Nonlinear Digital Filters - 1st Edition - ISBN: 9780123725363, 9780080550015

Nonlinear Digital Filters

1st Edition

Analysis and Applications

Authors: W. K. Ling
Hardcover ISBN: 9780123725363
eBook ISBN: 9780080550015
Imprint: Academic Press
Published Date: 30th March 2007
Page Count: 216
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Nonlinear Digital Filters provides an easy to understand overview of nonlinear behavior in digital filters, showing how it can be utilized or avoided when operating nonlinear digital filters.

It gives techniques for analyzing discrete-time systems with discontinuous linearity, enabling the analysis of other nonlinear discrete-time systems, such as sigma delta modulators, digital phase lock loops, and turbo coders. It uses new methods based on symbolic dynamics, enabling the engineer to easily operate reliable nonlinear digital filters.

It gives practical, 'real-world' applications of nonlinear digital filters and contains many examples.

The book is ideal for professional engineers working with signal processing applications, as well as advanced undergraduates and graduates conducting a nonlinear filter analysis project.

Key Features

  • Uses new methods based on symbolic dynamics, enabling the engineer more easily to operate reliable nonlinear digital filters
  • Gives practical, "real-world" applications of nonlinear digital filter
  • Includes many examples.


Electrical and electronic engineers working in digital signal processing and communications engineers.

Final year undergraduate and graduate level electrical and electronic engineering students studying a course in digital signal processing (a general course or a course on nonlinear signal processing); academic researchers

Table of Contents

Contents Chapter 1 Introduction 1.1 Why are digital filters associated with nonlinearities? 1.2 Challenges for the analysis and design of digital filters associated with nonlinearities 1.3 An overview of the book

Chapter 2 Mathematical reviews 2.1 Mathematical preliminary 2.2 Backgrounds on signals and systems 2.3 Backgrounds on sampling theorem 2.4 Backgrounds on bifurcation theorem 2.5 Absolute stability theorem

Chapter 3 Quantization in digital filters 3.1 Model of quantizer 3.2 Quantization noise analysis 3.3 Optimal code design 3.4 Summary 3.5 Exercises

Chapter 4 Saturation in digital filters 4.1 System model 4.2 Oscillation of digital filters associated with saturation nonlinearity 4.3 Stability of oscillations associated with saturation nonlinearity 4.4 Summary 4.5 Exercises

Chapter 5 Autonomous response of digital filters with two's complement arithmetic 5.1 System model 5.2 Linear and affine linear behaviors 5.3 Limit cycle behavior 5.4 Chaotic behavior 5.5 Summary 5.6 Exercises

Chapter 6 Step response of digital filters with two's complement arithmetic 6.1 Affine linear behaviors 6.2 Limit cycle behavior 6.3 Fractal behavior 6.4 Summary 6.5 Exercises

Chapter 7 Sinusoidal response of digital filters with two's complement arithmetic 7.1 No overflow case 7.2 Overflow case 7.3 Summary 7.4 Exercises

Chapter 8 Two's complement arithmetic in complex digital filters 8.1 First order complex digital filters 8.2 Second order complex digital filters 8.3 Summary 8.4 Exercises

Chapter 9 Quantization and two's complement arithmetic of digital filters 9.1 Nonlinear behavioral differences of finite and infinite state machines 9.2 Nonlinear behaviors of unstable second order digital filters 9.3 Nonlinear behaviors of digital filters with arbitrary orders and inital conditions 9.4 Summary 9.5 Exercises

Chapter 10 Properties and applications of digital filters with nonlinearities 10.1 Admissibility of symbolic sequences 10.2 Statistical property 10.3 Computer cryptography via digital filters associated with nonlinearities 10.4 Summary 10.5 Exercises

Bibliography Index


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© Academic Press 2007
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About the Author

W. K. Ling

Dr. Ling received the B.Eng.(Hons) and M.Phil. degrees from the department of Electrical and Electronic Engineering, the Hong Kong University of Science and Technology, in 1997 and 2000, respectively, and a Ph.D. degree in the department of Electronic and Information Engineering from the Hong Kong Polytechnic University in 2003. In 2004, he joined the King's College London as a Lecturer. His research interests include discontinuous nonlinear system theory with applications to digital filters with two's complement arithmetic and sigma delta modulators, continuous constrained optimization theory with applications to filters, filter banks and sigma delta modulators design, filter banks and wavelets theory with applications to multimedia and biomedical signal processing, and fuzzy, impulsive and optimal control theory with applications to sigma delta modulators and power electronics.

Affiliations and Expertise

King's College London