Efficient Application of the Voigt Functions in the Fourier Transform

Sanjar M. Abrarov, Rehan Siddiqui (), Rajinder K. Jagpal and Brendan M. Quine
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Sanjar M. Abrarov: Thoth Technology Inc., Algonquin Radio Observatory, Achray Road, RR6, Pembroke, ON K8A 6W7, Canada
Rehan Siddiqui: Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada
Rajinder K. Jagpal: Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada
Brendan M. Quine: Thoth Technology Inc., Algonquin Radio Observatory, Achray Road, RR6, Pembroke, ON K8A 6W7, Canada

Mathematics, 2025, vol. 13, issue 13, 1-23

Abstract: In this work, we develop a method for rational approximation of the Fourier transform (FT) based on the real and imaginary parts of the complex error function w ( z ) = e − z 2 ( 1 − erf ( − i z ) ) = K ( x , y ) + i L ( x , y ) , z = x + i y , where K ( x , y ) and L ( x , y ) are known as the Voigt and imaginary Voigt functions, respectively. In contrast to our previous rational approximation of the FT, the expansion coefficients in this method are not dependent on the values of a sampled function. As the values of the Voigt functions remain the same, this approach can be used for rapid computation with help of look-up tables. Mathematica codes with some examples are presented.

Keywords: rational approximation; Fourier transform; Voigt function; complex error function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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