Nonlinear Signal Processing - A Statistical Approach

Informationen zum Autor GONZALO R. ARCE received a PhD degree in electrical engineering from Purdue University in 1982. Since 1982, he has been with the faculty of the Department of Electrical and Computer Engineering at the University of Delaware where he is currently Charles Black Evans Distinguished Professor and Chairman. He has held visiting professor appointments at the Unisys Corporate Research Center and at the International Center for Signal and Image Processing, Tampere University of Technology, in Tampere, Finland. He holds seven U.S. patents, and his research has been funded by DoD, NSF, and numerous industrial organizations. He is an IEEE Fellow for his contributions to the theory and applications of nonlinear signal processing. Klappentext Nonlinear Signal Processing: A Statistical Approach focuses on unifying the study of a broad and important class of nonlinear signal processing algorithms which emerge from statistical estimation principles, and where the underlying signals are non-Gaussian, rather than Gaussian, processes. Notably, by concentrating on just two non-Gaussian models, a large set of tools is developed that encompass a large portion of the nonlinear signal processing tools proposed in the literature over the past several decades.Key features include:* Numerous problems at the end of each chapter to aid development and understanding* Examples and case studies provided throughout the book in a wide range of applications bring the text to life and place the theory into context* A set of 60+ MATLAB software m-files allowing the reader to quickly design and apply any of the nonlinear signal processing algorithms described in the book to an application of interest is available on the accompanying FTP site. Zusammenfassung Nonlinear Signal Processing: A Statistical Approach focuses on unifying the study of a broad and important class of nonlinear signal processing algorithms which emerge from statistical estimation principles, and where the underlying signals are non--Gaussian, rather than Gaussian, processes. Inhaltsverzeichnis Preface. Acknowledgments. Acronyms. 1. Introduction. 1.1 Non-Gaussian Random Processes. 1.1.1 Generalized Gaussian Distributions and Weighted Medians. 1.1.2 Stable Distributions and Weighted Myriads. 1.2 Statistical Foundations. 1.3 The Filtering Problem. 1.3.1 Moment Theory. PART I: STATISTICAL FOUNDATIONS. 2. Non-Gaussian Models. 2.1 Generalized Gaussian Distributions. 2.2 Stable Distributions. 2.2.1 Definitions. 2.2.2 Symmetric Stable Distributions. 2.2.3 Generalized Central Limit Theorem. 2.2.4 Simulation of Stable Sequences. 2.3 Lower Order Moments. 2.3.1 Fractional Lower Order Moments. 2.3.2 Zero Order Statistics. 2.3.3 Parameter Estimation of Stable Distributions. Problems. 3. Order Statistics. 3.1 Distributions of Order Statistics. 3.2 Moments of Order Statistics. 3.2.1 Order Statistics From Uniform Distributions. 3.2.2 Recurrence Relations. 3.3 Order Statistics Containing Outliers. 3.4 Joint Statistics of Ordered and Non-Ordered Samples. Problems. 4. Statistical Foundations of Filtering. 4.1 Properties of Estimators. 4.2 Maximum Likelihood Estimation. 4.3 Robust Estimation. Problems. PART II: SIGNAL PROCESSING WITH ORDER STATISTICS. 5. Median and Weighted Median Smoothers. 5.1 Running Median Smoothers. 5.1.1 Statistical Properties. 5.1.2 Root Signals (Fixed Points). 5.2 Weighted Median Smoothers. 5.2.1 The Center Weighted Median Smoother. 5.2.2 Permutation Weighted Median Smoothers. 5.3 Threshold Decomposition Representation. 5.3.1 Stack Smoothers. 5.4 Weighted...

List of contents

Preface.
 
Acknowledgments.
 
Acronyms.
 
1. Introduction.
 
1.1 Non-Gaussian Random Processes.
 
1.2 Statistical Foundations.
 
1.3 The Filtering Problem.
 
PART I: STATISTICAL FOUNDATIONS.
 
2. Non-Gaussian Models.
 
2.1 Generalized Gaussian Distributions.
 
2.2 Stable Distributions.
 
2.3 Lower Order Moments.
 
Problems.
 
3. Order Statistics.
 
3.1 Distributions of Order Statistics.
 
3.2 Moments of Order Statistics.
 
3.3 Order Statistics Containing Outliers.
 
3.4 Joint Statistics of Ordered and Non-Ordered Samples.
 
Problems.
 
4. Statistical Foundations of Filtering.
 
4.1 Properties of Estimators.
 
4.2 Maximum Likelihood Estimation.
 
4.3 Robust Estimation.
 
Problems.
 
PART II: SIGNAL PROCESSING WITH ORDER STATISTICS.
 
5. Median and Weighted Median Smoothers.
 
5.1 Running Median Smoothers.
 
5.2 Weighted Median Smoothers.
 
5.3 Threshold Decomposition Representation.
 
5.4 Weighted Medians in Least Absolute Deviation (LAD) Regression.
 
Problems.
 
6. Weighted Median Filters.
 
6.1 Weighted Median Filters With Real-Valued Weights.
 
6.2 Spectral Design of Weighted Median Filters.
 
6.3 The Optimal Weighted Median Filtering Problem.
 
6.4 Recursive Weighted Median Filters.
 
6.5 Mirrored Threshold Decomposition and Stack Filters.
 
6.6 Complex Valued Weighted Median Filter.
 
6.7 Weighted Median Filters for Multichannel Signals.
 
Problems.
 
7. Linear Combination or Order Statistics.
 
7.1 L-Estimates of Location.
 
7.2 L-Smoothers.
 
7.3 Ll-Filters.
 
7.4 Ljl; Permutation Filters.
 
7.5 Hybrid Median/Linear FIR Filters.
 
7.6 Linear Combination of Weighted Medians.
 
Problems.
 
PART III: SIGNAL PROCESSING WITH THE STABLE MODEL.
 
8. Myriad Smoothers.
 
8.1 FLOM Smoothers.
 
8.2 Running Myriad Smoothers.
 
8.3 Optimality of the Sample Myriad.
 
8.4 Weighted Myriad Smoothers.
 
8.5 Fast Weighted Myriad Computation.
 
8.6 Weighted Myriad Smoother Design.
 
Problems.
 
9. Weighted Myriad Filters.
 
9.1 Weighted Myriad Filters with Real-Valued Weights.
 
9.2 Fast Real-Valued Weighted Myriad Computation.
 
9.3 Weighted Myriad Filter Design.
 
Problems.
 
References.
 
Appendix A: Software Guide.
 
Index.

Report

"This comprehensive book...will be a good reference for both the trained statisticians and engineers." ( Technometrics , February 2006)

Product details

• Authors: Gonzalo Arce, Gonzalo R Arce, Gonzalo R. Arce
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 17.09.2004
• EAN: 9780471676249
• ISBN: 978-0-471-67624-9
• No. of pages: 460
• Dimensions: 153 mm x 242 mm x 26 mm
• Subjects: Education and learning > Teaching preparation > Vocational needs; Statistik, Statistics, Signalverarbeitung, Signal Processing, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Statistik in den Ingenieurwissenschaften, Engineering Statistics, Technische Statistik