Some integrals involving Heidler?s lightning return stroke current expression

On continuous numerical Fourier transform for transient analysis of lightning current related phenomena

“…Maximum time of integration estimated using the Marquardt method is T max = 51.826 s. Similar as before, Fig. 6 depicts a comparison of real and imaginary parts of the Heidler function in the frequency domain obtained using an analytical-numerical algorithm [14] and using the CNFT algorithm. Absolute error of the CNFT results is also depicted throughout the observation interval.…”

“…Only the double-exponential function can analytically be transformed into the frequency domain. Other functions such as Heidler function, Nucci function, Diendorfer and Uman function and NCBC function can be transformed using an analytical-numerical integration [13,14].…”

New Functions for Representing IEC 62305 Standard and Other Typical Lightning Stroke Currents

“…for The analytical integral of NCBC function for a subsequent negative stroke current 0.25/100μs, as given in [1], and the corresponding integral of Heidler's function [20] are compared in Fig. (7).…”

“…Heidler's function [20] for the subsequent negative stroke 0.25/100μs [1] and LPL III-IV. Integral of the square of NCBC function for parameters n=1, I m =25.2kA, t m =0.65μs, a=20 and b=0.00467, adequate to IEC 62305-1 subsequent negative stroke current 0.25/100μs [1] for LPL III-IV, is presented in Fig.…”

Fourier Transform Application in the Computation of Lightning Electromagnetic Field

“…Fourier transform of Heidler's function is calculated approximately (Andreotti et al, 2005). Some FFT results for Heidler's function are also given in (Vujevic & Lovric, 2010).…”