Frequency-domain Expressions of the Time-Windowed Electric Fields Radiated by a Lightning Flash

The electric fields radiated by a lightning discharge may represent an important source of damage for electric and electronic equipment. Often, an analysis of such fields in the frequency domain is necessary and their frequency-domain expressions have always been evaluated by considering an infinite time-window and omitting the zero-frequency term coming from the static component of the fields. This work shows that, in order to take into proper account such component, the classical expressions of the electric fields in the frequency domain should be modified by including a distributional term. This aspect may strongly affect numerical algorithms such as the Fast Fourier Transform (FFT), since the agreement between Fourier Transform (FT) and FFT is guaranteed only if the FT is a function. Starting from this issue, the present work proposes new frequency-domain expressions of the radial and vertical electric fields by assuming, more realistically, that the time window in which the fields are measured is finite. As a result, the new FT of each time-windowed field is wholly functional again, but it turns out to be modified with respect to its traditional expression.