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Computes the cross correlation of the input signals X and Y.

Details  

	X is the first input sequence.
	Y is the second input sequence.
	Rxy is the cross correlation of X and Y.

EMB CrossCorrelation Details

The cross correlation Rxy(t) of the sequences x(t) and y(t) is defined as

,

where the symbol denotes correlation.

The discrete implementation of the EMB CrossCorrelation VI is as follows. Let h represent a sequence whose indexing can be negative, let n be the number of elements in the input sequence X, let m be the number of elements in the sequence Y, and assume that the indexed elements of X and Y that lie outside their range are equal to zero,

x_j = 0, j < 0 or j n

and

y_j = 0, j < 0 or j m.

Then the EMB CrossCorrelation VI obtains the elements of h using

for j = –(n – 1), –(n – 2), …, –2, –1, 0, 1, 2, …, m – 1

The elements of the output sequence Rxy are related to the elements in the sequence h by

Rxy_i = h_{i – (n – 1)}

for i = 0, 1, 2, …, size – 1, size = n + m – 1,

where size is the number of elements in the output sequence Rxy.

Because you cannot index LabVIEW arrays with negative numbers, the corresponding cross correlation value at t = 0 is the n^th element of the output sequence Rxy. Therefore, Rxy represents the correlation values that the EMB CrossCorrelation VI shifted n times in indexing.