Signal processing with fractional lower order moments: stable processes and their applications
- 1 July 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 81 (7) , 986-1010
- https://doi.org/10.1109/5.231338
Abstract
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.Keywords
This publication has 71 references indexed in Scilit:
- Tests for the Chacteristic Exponent and the Scale Parameter of Symmetric Stable DistributionsCommunications in Statistics - Simulation and Computation, 1990
- Maximum Likelihood Estimates of Symmetric Stable Distribution ParametersCommunications in Statistics - Simulation and Computation, 1990
- Estimation of regression coefficients with the help of characteristic functionsJournal of Econometrics, 1989
- Estimation of Stable-Law Parameters: A Comparative StudyJournal of Business & Economic Statistics, 1989
- Approximate Likelihood and Probability Calculations Based on TransformsThe Annals of Statistics, 1984
- On Some Fourier Methods for InferenceJournal of the American Statistical Association, 1981
- Stable Distributions in Statistical Inference: 2. Information from Stably Distributed SamplesJournal of the American Statistical Association, 1975
- A Note on the Distribution of Stock Price ChangesJournal of the American Statistical Association, 1971
- Parameter Estimates for Symmetric Stable DistributionsJournal of the American Statistical Association, 1971
- Some Structure Theorems for the Symmetric Stable LawsThe Annals of Mathematical Statistics, 1970