Version:

Last Modified: January 9, 2017

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

Initial guesses of the amplitude, center, standard deviation, and offset for use in the iterative algorithm.

If **initial amplitude**, **initial center**, **initial standard deviation**, or **offset** is NaN, this node calculates the initial guess automatically.

Initial guess of the amplitude.

**Default: **NaN

Initial guess of the center.

**Default: **NaN

Initial guess of the standard deviation.

**Default: **NaN

Initial guess of the offset.

**Default: **NaN

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 the amplitude, center, standard deviation, 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**, **center**, **standard deviation**, and **offset** in two successive iterations is less than **tolerance**, this node returns the resulting **amplitude**, **center**, **standard deviation**, and **offset**.

**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

Upper and lower constraints for the amplitude, center, standard deviation, and offset.

Lower bound for the amplitude.

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

Upper bound for the amplitude.

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

Lower bound for the center.

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

Upper bound for the center.

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

Lower bound for the standard deviation.

**Default: **-Infinity, which means no lower bound is imposed on the standard deviation.

Upper bound for the standard deviation.

**Default: **Infinity, which means no upper bound is imposed on the standard deviation.

Lower bound for the offset.

**Default: **0

Upper bound for the offset.

**Default: **0

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**, **center**, **standard deviation**, and **offset** of the Gaussian 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 Gaussian 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 **amplitude**, **center**, **standard deviation**, and **offset** of the Gaussian 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 Gaussian 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 of fitting finds the **amplitude**, **center**, **standard deviation**, and **offset** 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 Gaussian fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform.

**Default: **Least Square

Offset of the fitted model.

Y-values of the fitted model.

This output can also return an array of double-precision, floating-point numbers.

Amplitude of the fitted model.

Center of the fitted model.

Standard deviation of the fitted model.

Weighted mean error of the fitted model.

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

$f=a\cdot \mathrm{exp}(-\frac{{(x-\mu )}^{2}}{2{\sigma}^{2}})+c$

where

*x*is the input sequence*a*is**amplitude**-
$\mu $ is
**center** -
$\sigma $ is
**standard deviation** *c*is**offset**

This node finds the values of *a*,
$\mu $,
$\sigma $, and *c* that best fit the observations (**x**, **y**).

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

$y\left[i\right]=a\cdot \mathrm{exp}(-\frac{{(x\left[i\right]-\mu )}^{2}}{2{\sigma}^{2}})+c$

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported