Fast and Accurate Linear Fitting for an Incompletely Sampled Gaussian Function With a Long Tail [Tips & Tricks]

Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data fitting into estimating the unknown parameters of a function. Among analytical functions for data fitting, the Gaussian function is the most widely used one due to its extensive applications in numerous science and engineering fields. To name just a few, the Gaussian function is highly popular in statistical signal processing and analysis, thanks to the central limit theorem
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, and the Gaussian function frequently appears in the quantum harmonic oscillator, quantum field theory, optics, lasers, and many other theories and models in physics
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; moreover, the Gaussian function is widely applied in chemistry for depicting molecular orbitals, in computer science for imaging processing, and in artificial intelligence for defining neural networks.