# Curve Fitting (Exponential) (G Dataflow)

Version:
Last Modified: January 9, 2017

Returns the exponential fit of a data set using a specific fitting method.  ## signal

The input signal.

This input accepts the following data types:

• Waveform
• Array of waveforms

This input changes to y when the data type is an array of double-precision, floating-point numbers. ## y

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. ## x

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. ## weight

An array of weights for the data set. ## tolerance

Value that determines when to stop the iterative adjustment of the amplitude, damping, 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, damping, and scale in two successive iterations is less than tolerance, this node returns the resulting amplitude, damping, and scale.

Default: 0.0001 ## error in

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

Default: No error ## parameter bounds

Upper and lower constraints for the amplitude, damping, and offset of the calculated exponential fit. ### amp min

Lower bound for the amplitude.

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

Upper bound for the amplitude.

Default: Infinity, which means no upper bound is imposed on the amplitude. ### damping min

Lower bound for the damping.

Default: -Infinity, which means no lower bound is imposed on the damping. ### damping max

Upper bound for the damping.

Default: Infinity, which means no upper bound is imposed on the damping. ### offset min

Lower bound for the offset.

Default: 0 ### offset max

Upper bound for the offset.

Default: 0 ## method

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, damping, and offset of the exponential model by minimizing the residue according to the following equation:

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

where

• N is the length of y or the number of data values in a waveform
• wi is the ith element of weight
• fi is the ith element of best exponential fit
• yi is the ith element of y or the ith data value in a waveform

Algorithm for the Least Absolute Residual Method

The least absolute residual method finds the amplitude, damping, and offset of the exponential 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
• wi is the ith element of weight
• fi is the ith element of best exponential fit
• yi is the ith element of y or the ith data value in a waveform

Algorithm for the Bisquare Method

The bisquare method of fitting finds the amplitude, damping, and offset using an iterative process, as shown in the following illustration. The node calculates residue according to the following equation:

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

where

• N is the length of y or the number of data values in a waveform
• wi is the ith element of weight
• fi is the ith element of best exponential fit
• yi is the ith element of y or the ith data value in a waveform.

Default: Least Square ## best exponential fit

A waveform or array representing the exponential curve that best fits the input signal. ## amplitude

Amplitude of the fitted model. ## damping

Damping of the fitted model. ## offset

Offset of the fitted model. ## error out

Error information. The node produces this output according to standard error behavior. ## residue

Weighted mean error of the fitted model.

## Algorithm for Calculating best exponential fit

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

$f=a{e}^{bx}+c$

where

• x is the input sequence
• a is amplitude
• b is damping
• c is offset

This node finds the values of a, b, and c that best fit the observations (x, y).

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

$y\left[i\right]=a{e}^{bx\left[i\right]}+c$

The following illustration shows an exponential fit result using this node. Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported