Nonlinear Signal Processing: A Statistical Approach

Nonlinear signal processing methods are finding numerous applications in such fields as imaging, teletraffic, communications, hydrology, geology, and economics--fields where nonlinear systems and non-Gaussian processes emerge. Within a broad class of nonlinear signal processing methods, this book provides a unified treatment of optimal and adaptive signal processing tools that mirror those of Wiener and Widrow, extensively presented in the linear filter theory literature. The methods detailed in this book can thus be tailored to effectively exploit non-Gaussian signal statistics in a system or its inherent nonlinearities to overcome many of the limitations of the traditional practices used in signal processing.

Chapters include:

• A review of non-Gaussian models, with an emphasis on the class of generalized Gaussian distributions and the class of stable distributions
• The basic principles of order statistics
• Maximum likelihood and robust estimation principles
• Signal processing tools based on weighted medians and stack filters
• Filters based on linear combinations of order statistics and various generalizations
• Signal processing methods tailored for signals described by stable distributions

Numerous problems, examples, and case studies enable rapid mastery of the topics discussed, and over 60 MATLAB m-files allow the reader to quickly design and apply the algorithms to any application.