Polynomial Signal Processing
Despite our growing understanding of the properties and capabilities of nonlinear filters, there persists the belief among engineers that these filters are too complex to implement. This book debunks the myth that all nonlinear filters are complex with its coverage of the polynomial filter. It examines all major aspects of the technology, including system modeling, speed analysis, image processing, communications, biological signal processing, semiconductor modeling, neutral sets, and more.
Why Read This Book
You will get a concentrated, practical treatment of polynomial (Volterra-style) signal processing that demystifies nonlinear filters and shows how to model and implement them efficiently. The book links solid mathematical foundations to real applications (image, communications, biomedical) so you can both analyze behavior and design usable polynomial filters.
Who Will Benefit
Researchers and engineers working on nonlinear filter design, system identification, or applications (image/communications/biomedical) who need a theory-to-implementation bridge.
Level: Advanced — Prerequisites: Solid background in linear DSP and signals & systems, multivariable calculus, basic linear algebra, and familiarity with linear filter design and spectral analysis.
Key Takeaways
- Derive and interpret polynomial/Volterra series models for nonlinear systems.
- Design and analyze polynomial filter structures and their stability/identifiability properties.
- Implement polynomial filters efficiently, including reduced-complexity and fast-structure approaches.
- Estimate polynomial kernels (system identification) from data and assess estimation error and robustness.
- Apply polynomial filtering techniques to practical problems in image, communications, and biomedical signal processing.
- Evaluate computational cost and numerical issues when deploying nonlinear filters in real systems.
Topics Covered
- Introduction and motivation for polynomial signal processing
- Mathematical preliminaries: tensors, multidimensional convolutions, and notation
- Volterra series and polynomial representations of nonlinear systems
- Properties of polynomial filters: causality, invertibility, and stability
- Polynomial filter structures and realizations
- Computational complexity and fast algorithms for polynomial filtering
- Estimation and identification of polynomial/Volterra kernels
- Noise, stochastic analysis, and performance measures
- Applications in image processing and computer vision
- Applications in communications and speech/biomedical signal processing
- Semiconductor modeling and other specialized applications
- Conclusions, practical implementation notes, and appendices
How It Compares
Covers the Volterra/polynomial-filter niche more directly and implementation-focused than broader nonlinear-DSP or statistical approaches; complements general nonlinear DSP texts that emphasize statistical or adaptive methods.
