Nonlinear Digital Filtering with Python: An Introduction, 1st Edition (Hardback) book cover

Nonlinear Digital Filtering with Python

An Introduction, 1st Edition

By Ronald K. Pearson, Moncef Gabbouj

CRC Press

286 pages | 39 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781498714112
pub: 2015-09-25
SAVE ~$22.00
eBook (VitalSource) : 9781315214269
pub: 2018-09-03
from $28.98

FREE Standard Shipping!


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.


"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

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

About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
MEDICAL / Biotechnology
TECHNOLOGY & ENGINEERING / Mobile & Wireless Communications