Table Of Contents

Signal Correlation (Auto Correlation) (G Dataflow)

Version:
    Last Modified: March 3, 2017

    Computes the auto-correlation of a signal.

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

    Default: 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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    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

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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: 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

    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

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    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

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    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
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    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 Auto-Correlation

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

    R x x ( t ) = x ( t ) x ( t ) = x * ( τ ) x ( t + τ ) d τ

    where the symbol 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 N

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

    Y j = k = 0 N 1 x k * 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 = 1 N | j | k = 0 N 1 x k * 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 = 1 N k = 0 N 1 x k * 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: DAQExpress does not support FPGA devices


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