Signal Correlation (Auto Correlation) (G Dataflow)

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Last Modified: June 25, 2019

Computes the auto-correlation of a signal.

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 only if x 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

normalization

The normalization method to use to compute the auto correlation of the input signal.

This input is available only if x is a waveform or an array.

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

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 auto-correlation.

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

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

Default: True

Rxx

Autocorrelation of the input signal.

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

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 Auto-Correlation

The auto-correlation Rxx(t) of a function x(t) is defined as

R x x (t) = x (t) \otimes x (t) = \int_{- \infty}^{\infty} x^{*} (τ) \cdot x (t + τ) d τ

where the symbol $\otimes$ denotes correlation.

For the discrete implementation of this node, 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 relationship:

x_{j} = 0, j < 0 o r j \geq N

Then this node obtains the elements of Y using the following formula:

Y_{j} = \sum_{k = 0}^{N - 1} {x_{k}}^{*} \cdot x_{j + k}

for $j = - (N - 1), - (N - 2), ..., - 1, 0, 1, ..., (N - 2), (N - 1)$

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

{R x x}_{i} = y_{i - (N - 1)}

for $i = 0, 1, 2, ..., 2 N - 2$

Notice that the number of elements in the output sequence Rxx is $2 N - 1$ . Because you cannot use negative numbers to index arrays, the corresponding correlation value at t = 0 is the Nth element of the output sequence Rxx. Therefore, Rxx 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:

y_{j} = \frac{1}{N - | j |} \sum_{k = 0}^{N - 1} x_{k}^{*} \cdot x_{j + k}

for j = -(N-1), -(N-2), ..., -1, 0, 1, ..., (N-2), (N-1), and

{R x x (u n b i a s e d)}_{i} = y_{i - (N - 1)}

for i = 0, 1, 2, ..., 2N-2

How This Node Applies Biased Normalization

This node applies biased normalization as follows:

y_{j} = \frac{1}{N} \sum_{k = 0}^{N - 1} x_{k}^{*} \cdot x_{j + k}

for j = -(N-1), -(N-2), ..., -1, 0, 1, ..., (N-2), (N-1), and

{R x x (b i a s e d)}_{i} = y_{i - (N - 1)}

for i = 0, 1, 2, ..., 2N-2

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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

Table Of Contents

reset

x

normalization

sample length x

error in

use history data

Rxx

error out

Algorithm for Calculating the Auto-Correlation

How This Node Applies Unbiased Normalization

How This Node Applies Biased Normalization

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