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

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

Resolve the captcha to access the links!