Table Of Contents

Create Polynomial from PFE (G Dataflow)

Version:
    Last Modified: March 15, 2017

    Uses partial fraction expansion (PFE) to reconstruct a rational polynomial.

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    polynomial

    Coefficients, in ascending order of power, for the quotient polynomial.

    Use the Partial Fraction Expansion node to obtain polynomial.

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    poles

    Unique roots of the denominator polynomial.

    Use the Partial Fraction Expansion node to obtain poles.

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    residues

    Numerators of the partial fractions that result for each pole.

    Use the Partial Fraction Expansion node to obtain residues.

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    multiplicity

    Number of times each unique root in the denominator polynomial occurs.

    Use the Partial Fraction Expansion node to obtain multiplicity. If multiplicity is empty, this node calculates the number of nonzero elements in each row of residues and regards that number as the multiplicity of the corresponding pole.

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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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    option

    Method this node uses to handle the co-factors of the numerator and denominator polynomials.

    Name Value Description
    Cancel Co-factors 0 Computes the greatest common denominator (GCD) for the numerator and denominator polynomials before returning the output data.
    Reserve Co-factors 1 Keeps the numerator and denominator polynomial unchanged and returns the output data directly.

    Default: Cancel Co-factors

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    numerator

    Numerator coefficients, in ascending order of power, of the rational polynomial.

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    denominator

    Denominator coefficients, in ascending order of power, of the rational polynomial.

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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 Reconstructing a Rational Polynomial Using Partial Fraction Expansion

    The node uses the following equation to reconstruct a rational polynomial:

    P ( x ) Q ( x ) = A ( x ) + k = 1 m 0 a 0 k ( x r 0 ) k + k = 1 m 1 a 1 k ( x r 1 ) k + k = 1 m 2 a 2 k ( x r 2 ) k + + k = 1 m n 1 a ( n 1 ) k ( x r n 1 ) k

    where

    • P(x) is the numerator polynomial
    • Q(x) is the denominator polynomial
    • A(x) is the quotient polynomial
    • n is the number of unique roots in the denominator polynomial
    • ri is the ith number of unique roots in the denominator polynomial
    • mi is the number of times each unique root in the denominator polynomial occurs
    • aik is the (i, k)th numerator of the partial fractions that result for each pole

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: This product does not support FPGA devices


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