44 207 242 6447 Autocorrelation A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. Definitions[edit] Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Statistics[edit] where "E" is the expected value operator. If Xt is a second-order stationary process then the mean μ and the variance σ2 are time-independent, and further the autocorrelation depends only on the lag between t and s: the correlation depends only on the time-distance between the pair of values but not on their position in time. and the fact that this is an even function can be stated as It is common practice in some disciplines, other than statistics and time series analysis, to drop the normalization by σ2 and use the term "autocorrelation" interchangeably with "autocovariance". Signal processing[edit] , the continuous autocorrelation where at lag is , or
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Mathletics - Inspiring Better Results Cross-correlation In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomographic averaging, cryptanalysis, and neurophysiology. For continuous functions f and g, the cross-correlation is defined as: where f* denotes the complex conjugate of f and t is the time lag. Similarly, for discrete functions, the cross-correlation is defined as: 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 unless the signal is a trivial zero signal. If and is formally given by the cross-correlation (in the signal-processing sense) Explanation[edit] . is maximized. where Let is
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