1st Edition

Nonlinear Digital Filtering with Python An Introduction

By Ronald K. Pearson, Moncef Gabbouj Copyright 2016
    308 Pages 39 B/W Illustrations
    by CRC Press

    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.

    Linear vs. Nonlinear Filters: An Example
    Why Nonlinearity? Data Cleaning Filters
    The Many Forms of Nonlinearity
    Python and Reproducible Research
    Organization of This Book

    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
    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


    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.

    "The authors bring the reader from the consolidated world of linear filters into the variegate universe of nonlinear filters, and show how the main subclasses of digital nonlinear filters can be described on the basis of their structural and/or behavioral characteristics. This approach is complemented by the use of a free, open-source computing environment—Python—for the implementation of the nonlinear digital filters presented in each chapter."
    —Giovanni L. Sicuranza, University of Trieste, Italy