Denoising of measured lightning electric field signals using adaptive filters in the fractional Fourier domain

In this paper, adaptive filters are applied (in the fractional Fourier transform domain - FRFd) for denoising lightning electric-field signals, both in high and low signal-to-noise-ratio (SNR) environments. These filters are based on the concentration energy property of the fractional Fourier transform (FRFT). The proposed method integrates the advantages of leakage least mean square (LLMS) and normalized least mean square (NLMS) algorithms, including a leakage factor γ and a normalized step-size μ, in order to reduce the memory effect when tracking a non-stationary signal and also to reduce the effect of the input signal power on the algorithm performance, respectively. Parameter estimation of adaptive filters is analyzed in several case studies for various lightning-generated electric field signals. The adaptive algorithm is shown to provide better performance in low SNR environments. Finally, some analyses (in terms of temporal parameters of lightning electric-field signals) are included to demonstrate the validity of the method.