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An Analytical Method for the Deconvolution of Voigtian Profiles

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Abstract

In spectroscopy, the spectral lineshape is often well described by a Voigtian function, which is the convolution of a Lorentzian function and a Gaussian function. A number of researchers have suggested ways to approximate the Voigtian profile. Herein, we report an analytical method to deconvolve it. Our method calculates the component Lorentzian and Gaussian linewidth of a Voigtian function by solving some polynomial equations in terms of even-order derivatives of the Voigtian function evaluated at the center. In the absence of noise, the Lorentzian and Gaussian linewidths obtained by the deconvolution of computer-generated Voigtian absorption spectra are accurate within an error of 0.01 %. While the accuracy of our new method is affected by noise, it can be improved by employing a Savitzky–Golay filter and/or a Lorentzian filter function. Our new method will be useful in magnetic resonance spectroscopy, optical spectroscopy, and other fields of science.

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Acknowledgments

This work was supported by a grant from Brain Korea 21 for Leading Universities and Students. The author thanks Professor Jay Zweier for his support. The author is also grateful to Professor Sunil Saxena of the University of Pittsburgh for helpful suggestions regarding writing style.

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Authors and Affiliations

  1. Davis Heart and Lung Research Institute, The Ohio State University Wexner Medical Center, Columbus, OH, 43210, USA

    Byong-kyu Shin

  2. College of Pharmacy, Seoul National University, Seoul, 151-742, Korea

    Byong-kyu Shin

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  1. Byong-kyu Shin
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Correspondence to Byong-kyu Shin.

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Shin, Bk. An Analytical Method for the Deconvolution of Voigtian Profiles. Appl Magn Reson 47, 429–452 (2016). https://doi.org/10.1007/s00723-016-0769-5

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  • DOI: https://doi.org/10.1007/s00723-016-0769-5

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