Gaussian Models

About Gaussian Models

The Gaussian model fits peaks, and is given by

$y = \sum_{i = 1}^{n} a_{i} e^{[- {(\frac{x - b_{i}}{c_{i}})}^{2}]}$

whereais the amplitude,bis the centroid (location),cis related to the peak width,nis the number of peaks to fit, and 1 ≤n≤ 8.

Gaussian peaks are encountered in many areas of science and engineering. For example, Gaussian peaks can describe line emission spectra and chemical concentration assays.

Fit Gaussian Models Interactively

Open the Curve Fitting app by enteringcftool. Alternatively, click Curve Fitting on the Apps tab.
In the Curve Fitting app, select curve data (X dataandY data, or justY dataagainst index).
Curve Fitting app creates the default curve fit,Polynomial.
Change the model type fromPolynomialtoGaussian.

You can specify the following options:

Choose the number of terms:1to8.
Look in theResultspane to see the model terms, the values of the coefficients, and the goodness-of-fit statistics.
(Optional) ClickFit Optionsto specify coefficient starting values and constraint bounds, or change algorithm settings.
The toolbox calculates optimized start points for Gaussian models, based on the current data set. You can override the start points and specify your own values in the Fit Options dialog box.
Gaussians have the width parameterc1constrained with a lower bound of0. The default lower bounds for most library models are-Inf, which indicates that the coefficients are unconstrained.
For more information on the settings, seeSpecifying Fit Options and Optimized Starting Points.

Fit Gaussian Models Using the fit Function

Open Live Script

This example shows how to use the适合function to fit a Gaussian model to data.

The Gaussian library model is an input argument to the适合and适合typefunctions. Specify the model typegaussfollowed by the number of terms, e.g.,'gauss1'through'gauss8'.

Fit a Two-Term Gaussian Model

负载some data and fit a two-term Gaussian model.

[x,y] = titanium; f = fit(x.',y.','gauss2')

f = General model Gauss2: f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2) Coefficients (with 95% confidence bounds): a1 = 1.47 (1.426, 1.515) b1 = 897.7 (897, 898.3) c1 = 27.08 (26.08, 28.08) a2 = 0.6994 (0.6821, 0.7167) b2 = 810.8 (790, 831.7) c2 = 592.9 (500.1, 685.7)

plot(f,x,y)

Curve Fitting Toolbox Documentation

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