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. Content: Introduction Linear vs. Nonlinear Filters: An Example Why Nonlinearity? Data Cleaning Filters The Many Forms of Nonlinearity Python and Reproducible Research Organization of This Book Python A 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 Filters Linear Digital Filters Linearity, Smoothness, and Harmonics Volterra Filters Universal Approximations Median Filters and Some Extensions The 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 Behavior Linearity vs. Additivity Homogeneity and Positive Homogeneity Generalized Homogeneity Location-Invariance Restricted Linearity Summary: Nonlinear Structure vs. Behavior Composite Structures: Bottom-Up Design A Practical Overview Cascade Interconnections and Categories Parallel Interconnections and Groupoids Clones: More General Interconnections Python Implementations Extensions to More General Settings Recursive Structures and Stability What Is Different about Recursive Filters? Recursive Filter Classes Initializing Recursive Filters BIBO Stability Steady-State Responses Asymptotic Stability Inherently Nonlinear Behavior Fading Memory Filters Structured Lipschitz Filters Behavior of Key Nonlinear Filter Classes Stability of Interconnected Systems Challenges and Potential of Recursive Filters "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 PythonUses results from algebra and the theory of functional equations to construct and characterize behaviorally defined nonlinear filter classesAnalyzes the impact of a range of useful interconnection strategies on filter behavior, providing Python implementations of the presented filters and interconnection strategiesProposes practical, bottom-up strategies for designing more complex and capable filters from simpler components in a way that preserves the key properties of these componentsIllustrates the behavioral consequences of allowing recursive (i.e., feedback) interconnections in nonlinear digital filters while highlighting a challenging but promising research frontierNonlinear 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."--Provided by publisher