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Nonlinear Digital Filtering with Python
An Introduction




ISBN 9781498714112
Published September 25, 2015 by CRC Press
300 Pages 39 B/W Illustrations

 
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Book Description

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.

Table of Contents

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

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Author(s)

Biography

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.

Reviews

"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

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