Last Modified: February 27, 2020

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

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

Use the Partial Fraction Expansion node to obtain **polynomial**.

Unique roots of the denominator polynomial.

Use the Partial Fraction Expansion node to obtain **poles**.

Numerators of the partial fractions that result for each pole.

Use the Partial Fraction Expansion node to obtain **residues**.

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.

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.

**Default: **No error

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

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

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

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

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

$\frac{P\left(x\right)}{Q\left(x\right)}=A\left(x\right)+\underset{k=1}{\overset{{m}_{0}}{\sum}}\frac{{a}_{0k}}{{(x-{r}_{0})}^{k}}+\underset{k=1}{\overset{{m}_{1}}{\sum}}\frac{{a}_{1k}}{{(x-{r}_{1})}^{k}}+\underset{k=1}{\overset{{m}_{2}}{\sum}}\frac{{a}_{2k}}{{(x-{r}_{2})}^{k}}+\dots +\underset{k=1}{\overset{{m}_{n-1}}{\sum}}\frac{{a}_{(n-1)k}}{{(x-{r}_{n-1})}^{k}}$

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*r*_{i}is the*i*^{th}number of unique roots in the denominator polynomial*m*_{i}is the number of times each unique root in the denominator polynomial occurs*a*_{ik}is the (*i*,*k*)^{th}numerator of the partial fractions that result for each pole

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported

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