16CorEst - MAE591 Random Data Correlation Function Estimate...

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MAE591 Random Data Correlation Function Estimate 1. Correlation (Covariance) and Convolution : Direct Computation Auto-correlation defines the degree to which a function is correlated with itself as a function of time delay, while cross-correlation defines the degree of “alikeness” between two time histories as a function of time shift. Note that correlation is identical to covariance when the means are removed. The estimated cross-correlation between x and , n = 0, 1, 2, . ., N -1, is: ) ( n ) ( n y = + = 1 0 ) ( ) ( 1 ) ( ˆ r N n xy r n y n x r N rh R , m m r , , 2 , 1 , 0 , 1 , 2 , " " = where r is the lag and m is the maximum lag, which is normally taken as m , i.e. N 1 . 0 < 10 max r T mh < = τ . Convolution can be viewed as flipping the y function end for end and computing a cross- correlation, i.e. 1 1 , , 2 , 1 , 0 , ) ( ) ( 1 , , 2 , 1 , 0 ) ( ) ( ) ( 1 0 = + = + = = = = = N N r n N y n x h N r n r y n x h r c N n r n xy " A A A " A 2. Correlation and Convolution via FFT
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This note was uploaded on 11/21/2009 for the course ME . taught by Professor . during the Spring '09 term at Korea University.

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16CorEst - MAE591 Random Data Correlation Function Estimate...

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