AutoCorrelation (Not in Base Package)

Computes the autocorrelation of the input sequence X. Details  

	X is the input sequence.
	Rxx is the autocorrelation of the Input Sequence.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

AutoCorrelation Details

The autocorrelation Rxx(t) of a function x(t) is defined as

where the symbol denotes correlation.

For the discrete implementation of the AutoCorrelation 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, as shown in the following relationships.

x_j = 0, j < 0 or j n

Then the AutoCorrelation VI obtains the elements of Y using

,

for j = -(n-1), -(n-2), …, -2, -1, 0, 1, 2, …, n-1

The elements of the output sequence Rxx are related to the elements in the sequence Y by

Rxx_i = y_{i – (n – 1)},

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 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.