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Efficient Application of the Voigt Functions in the Fourier Transform

Author

Listed:
  • Sanjar M. Abrarov

    (Thoth Technology Inc., Algonquin Radio Observatory, Achray Road, RR6, Pembroke, ON K8A 6W7, Canada
    Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada
    Department Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada)

  • Rehan Siddiqui

    (Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada
    Department Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada
    Department Physics and Astronomy, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada)

  • Rajinder K. Jagpal

    (Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada
    Department Physics and Astronomy, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada)

  • Brendan M. Quine

    (Thoth Technology Inc., Algonquin Radio Observatory, Achray Road, RR6, Pembroke, ON K8A 6W7, Canada
    Department Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada
    Department Physics and Astronomy, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada)

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.

Suggested Citation

  • Sanjar M. Abrarov & Rehan Siddiqui & Rajinder K. Jagpal & Brendan M. Quine, 2025. "Efficient Application of the Voigt Functions in the Fourier Transform," Mathematics, MDPI, vol. 13(13), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2048-:d:1683838
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