# Signal Correlation (Cross Correlation) (G Dataflow)

Computes the cross correlation of two signals.

## 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: False

## 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

## 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

## 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.

Name Description
direct

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

frequency domain

Computes the cross correlation using an FFT-based technique.

Default: frequency domain

## 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.

Name Description
none

Does not apply normalization.

unbiased

Applies unbiased normalization.

biased

Applies biased normalization.

Default: none

## 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: 100

## 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: 100

## error in

Error conditions that occur before this node runs.

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

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## 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: True

## 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

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## 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:

$Rxy\left(t\right)=x\left(t\right)\otimes y\left(t\right)={\int }_{-\infty }^{\infty }x*\left(\tau \right)\cdot y\left(t+\tau \right)d\tau$

where the symbol $\otimes$ denotes correlation.

The discrete implementation of cross correlation 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, as shown by the following equations:
${x}_{j}=0,\text{\hspace{0.17em}}j<0\text{\hspace{0.17em}}\text{\hspace{0.17em}}orj\ge N$

and

${y}_{j}=0,\text{\hspace{0.17em}}j<0\text{\hspace{0.17em}}\text{\hspace{0.17em}}or\text{\hspace{0.17em}}j\ge M$

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

${h}_{j}=\underset{k=0}{\overset{N-1}{\sum }}{{x}_{k}}^{*}\cdot {y}_{j+k}$

for $j=-\left(N-1\right),-\left(N-2\right),\text{\hspace{0.17em}}...\text{\hspace{0.17em}},-1,0,1,\text{\hspace{0.17em}}...\text{\hspace{0.17em}},\left(M-2\right),\left(M-1\right)$

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

${Rxy}_{i}={h}_{i-\left(N-1\right)}$

for $i=0,1,2,...\text{\hspace{0.17em}},N+M-2$

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:

${R}_{xy}{\left(unbiased\right)}_{j}=\frac{1}{f\left(j\right)}{Rxy}_{j}$

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

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

## How This Node Applies Biased Normalization

This node applies biased normalization as follows:

${R}_{xy}{\left(biased\right)}_{j}=\frac{1}{\mathrm{max}\left(M,N\right)}{Rxy}_{j}$

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

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

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application