Generalized Fractional Lower-Order Spectrum of Alpha Stable Distribution Process

Generalized Fractional Lower-order Covariance Spectrum (GFLO-CVS), Cyclic Spectrum (GFLO-CYS) and Higher-order Spectrum (GFLO-HOS) are proposed. After a nonlinear transform is used in alpha stable distribution process for getting finite second-order or high-order moment, consequently, Fourier transform of transformed stochastic process can be employed to analyze characteristic in frequency domain. Transforming functions are similar to logarithm, sigmoid, arctangent, etc., not depended on a prior knowledge of characteristic exponent alpha, and facilitative for practice application. Simulations show that the proposed fractional low-order spectrums have excellent robust and can be identified Harmonics in alpha stable distribution process.