Semianalytical Approach to the Inverse Fourier Transform and Its Application in Evaluating Lightning Horizontal Electric Field

A semianalytical inverse Fourier transform, which can evaluate the time response at arbitrary time, is proposed. The basic idea is fitting the response in frequency domain by a sum of piecewise cubic spline functions with an adaptive sampling strategy, and the response in time domain is evaluated with the help of the moment functions to avoid calculating the highly oscillatory integral. A recursive algorithm is derived, which can efficiently calculate the moment functions with different ranks. As an application of the proposed approach, the underground horizontal electric field of a lightning channel is evaluated in the time domain. In comparison with the results in the published literature, the numerical examples show that the proposed approach can save the computational time at least 50 times compared to the one using a conventional inverse Fourier transform technique. The proposed approach, in fact, can be generalized to apply to other scenarios when the inverse Fourier transform is involved.