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Publication# Taking advantage of multiplet structure for lineshape analysis in Fourier space

Abstract

Lineshape analysis is a recurrent and often computationally intensive task in optics, even more so for multiple peaks in the presence of noise. We demonstrate an algorithm which takes advantage of peak multiplicity (N) to retrieve line shape information. The method is exemplified via analysis of Lorentzian and Gaussian contributions to individual lineshapes for a practical spectroscopic measurement, and benefits from a linear increase in sensitivity with the number N. The robustness of the method and its benefits in terms of noise reduction and order of magnitude improvement in run-time performance are discussed. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Ontological neighbourhood

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

Fourier series

A Fourier series (ˈfʊrieɪ,_-iər) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

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