Nonlinear Digital Filters

Nonlinear Digital Filters

by W. K. Ling
Released May 2007
Publisher(s): Academic Press
ISBN: 9780080550015

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Book description

This book 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.

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, together with Matlab source code available on an accompanying website

Nonlinear Digital Filters: Analysis and Applications is ideal for professional engineers working with signal processing applications, as well as advanced undergraduates and graduates conducting a nonlinear filter analysis project.

Companion website at http://books.elsevier.com/9780123725363

· 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, together with Matlab source code available on an accompanying website

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Preface
  6. Inside Front Cover
  7. Chapter 1: INTRODUCTION
    1. WHY ARE DIGITAL FILTERS ASSOCIATED WITH NONLINEARITIES?
    2. CHALLENGES FOR THE ANALYSIS AND DESIGN OF DIGITAL FILTERS ASSOCIATED WITH NONLINEARITIES
    3. AN OVERVIEW
  8. Chapter 2: REVIEWS
    1. MATHEMATICAL PRELIMINARY
    2. BACKGROUNDS ON SIGNALS AND SYSTEMS
    3. BACKGROUNDS ON SAMPLING THEOREM
    4. BACKGROUNDS ON BIFURCATION THEOREM
    5. ABSOLUTE STABILITY THEOREM
    6. EXERCISES
  9. Chapter 3: QUANTIZATION IN DIGITAL FILTERS
    1. MODEL OF QUANTIZER
    2. QUANTIZATION NOISE ANALYSIS
    3. OPTIMAL CODE DESIGN
    4. SUMMARY
    5. EXERCISES
  10. Chapter 4: SATURATION IN DIGITAL FILTERS
    1. SYSTEM MODEL
    2. OSCILLATIONS OF DIGITAL FILTERS ASSOCIATED WITH SATURATION NONLINEARITY
    3. STABILITY OF OSCILLATIONS OF DIGITAL FILTERS ASSOCIATED WITH SATURATION NONLINEARITY
    4. SUMMARY
    5. EXERCISES
  11. Chapter 5: AUTONOMOUS RESPONSE OF DIGITAL FILTERS WITH TWO’S COMPLEMENT ARITHMETIC
    1. SYSTEM MODEL
    2. LINEAR AND AFFINE LINEAR BEHAVIORS
    3. LIMIT CYCLE BEHAVIOR
    4. CHAOTIC BEHAVIOR
    5. SUMMARY
    6. EXERCISES
  12. Chapter 6: STEP RESPONSE OF DIGITAL FILTERS WITH TWO’S COMPLEMENT ARITHMETIC
    1. AFFINE LINEAR BEHAVIOR
    2. LIMIT CYCLE BEHAVIOR
    3. FRACTAL BEHAVIOR
    4. SUMMARY
    5. EXERCISES
  13. Chapter 7: SINUSOIDAL RESPONSE OF DIGITAL FILTERS WITH TWO’S COMPLEMENT ARITHMETIC
    1. NO OVERFLOW CASE
    2. Set of initial conditions
    3. OVERFLOW CASE
    4. SUMMARY
    5. EXERCISES
  14. Chapter 8: TWO’S COMPLEMENT ARITHMETIC IN COMPLEX DIGITAL FILTERS
    1. FIRST ORDER COMPLEX DIGITAL FILTERS
    2. SECOND ORDER COMPLEX DIGITAL FILTERS
    3. SUMMARY
    4. EXERCISES
  15. Chapter 9: QUANTIZATION AND TWO’S COMPLEMENT ARITHMETIC IN DIGITAL FILTERS
    1. NONLINEAR BEHAVIORAL DIFFERENCES OF FINITE AND INFINITE STATE MACHINES
    2. NONLINEAR BEHAVIOR OF UNSTABLE SECOND ORDER DIGITAL FILTERS
    3. NONLINEAR BEHAVIORS OF DIGITAL FILTERS WITH ARBITRARY ORDERS AND INITIAL CONDITIONS
    4. SUMMARY
    5. EXERCISES
  16. Chapter 10: PROPERTIES AND APPLICATIONS OF DIGITAL FILTERS WITH NONLINEARITIES
    1. ADMISSIBILITY OF SYMBOLIC SEQUENCES
    2. STATISTICAL PROPERTY
    3. COMPUTER CRYPTOGRAPHY VIA DIGITAL FILTERS ASSOCIATED WITH NONLINEARITIES
    4. SUMMARY
    5. EXERCISES
  17. FURTHER READING
  18. Index

Product information

  • Title: Nonlinear Digital Filters
  • Author(s): W. K. Ling
  • Release date: May 2007
  • Publisher(s): Academic Press
  • ISBN: 9780080550015