Signal processing with fractional lower order moments: stable processes and their applications

• Published in: Proceedings of the IEEE Vol. 81; no. 7; pp. 986 - 1010
• Main Authors: Shao, M., Nikias, C.L.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-07-1993; Institute of Electrical and Electronics Engineers
• Subjects: Acoustic noise; Applied sciences; Degradation; Density functional theory; Exact sciences and technology; Gaussian distribution; Gaussian noise; Information, signal and communications theory; Limiting; Low-frequency noise; Matched filters; Mathematical methods; Probability distribution; Signal processing; Telecommunications and information theory; Gaussian distribution; Signal processing; Parameter estimation; Stability; Linear estimation
• ISSN: 0018-9219; 1558-2256
• DOI: 10.1109/5.231338

Non-Gaussian statistical signal processing is important when signals and/or noise deviate from the ideal Gaussian model. Stable distributions are among the most important non-Gaussian models. They share defining characteristics with the Gaussian distribution, such as the stability property and central limit theorems, and in fact include the Gaussian distribution as a limiting case. To help engineers better understand the stable models and develop methodologies for their applications in signal processing. A tutorial review of the basic characteristics of stable distributions and stable signal processing is presented. The emphasis is 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.< >