Evolutionary Spectral Density Estimate for Symmetric α-Stable Process

In this paper, we study the spectral analysis of a non-stationary Symmetric α-Stable (S.α.S) signals, 1<α<2. This approach consists of constructing an evolutionary spectral measure by analogy to that defined in the spectral theory of second-order processes. The goal of this work is to define the evolutionary spectral density, by considering the class of oscillatory signals (S.α.S). Since, we give an asymptotic unbiased estimator of this density and we show that the variance of this estimator converges to zero.