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X is the input sequence. |
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Rxx is the autocorrelation of the Input Sequence. |
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error returns any error or warning from the VI. Refer to Signal Processing Error Codes for more information about these conditions. |
The autocorrelation Rxx(t) of a function x(t) is defined as
where the symbol denotes correlation.
For the discrete implementation of the AutoCorrelatio VI, let Y represent a sequence whose indexing can be negative, let n be the number of elements in the input sequence X, and assume that the indexed elements of X that lie outside its range are equal to zero,
.
Then the AutoCorrelation VI obtains the elements of Y using
,
for j = (n1), (n2), ,2,1, 0, 1, 2, , n1
The elements of the output sequence Rxx are related to the elements in the sequence Y by
,
for i = 0, 1, 2, ,2n-2
Notice that the number of elements in the output sequence Rxx is 2n - 1. Because you cannot use negative numbers to index LabVIEW and LabVIEW Datalogging and Supervisory Control (DSC) module arrays, the corresponding correlation value at t = 0 is the nth element of the output sequence Rxx. Therefore, Rxx represents the correlation values that the AutoCorrelation VI shifted n times in indexing. The following block diagram shows one way to display the correct indexing for the autocorrelation function.
The following graph is the result of the preceding block diagram.