Nonlinear Digital Filters

Analysis and Applications


  • W. K. Ling, King's College London

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 websiteNonlinear 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
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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


Book information

  • Published: March 2007
  • ISBN: 978-0-12-372536-3

Table of Contents

ContentsChapter 1 Introduction1.1 Why are digital filters associated with nonlinearities?1.2 Challenges for the analysis and design of digital filters associated with nonlinearities1.3 An overview of the bookChapter 2 Mathematical reviews2.1 Mathematical preliminary2.2 Backgrounds on signals and systems2.3 Backgrounds on sampling theorem2.4 Backgrounds on bifurcation theorem2.5 Absolute stability theoremChapter 3 Quantization in digital filters3.1 Model of quantizer3.2 Quantization noise analysis3.3 Optimal code design3.4 Summary3.5 ExercisesChapter 4 Saturation in digital filters4.1 System model4.2 Oscillation of digital filters associated with saturation nonlinearity4.3 Stability of oscillations associated with saturation nonlinearity4.4 Summary4.5 ExercisesChapter 5 Autonomous response of digital filters with two's complement arithmetic5.1 System model5.2 Linear and affine linear behaviors5.3 Limit cycle behavior5.4 Chaotic behavior5.5 Summary5.6 ExercisesChapter 6 Step response of digital filters with two's complement arithmetic6.1 Affine linear behaviors6.2 Limit cycle behavior6.3 Fractal behavior6.4 Summary6.5 ExercisesChapter 7 Sinusoidal response of digital filters with two's complement arithmetic7.1 No overflow case7.2 Overflow case7.3 Summary7.4 ExercisesChapter 8 Two's complement arithmetic in complex digital filters8.1 First order complex digital filters8.2 Second order complex digital filters8.3 Summary8.4 ExercisesChapter 9 Quantization and two's complement arithmetic of digital filters9.1 Nonlinear behavioral differences of finite and infinite state machines9.2 Nonlinear behaviors of unstable second order digital filters9.3 Nonlinear behaviors of digital filters with arbitrary orders and inital conditions9.4 Summary9.5 ExercisesChapter 10 Properties and applications of digital filters with nonlinearities10.1 Admissibility of symbolic sequences10.2 Statistical property10.3 Computer cryptography via digital filters associated with nonlinearities10.4 Summary10.5 ExercisesBibliographyIndex