Nonlinear Digital Filters: Analysis and Applications
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Table of contents
- Copyright Pageiv
- Contentsv
- Prefacevii
- Chapter 1 Introduction1
- Why are digital filters associated with nonlinearities?1
- Challenges for the analysis and design of digital filters associated with nonlinearities6
- An overview7
- Chapter 2 Reviews8
- Mathematical preliminary8
- Backgrounds on signals and systems13
- Backgrounds on sampling theorem25
- Backgrounds on bifurcation theorem27
- Absolute stability theorem28
- Exercises28
- Chapter 3 Quantization in Digital Filters32
- Model of quantizer32
- Quantization noise analysis36
- Optimal code design42
- Summary51
- Exercises52
- Chapter 4 Saturation in Digital Filters53
- System model53
- Oscillations of digital filters associated with saturation nonlinearity54
- Stability of oscillations of digital filters associated with saturation nonlinearity58
- Summary59
- Exercises60
- Chapter 5 Autonomous Response of Digital Filters with Two's Complement Arithmetic61
- System model61
- Linear and affine linear behaviors63
- Limit cycle behavior70
- Chaotic behavior75
- Summary77
- Exercises77
- Chapter 6 Step Response of Digital Filters with Two's Complement Arithmetic78
- Affine linear behavior78
- Limit cycle behavior92
- Fractal behavior104
- Summary109
- Exercises109
- Chapter 7 Sinusoidal Response of Digital Filters with Two's Complement Arithmetic114
- No overflow case114
- Overflow case127
- Summary138
- Exercises138
- Chapter 8 Two's Complement Arithmetic in Complex Digital Filters139
- First order complex digital filters139
- Second order complex digital filters144
- Summary150
- Exercises151
- Chapter 9 Quantization and Two's Complement Arithmetic in Digital Filters152
- Nonlinear behavioral differences of finite and infinite state machines152
- Nonlinear behavior of unstable second order digital filters156
- Nonlinear behaviors of digital filters with arbitrary orders and initial conditions162
- Summary170
- Exercises171
- Chapter 10 Properties and Applications of Digital Filters with Nonlinearities172
- Admissibility of symbolic sequences172
- Statistical property179
- Computer cryptography via digital filters associated with nonlinearities188
- Summary195
- Exercises197
- Further Reading199
- Index205
- A205
- B205
- C205
- D205
- E205
- F205
- G205
- H205
- I205
- J205
- L205
- M206
- N206
- O206
- P206
- Q206
- R206
- S206
- T206
- U206
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
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