# Normalize Rational Polynomials (With Lowest Denominator Term) (G Dataflow)

Normalizes numerator and denominator of rational polynomials by using the lowest denominator term.

## numerator

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

This input accepts the following data types:

• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers

## denominator

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

This input accepts the following data types:

• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers

## 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

## normalized numerator

Normalized numerator coefficients, in ascending order of power, of the rational polynomial.

This output can return the following data types:

• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers

## normalized denominator

Normalized denominator coefficients, in ascending order of power, of the rational polynomial.

This output can return the following data types:

• 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

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 Normalizing Rational Polynomials with Lowest Denominator Term

The following equations define the numerator and denominator polynomials of a rational polynomial:

$\mathrm{numerator}=\sum _{i=0}^{n}{N}_{i}{x}^{i}$
$\mathrm{denominator}=\sum _{k=0}^{m}{D}_{k}{x}^{k}$

where

• n is the number of numerator coefficients in the rational polynomial
• m is the number of denominator coefficients in the rational polynomial
• N i is the i th numerator in the rational polynomial
• D k is the k th denominator in the rational polynomial

This node finds the lowest nonzero denominator D j in the rational polynomial where D j ≠ 0 and D j-1 = D j-2 = … = D 1 = D 0 = 0.

This node uses the following equation to normalize the numerator and denominator polynomials with D j :

$\frac{\sum _{i=0}^{n}\left({N}_{i}\text{}/\text{}{D}_{j}\right){x}^{i}}{\sum _{k=0}^{m}\left({D}_{k}\text{}/\text{}{D}_{j}\right){x}^{k}}$

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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