On the Fourier transform of measured electric fields radiated by a lightning return stroke

The Fourier transform (FT) of the electric field (EF) radiated by a lightning return stroke is shown to include a distributional term at zero frequency, which prevents numerical algorithms, such as fast FT, from working properly. Inspired by the finite duration of any field measurement in real applications, we introduce a time-windowing strategy, whereby the integration time-interval of the FT becomes bounded. As a result, the distributional term is removed from the FT, whereas the functional part of the FT is modified throughout the whole range of frequencies, in such a way that a good performance of the numerical algorithms can be restored. The dependence of the modified spectra of the EFs on the length of the time window is also investigated and three numerical experiments with different channel-base currents are performed to validate the whole resulting framework.