Signal processing with alpha-stable distributions and applications - Chrysostomos L. Nikias

The recent explosion in the speed and power of computers has now made available the much more accurate, non–Gaussian models in signal processing algorithms. This book offers, for the first time, a full and lucid introduction to a very useful type of these non–Gaussian models, namely those specified by alpha–stable distributions.

Signal Processing with Alpha–Stable Distributions and Applications presents a long–awaited survey of the statistical properties, methods, and applications of symmetrical alpha–stable distributions. Its emphasis on practical rather than theoretical aspects will appeal to both researchers and practicing engineers in signal processing. Major topics covered in this comprehensive resource include:

• Statistical methods in signal processing, including both the Gaussian and alpha–stable models
• The stable distribution, its characterization and statistical properties
• Fractional lower–order moments
• Covariation and statistical conditional expectation of symmetric alpha–stable random variables
• Methods for estimating the parameters of a stable distribution from sample data
• Three conventional methods for estimating covariations: fractional lower–order moment estimator, the screened ratio estimator, and the least–squares estimator
• Methods for estimating MA, AR, and ARMA model parameters
• Methods for modeling impulsive signals
• Designing and implementing optimum and suboptimum signal detectors in the presence of impulsive noise
• Overview of current applications and future research trends of alpha–stable distributions for signal processing problems