Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches (Signals and Communication Technology
Focuses on System Identification applications of the adaptive methods presented. but which can also be applied to other applications of adaptive nonlinear processes.
Covers recent research results in the area of adaptive nonlinear system identification from the authors and other researchers in the field.
Why Read This Book
You should read this book if you need a targeted treatment of adaptive methods for nonlinear system modeling — it bridges Volterra/Wiener theory and practical adaptive algorithms. You will get worked examples, algorithm derivations, and application-oriented discussions that help move from theory to implementation in DSP tasks involving nonlinearities.
Who Will Benefit
Advanced graduate students, DSP engineers and researchers working on nonlinear adaptive filtering, channel/equalizer design, echo cancellation, or any application requiring Volterra/Wiener model identification.
Level: Advanced — Prerequisites: Undergraduate-level signals and systems, linear adaptive filtering (e.g., LMS), probability and estimation fundamentals, and familiarity with MATLAB for experiments.
Key Takeaways
- Implement Volterra and Wiener series representations for weakly nonlinear systems.
- Derive and apply adaptive algorithms (gradient/LMS-style and recursive variants) for Volterra/Wiener model identification.
- Analyze convergence, stability, and computational complexity of adaptive nonlinear estimators.
- Apply regularization, model-order selection, and kernel reduction techniques to control complexity.
- Evaluate performance on practical problems such as nonlinear channel equalization and echo/feedback cancellation.
Topics Covered
- 1. Introduction and Motivation for Nonlinear System Identification
- 2. Mathematical Preliminaries and Notation
- 3. Volterra Series: Theory and Properties
- 4. Wiener Models and Series Representations
- 5. Parametric and Nonparametric Identification Approaches
- 6. Adaptive Algorithms for Volterra Filters (Gradient/LMS variants)
- 7. Recursive and Fast Implementations
- 8. Regularization, Sparsity, and Model Order Selection
- 9. Practical Implementation Issues and Complexity Reduction
- 10. Simulation Studies and Application Case Studies
- 11. Extensions, Recent Research Directions and Future Work
- Appendices: Useful Derivations and MATLAB Examples
Languages, Platforms & Tools
How It Compares
Complementary to Schetzen's Volterra/Wiener theory text (which is more theoretical), this book emphasizes adaptive algorithms and practical identification; it also complements Haykin's Adaptive Filter Theory by focusing specifically on nonlinear Volterra/Wiener approaches rather than linear adaptive filters.
