  This paper presents a new approach in application of the Fourier transform to
the complex error function resulting in an efficient rational approximation.
Specifically, the computational test shows that with only $17$ summation terms
the obtained rational approximation of the complex error function provides the
average accuracy ${10^{ - 15}}$ over the most domain of practical importance $0
\le x \le 40,000$ and ${10^{ - 4}} \le y \le {10^2}$ required for the
HITRAN-based spectroscopic applications. Since the rational approximation does
not contain trigonometric or exponential functions dependent upon the input
parameters $x$ and $y$, it is rapid in computation. Such an example
demonstrates that the considered methodology of the Fourier transform may be
advantageous in practical applications.
