Cross Correlation

Computes the cross correlation of two signals.

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Inputs/Outputs

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reset

A Boolean that specifies whether to reset the internal state of the node.

True Resets the internal state of the node.
False Does not reset the internal state of the node.

This input is available when either of the input sequences is a double-precision, floating-point number.

Default value: False

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x

The input signal.

This input supports the following data types.

  • Waveform
  • 1D array of waveforms
  • Double-precision, floating-point number
  • 1D array of double-precision, floating-point numbers
  • 1D array of complex double-precision, floating-point numbers
  • 2D array of double-precision, floating-point numbers
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y

The second input signal, which you want to cross correlate with the first input signal.

This input supports the following data types:

  • Waveform
  • 1D array of waveforms
  • Double-precision, floating-point number
  • 1D array of double-precision, floating-point numbers
  • 1D array of complex double-precision, floating-point numbers
  • 2D array of double-precision, floating-point numbers
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algorithm

The correlation method to use.

This input is available only if both x and y are arrays or waveforms.

If x and y are small, the direct method typically is faster. If x and y are large, the frequency domain method typically is faster. Additionally, slight numerical differences can exist between the two methods.

direct

Computes the cross correlation using the direct method of linear correlation.

frequency domain

Computes the cross correlation using an FFT-based technique.

Default value: frequency domain

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normalization

The normalization method to use to compute the cross correlation between the two input signals.

This input is available only if both x and y are arrays or waveforms.

none

Does not apply normalization.

unbiased

Applies unbiased normalization.

biased

Applies biased normalization.

Default value: none

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sample length x

Length of each set of x-values.

This node computes each set of values separately.

sample length x must be greater than 0.

This input is available only if x is a double-precision, floating-point number.

Default value: 100

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sample length y

Length of each set of y-values.

This node computes each set of values separately.

sample length y must be greater than 0.

This input is available only if y is a double-precision, floating-point number.

Default value: 100

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error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Default value: No error

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use history data

A Boolean that specifies whether to use the data points before the current block to compute the cross-correlation.

True Uses the data points before the current block to compute the cross-correlation.
False Does not use the data points before the current block to compute the cross-correlation.

This input is available only if one of the input sequences is a double-precision, floating-point number.

Default value: True

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Rxy

Cross correlation of the two input signals.

This output can return the following data types:

  • Waveform
  • 1D array of waveforms
  • 1D array of double-precision, floating-point numbers
  • 1D array of complex double-precision, floating-point numbers
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error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Algorithm for Calculating the Cross Correlation

The cross correlation Rxy(t) of the sequences x(t) and y(t) is defined by the following equation:

R x y ( t ) = x ( t ) ⊗ y ( t ) = ∫ − ∞ ∞ x * ( τ ) ⋅ y ( t + τ ) d τ R x y ( t ) = x ( t ) ⊗ y ( t ) = ∫ − ∞ ∞ x * ( τ ) ⋅ y ( t + τ ) d τ

where the symbol

⊗
denotes correlation.

h N x M y x y
x j = 0 ,   j < 0     o r ⁢ j ≥ N x j = 0 ,   j < 0     o r ⁢ j ≥ N

and

y j = 0 ,   j < 0 ⁢ ⁢     o r ⁢   j ≥ M y j = 0 ,   j < 0 ⁢ ⁢     o r ⁢   j ≥ M

Then this node obtains the elements of h using the following equation:

h j = ∑ k = 0 N − 1 x k * ⋅ y j + k h j = ∑ k = 0 N − 1 x k * ⋅ y j + k

for

j=−(N−1),−(N−2), ...⁢ ,−1,0,1, ...⁢ ,(M−2),(M−1)

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

R x y i = h i − ( N − 1 ) R x y i = h i − ( N − 1 )

for

i=0,1,2,...⁢ ,N+M−2

Because you cannot index arrays with negative numbers, the corresponding cross correlation value at t = 0 is the Nth element of the output sequence Rxy. Therefore, Rxy represents the correlation values that this node shifts N times in indexing.

How This Node Applies Unbiased Normalization

This node applies unbiased normalization as follows:

R x y ( u n b i a s e d ) j = 1 f ( j ) R x y j R x y ( u n b i a s e d ) j = 1 f ( j ) R x y j

for j = 0, 1, 2, ..., M + N - 2

where Rxy is the cross correlation between x and y with no normalization. f(j) is:


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How This Node Applies Biased Normalization

This node applies biased normalization as follows:

R x y ( b i a s e d ) j = 1 max ⁡ ( M , N ) R x y j R x y ( b i a s e d ) j = 1 max ⁡ ( M , N ) R x y j

for j = 0, 1, 2, ..., M + N - 2

where Rxy is the cross correlation between x and y with no normalization.