Gaussian-Lorentzian Fitting
Table of contents
How to Use
To use Gaussian-Lorentzian Fitting for baseline removal:
- Upload data and select the spectra you want to process.
- Navigate to the sidebar and turn on the “Baseline Removal” toggle.
- Select “Gaussian-Lorentzian Fitting” from the drop-down menu.
- Configure parameters:
- Choose the number of fitting ranges to use.
- Use the textboxes that appear to set the bounds of those ranges.
- Click “Apply fitting ranges” to apply the values specified.
Behavior
Gaussian-Lorentzian fitting uses a Gaussian-Lorentzian hybrid to fit to the data and find a baseline.
A hybrid of both a Gaussian and Lorentzian curve is fitted to the data in each range to determine the baseline. A Gaussian curve takes the following mathematical form:
\[A e^{-\frac{(x-p)^2}{2\sigma^2}}\]where $A$ is the amplitude of the peak of the curve, $p$ represents the location of the peak, and $\sigma$ represents the standard deviation of the peak (related to its width). A Lorentzian curve looks similar but takes a different mathematical form:
\[\frac{S}{\pi} \cdot \frac{\gamma}{(x-p)^2+\gamma^2}\]where $S$ is the area under the curve, and $\gamma$ is related to the width of the peak. The Gaussian and Lorentzian curves are combined simply by adding them together; this is the curve tweaked by the algorithm to be fitted to your data and subtracted off as a baseline.