Nonlinear Digital Filters

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.

• 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

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