of \ scriptstyle s _ { c'}, this is what we consider:
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A similar result holds for power : the area under the power spectral density curve is equal to the total signal power, which is R ( 0 ), the autocorrelation function at zero lag.
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The " n "-point autocorrelation functions for " n " greater than 2 or cross-correlation functions for particular object types are defined similarly to the two-point autocorrelation function.
