SIGNAL-PROCESSING WITH FRACTIONAL LOWER ORDER MOMENTS - STABLE PROCESSES AND THEIR APPLICATIONS

Non-Gaussian statistical signal processing is important when signals a nd/or noise deviate from the ideal Gaussian model. Stable distribution s are among the most important non-Gaussian models. They share definin g characteristics with the Gaussian distribution, such as the stabilit y property and central limit theorems, and. in fact include the Gaussi an distribution as a limiting case. To help engineers better understan d the stable models and develop methodologies for their applications i n signal processing, this paper presents a tutorial review of the basi c characteristics of stable distributions and stable signal processing . The emphasis will be on the differences and similarities between sta ble signal processing methods based on fractional lower order moments and Gaussian signal processing methods based on second-order moments.