Piece-Wise Fourier Transform of Aperiodic Functions

Abstract

One new step-by-step procedure to obtain Fourier transform of some aperiodic waveshapes, without using Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) and window functions, is presented in this paper. Waveshapes are approximated by multi-peaked analytically extended function (MP-AEF) which is a piece-wise function. The main advantage of this procedure is that it can handle signals with sharp peaks, as opposite to other Fourier transform procedures, which makes it suitable for lightning currents' waveshapes. The procedure is confirmed on single-wave cosine, triangular, trapezoidal, and double-exponential waveshapes. The advantage of this procedure is that it provides Fourier transform for any chosen time interval of observation as well as for infinite time duration signals.