Contents 1. Introduction
Frequency domain analysis is the important aspect, but stable distribution [1]–[2] signal or noise has no second-order statistics (SOS), higher-order statistics (HOS), and traditional power density spectrum (PDF). To depict its frequency domain characteristics, a fractional lower-order spectrum, named -spectrum, is defined through a FIR system model in [3] and another fractional lower-order spectrum (covariation spectrum, CS) is did through Fourier transform to auto-covariation function in [4]. spectrum and covariation spectrum are only applied alpha stable distribution stochastic process of its parameter in . If , spectrum estimation methods above will be not fitting, as definition of the covariation function is meaning only when characteristic exponent is in . Therefore, a fractional lower-order covariance spectrum (FLOCS) of alpha stable distribution stochastic process is defined in [5]. The algorithm can estimate accurately harmonic frequencies in alpha stable distribution process among . Its quality and connections with covariation spectrum are studied in [5], fractional lower-order spectrums above can need to identify characteristic exponent , and is not facilitative for practice application. So a generalized fractional lower-order covariance spectrum (GFLO-CVS) is defined through expanding the form of nonlinear transforming in [6], and generalized fractional lower-order cyclic spectrum (GFLO-CYS) and multi-spectrum (GFLO-CMS), too.
