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Curve Fitting (Exponential) (G Dataflow)

Version:
    Last Modified: January 9, 2017

    Returns the exponential fit of a data set using a specific fitting method.

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    signal

    The input signal.

    This input accepts the following data types:

    • Waveform
    • Array of waveforms

    This input changes to y when the data type is an array of double-precision, floating-point numbers.

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    y

    An array of dependent values representing the y-values of the data set.

    This input changes to signal when the data type is a waveform or an array of waveforms.

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    x

    An array of independent values representing the x-values of the data set.

    This input is available only if you wire an array of double-precision floating-point numbers to y or signal.

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    weight

    An array of weights for the data set.

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    tolerance

    Value that determines when to stop the iterative adjustment of the amplitude, damping, and offset.

    If tolerance is less than or equal to 0, this node sets tolerance to 0.0001.

    How tolerance Affects the Outputs with Different Fitting Methods

    For the Least Square and Least Absolute Residual methods, if the relative difference between residue in two successive iterations is less than tolerance, this node returns the resulting residue. For the Bisquare method, if any relative difference between amplitude, damping, and scale in two successive iterations is less than tolerance, this node returns the resulting amplitude, damping, and scale.

    Default: 0.0001

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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.

    Default: No error

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    parameter bounds

    Upper and lower constraints for the amplitude, damping, and offset of the calculated exponential fit.

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    amp min

    Lower bound for the amplitude.

    Default: -Infinity, which means no lower bound is imposed on the amplitude.

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    amp max

    Upper bound for the amplitude.

    Default: Infinity, which means no upper bound is imposed on the amplitude.

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    damping min

    Lower bound for the damping.

    Default: -Infinity, which means no lower bound is imposed on the damping.

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    damping max

    Upper bound for the damping.

    Default: Infinity, which means no upper bound is imposed on the damping.

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    offset min

    Lower bound for the offset.

    Default: 0

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    offset max

    Upper bound for the offset.

    Default: 0

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    method

    The fitting method.

    Name Value Description
    Least Square 0 Uses the least square method.
    Least Absolute Residual 1 Uses the least absolute residual method.
    Bisquare 2 Uses the bisquare method.

    Algorithm for the Least Square Method

    The least square method of fitting finds the amplitude, damping, and offset of the exponential model by minimizing the residue according to the following equation:

    1 N i = 0 N 1 w i ( f i y i ) 2

    where

    • N is the length of y or the number of data values in a waveform
    • wi is the ith element of weight
    • fi is the ith element of best exponential fit
    • yi is the ith element of y or the ith data value in a waveform

    Algorithm for the Least Absolute Residual Method

    The least absolute residual method finds the amplitude, damping, and offset of the exponential model by minimizing the residue according to the following equation:

    1 N i = 0 N 1 w i | f i y i |

    where

    • N is the length of y or the number of data values in a waveform
    • wi is the ith element of weight
    • fi is the ith element of best exponential fit
    • yi is the ith element of y or the ith data value in a waveform

    Algorithm for the Bisquare Method

    The bisquare method of fitting finds the amplitude, damping, and offset using an iterative process, as shown in the following illustration.

    The node calculates residue according to the following equation:

    1 N i = 0 N 1 w i ( f i y i ) 2

    where

    • N is the length of y or the number of data values in a waveform
    • wi is the ith element of weight
    • fi is the ith element of best exponential fit
    • yi is the ith element of y or the ith data value in a waveform.

    Default: Least Square

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    best exponential fit

    A waveform or array representing the exponential curve that best fits the input signal.

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    amplitude

    Amplitude of the fitted model.

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    damping

    Damping of the fitted model.

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    offset

    Offset of the fitted model.

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    error out

    Error information. The node produces this output according to standard error behavior.

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    residue

    Weighted mean error of the fitted model.

    Algorithm for Calculating best exponential fit

    This node uses the iterative general least square method and the Levenberg-Marquardt method to fit data to an exponential curve of the general form described by the following equation:

    f = a e b x + c

    where

    • x is the input sequence
    • a is amplitude
    • b is damping
    • c is offset

    This node finds the values of a, b, and c that best fit the observations (x, y).

    The following equation specifically describes the exponential curve resulting from the exponential fit algorithm:

    y [ i ] = a e b x [ i ] + c

    The following illustration shows an exponential fit result using this node.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


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