Evolutionary Spectral Density Estimate for Symmetric α-Stable Process
Said Safi1 and Rachid Sabre2,*
1. Laboratory of Mathematics, International High school Louis Massignon, Casablanca, Morroco
2. Laboratory Biogéosciences CNRS, University of Burgundy/Agrosup Dijon, France
Email: safi112004@gmail.com (S.S.); r.sabre@agrosupdijon.fr (R.S.)
*Corresponding author
2. Laboratory Biogéosciences CNRS, University of Burgundy/Agrosup Dijon, France
Email: safi112004@gmail.com (S.S.); r.sabre@agrosupdijon.fr (R.S.)
*Corresponding author
Abstract—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.
Keywords—spectral, density, stationary, evolutionary alpha-stable
Keywords—spectral, density, stationary, evolutionary alpha-stable
Cite: Said Safi and Rachid Sabre, "Evolutionary Spectral Density Estimate for Symmetric α-Stable Process," International Journal of Signal Processing Systems, vol. 13, pp. 1-10, 2025. doi: 10.18178/ijsps.2025.13.1-10
Copyright © 2026 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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