Piece-Wise Fourier Transform of the Typical Lightning Discharge Currents

Piece-Wise Fourier Transform (PWFT) procedure is presented in this paper and applied to the typical lightning discharge currents: 10/350 $\mu \mathrm{s}/\mu \mathrm{s}$ of the positive stroke, 1/200 $\mu \mathrm{s}/\mu \mathrm{s}$ of the first, and 0.25/100 $\mu \mathrm{s}/\mu \mathrm{s}$ of the subsequent stroke, as defined in the IEC 62305 Standard. These currents are approximated by the Analytically Extended Function (AEF) and their frequency spectra are obtained. The same procedure is applied to the measured impulse currents represented by the double-exponential functions. The PWFT procedure is suitable for the impulse waveshapes with multiple peaks which is often needed in the frequency analysis of lightning currents and fields.