Non-Gaussian signal processing is becoming increasingly important as more and more phenomena in signal processing are found to deviate from the ideal Gaussian model.
Stable distributions are among the most important non-Gaussian models.
They share important characteristics with the Gaussian distribution, such as the stability property and central limit theorems, and have found applications in such diverse fields as physics, economics as well as electrical engineering. To help engineers better understand stable models and develop methodologies for their applications in signal processing, this paper presents a tutorial review of the basic characteristics of stable laws and stable signal processing. The emphasis will be on the differences and similarities between stable signal processing methods based on fractional lower order moments and Gaussian signal processing methods based on second-order moments.