## Gaussian Models

### About Gaussian Models

The Gaussian model fits peaks, and is given by

$$y={\displaystyle \sum _{i=1}^{n}{a}_{i}{e}^{\left[-{\left(\frac{x-{b}_{i}}{{c}_{i}}\right)}^{2}\right]}}$$

where *a* is the amplitude, *b* is the
centroid (location), *c* is related to the peak width,
*n* is 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 Fitter app by entering

`curveFitter`

at the MATLAB^{®}command line. Alternatively, on the**Apps**tab, in the**Math, Statistics and Optimization**group, click Curve Fitter.In the Curve Fitter app, select curve data. On the

**Curve Fitter**tab, in the**Data**section, click**Select Data**. In the**Select Fitting Data**dialog box, select**X data**and**Y data**, or just**Y data**against an index.Click the arrow in the

**Fit Type**section to open the gallery, and click**Gaussian**in the**Regression Models**group.

You can specify the following options in the **Fit
Options** pane:

Specify the number of terms as a positive integer in the range [1 8]. Look in the

**Results**pane to see the model terms, values of the coefficients, and goodness-of-fit statistics.Optionally, in the

**Advanced Options**section, specify coefficient starting values and constraint bounds, or change algorithm settings. The app calculates optimized start points for**Gaussian**fits, based on the data set. You can override the start points and specify your own values in the**Fit Options**pane.Gaussian fits have the width parameter

`c1`

constrained with a lower bound of`0`

. The default lower bounds for most library models are`-Inf`

, which indicates that the coefficients are unconstrained.

For more information on the settings, see Specify Fit Options and Optimized Starting Points.

### Fit Gaussian Models Using the fit Function

This example shows how to use the `fit`

function to fit a Gaussian model to data.

The Gaussian library model is an input argument to the `fit`

and `fittype`

functions. Specify the model type `gauss`

followed by the number of terms, e.g., `'gauss1'`

through `'gauss8'`

.

**Fit a Two-Term Gaussian Model**

Load 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)

## See Also

### Apps

### Functions

`fit`

|`fittype`

|`fitoptions`