Version:

Last Modified: January 9, 2017

Finds the set of polynomial fit coefficients that best represents an input signal or input data set using a specific fitting method.

Constraints on the polynomial coefficients of certain order.

Use this input if you know the exact values of certain polynomial coefficients.

Constrained order.

**Default: **0

Coefficient of the specific order.

**Default: **0

Order of the polynomial.

**polynomial order** must be greater than or equal to 0. If **polynomial order** is less than zero, this node sets **polynomial coefficients** to an empty array and returns an error. In real applications, **polynomial order** is less than 10. If **polynomial order** is greater than 25, the node sets **polynomial coefficients** to zero and returns a warning.

**Default: **2

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.

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**.

An array of weights for the data set.

Value that determines when to stop the iterative adjustment of coefficients when you use the Least Absolute Residual or Bisquare methods.

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 Absolute Residual method, if the relative difference of the weighted mean error of the polynomial fit in two successive iterations is less than **tolerance**, this node returns resulting **polynomial coefficients**. For the Bisquare method, if any relative difference between **polynomial coefficients** in two successive iterations is less than **tolerance**, this node returns the resulting **polynomial coefficients**.

**Default: **0.0001

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

**Default: **No error

Algorithm this node uses to compute the polynomial curve that best fits the input values.

Name | Value | Description |
---|---|---|

SVD | 0 | Uses the SVD algorithm. |

Givens | 1 | Uses the Givens algorithm. |

Givens2 | 2 | Uses the Givens2 algorithm. |

Householder | 3 | Uses the Householder algorithm. |

LU Decomposition | 4 | Uses the LU Decomposition algorithm. |

Cholesky | 5 | Uses the Cholesky algorithm. |

SVD for Rank Deficient H | 6 | Uses the SVD for Rank Deficient H algorithm. |

**Default: **SVD

Method of fitting data to a polynomial curve.

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 finds the polynomial coefficients of the polynomial model by minimizing the residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum}}{w}_{i}{({f}_{i}-{y}_{i})}^{2}$

where

*N*is the length of**y**or the number of data values in a waveform*w*_{i}is the*i*^{th}element of**weight***f*_{i}is the*i*^{th}element of**best polynomial fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform

Algorithm for the Least Absolute Residual Method

The least absolute residual method finds the polynomial coefficients of the polynomial model by minimizing the residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum}}{w}_{i}|{f}_{i}-{y}_{i}|$where

*N*is the length of**y**or the number of data values in a waveform*w*_{i}is the*i*^{th}element of**weight***f*_{i}is the*i*^{th}element of**best polynomial fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform

Algorithm for the Bisquare Method

The bisquare method finds the polynomial coefficients using an iterative process, as shown in the following illustration.

The node calculates residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum}}{w}_{i}{({f}_{i}-{y}_{i})}^{2}$

where

*N*is the length of**y**or the number of data values in a waveform*w*_{i}is the*i*^{th}element of**weight***f*_{i}is the*i*^{th}element of**best polynomial fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform

**Default: **Least Square

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

Coefficients of the fitted model in ascending order of power. The total number of elements in polynomial coefficients is *m* + 1, where* m* is **polynomial order**.

Weighted mean error of the fitted model.

This node fits data to a polynomial function of the general form described by the following equation:

${f}_{i}=\underset{j=0}{\overset{m}{\sum}}{a}_{j}{x}_{i}^{j}$

where

*f*is the output sequence**best polynomial fit***x*is the input sequence calculated from the**dt**component of the input signal*a*is**polynomial coefficients***m*is**polynomial order**

This node finds the value of *a* that best fits the observations (X, Y). When the input signal is an array of double-precision, floating-point numbers, X is the **x** component of the input signal and Y is **y** component of the input signal. When the input signal is a waveform or an array of waveforms, X is the input sequence calculated from the start time of the waveform and Y is the data values in the waveform.

The following equation describes the polynomial curve resulting from the general polynomial fit algorithm:

$y\left[i\right]=\underset{j=0}{\overset{m}{\sum}}{a}_{j}{(x[i])}^{j}$

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported