Nonlinear Digital Filtering with Python: An Introduction

Nonlinear Digital Filtering with Python: An Introduction

English | 2015 | ISBN: 978-1498714112 | 300 Pages | PDF | 10 MB

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

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