White Alpha Stable Distribution Noise with Analysis of its Pseudo-Power Spectrum

A white alpha stable distribution noise (WASDN) and its pseudo-power spectrum (PPS) is exactly proposed in this paper to analyze better frequency domain characteristic of alpha stable distribution noise. By a PPS estimate method based on fast Fourier transform (FFT), we can conclude that the method can have finite variance only there is four-order moments to transformed sequence and the estimate variance can be effectively reduced if a symmetric window function is multiplied transformed sequence. Simulators show the correctness of the arithmetic.