Nonlinear signal processing : a statistical approach / / Gonzalo R. Arce

• Record Nr.: UNINA9910827984003321
• Autore: Arce Gonzalo R
• Pubbl/distr/stampa: Hoboken ; ; Chichester, : Wiley, 2005
• ISBN: 1-280-27293-7; 9786610272938; 0-470-32361-2; 0-471-69184-4; 0-471-69185-2
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (483 p.)
• Disciplina: 621.3822
• Soggetti: Signal processing - Mathematics; Statistics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 365-379) and index.
• Nota di contenuto: Nonlinear Signal Processing: A Statistical Approach; Preface; Acknowledgments; Contents; Acronyms; 1 Introduction; 1.1 NonGaussian 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 NonGaussian 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 Moments2.3.1 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 NonOrdered 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 Statistics5 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 Medians in Least Absolute Deviation (LAD) Regression; 5.4.1 Foundation and Cost Functions; 5.4.2 LAD Regression with Weighted Medians; 5.4.3 Simulation; Problems; 6 Weighted Median Filters; 6.1 Weighted Median Filters With Real-Valued Weights6.1.1 Permutation-Weighted Median Filters; 6.2 Spectral Design of Weighted Median Filters; 6.2.1 Median Smoothers and Sample Selection Probabilities; 6.2.2 SSPs for Weighted Median Smoothers; 6.2.3 Synthesis of WM Smoothers; 6.2.4 General Iterative Solution; 6.2.5 Spectral Design of Weighted Median Filters Admitting Real-Valued Weights; 6.3 The Optimal Weighted Median Filtering Problem; 6.3.1 Threshold Decomposition For Real-Valued Signals; 6.3.2 The Least Mean Absolute (LMA) Algorithm; 6.4 Recursive Weighted Median Filters; 6.4.1 Threshold Decomposition Representation of Recursive WM Filters6.4.2 Optimal Recursive Weighted Median Filtering; 6.5 Mirrored Threshold Decomposition and Stack Filters; 6.5.1 Stack Filters; 6.5.2 Stack Filter Representation of Recursive WM Filters; 6.6 Complex-Valued Weighted Median Filters; 6.6.1 Phase-Coupled Complex WM Filter; 6.6.2 Marginal Phase-Coupled Complex WM Filter; 6.6.3 Complex threshold decomposition; 6.6.4 Optimal Marginal Phase-Coupled Complex WM; 6.6.5 Spectral Design of Complex-Valued Weighted Medians; 6.7 Weighted Median Filters for Multichannel Signals; 6.7.1 Marginal WM filter
• Sommario/riassunto: 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