Spectral methods for stationary harmonizable alpha-stable processes

We address the problem of estimation of the fractional-power spectrum of certain classes of symmetric, alpha-stable (SαS) processes. We start with a summary of the key definitions and results from the theory of stationary, harmonizable SαS processes and proceed to discuss the performance of fractional-power periodograms. Next, we present a high resolution fractional-power spectrum estimation algorithm that we term "the minimum dispersion distortionless response." The algorithm is a generalization of the classical Maximum Likelihood Method of Capon. Preliminary tests of the algorithms are run on simulated data.