Nonlinear Digital Filtering with Python An Introduction

Nonlinear Digital Filtering with Python: An Introduction discusses important structural filter classes including the median filter and a number of its extensions (e.g., weighted and recursive median filters), and Volterra filters based on polynomial nonlinearities. Adopting both structural and behavioral approaches in characterizing and designing nonlinear digital filters, this book: Begins with an expedient introduction to programming in the free, open-source computing environment of Python Uses results from algebra and the theory of functional equations to construct and characterize behaviorally defined nonlinear filter classes Analyzes the impact of a range of useful interconnection strategies on filter behavior, providing Python implementations of the presented filters and interconnection strategies Proposes practical, bottom-up strategies for designing more complex and capable filters from simpler components in a way that preserves the key properties of these components Illustrates the behavioral consequences of allowing recursive (i.e., feedback) interconnections in nonlinear digital filters while highlighting a challenging but promising research frontier Nonlinear Digital Filtering with Python: An Introduction supplies essential knowledge useful for developing and implementing data cleaning filters for dynamic data analysis and time-series modeling.

IntroductionLinear vs. Nonlinear Filters: An Example Why Nonlinearity? Data Cleaning Filters The Many Forms of Nonlinearity Python and Reproducible Research Organization of This Book PythonA High-Level Overview of the Language Key Language Elements Caveat Emptor: A Few Python Quirks A Few Filtering Examples Learning More about Python Linear and Volterra FiltersLinear Digital Filters Linearity, Smoothness, and Harmonics Volterra Filters Universal Approximations Median Filters and Some ExtensionsThe Standard Median Filter Median Filter Cascades Order Statistic Filters The Recursive Median Filter Weighted Median Filters Threshold Decompositions and Stack Filters The Hampel Filter Python Implementations Chapter Summary Forms of Nonlinear BehaviorLinearity vs. Additivity Homogeneity and Positive HomogeneityGeneralized HomogeneityLocation-InvarianceRestricted Linearity Summary: Nonlinear Structure vs. Behavior Composite Structures: Bottom-Up DesignA Practical OverviewCascade Interconnections and Categories Parallel Interconnections and GroupoidsClones: More General InterconnectionsPython ImplementationsExtensions to More General Settings Recursive Structures and StabilityWhat Is Different about Recursive Filters?Recursive Filter ClassesInitializing Recursive FiltersBIBO StabilitySteady-State ResponsesAsymptotic StabilityInherently Nonlinear BehaviorFading Memory FiltersStructured Lipschitz FiltersBehavior of Key Nonlinear Filter ClassesStability of Interconnected SystemsChallenges and Potential of Recursive Filters

Ronald K. Pearson is a data scientist with DataRobot. He previously held industrial, business, and academic positions at organizations including the DuPont Company, Swiss Federal Institute of Technology (ETH Zurich), Tampere University of Technology, and Travelers Companies. He holds a Ph.D in electrical engineering and computer science from the Massachusetts Institute of Technology, and has published conference and journal papers on topics ranging from nonlinear dynamic model structure selection to the problems of disguised missing data in predictive modeling. Dr. Pearson has authored or co-authored four previous books, the most recent being Exploring Data in Engineering, the Sciences, and Medicine. Moncef Gabbouj is an Academy of Finland professor of signal processing at Tampere University of Technology. He holds a B.Sc in electrical engineering from Oklahoma State University, and an M.Sc and Ph.D in electrical engineering from Purdue University. Dr. Gabbouj is internationally recognized for his research in nonlinear signal and image processing and analysis. His research also includes multimedia analysis, indexing and retrieval, machine learning, voice conversion, and video processing and coding. Previously, Dr. Gabbouj held visiting professorships at institutions including the Hong Kong University of Science and Technology, Purdue University, University of Southern California, and American University of Sharjah.