Wavelets and Subband Coding (Prentice Hall Signal Processing Series)
A central goal of signal processing is to describe real life signals, be it for computation, compression, or understanding. This book presents a unified view of wavelets and subband coding with a signal processing perspective. Covers the discrete-time case, or filter banks; development of wavelets; continuous wavelet and local Fourier transforms; efficient algorithms for filter banks and wavelet computations; and signal compression. For electrical engineers and computer scientists.
Why Read This Book
You should read this book if you want a rigorous, engineering-oriented foundation in wavelet transforms and their direct connection to multirate filter banks and subband coding. You will get both the theoretical underpinnings (multiresolution analysis, continuous and discrete wavelets) and practical algorithms for fast wavelet transforms and perfect-reconstruction filter-bank design.
Who Will Benefit
Graduate students, DSP engineers, and researchers who need to design and analyze wavelet transforms, filter banks, or subband compression systems for audio, communications, or image/signal processing applications.
Level: Advanced — Prerequisites: Solid understanding of discrete-time signals and systems, Fourier and z-transforms, linear systems theory, basic linear algebra, and familiarity with digital filter concepts; MATLAB experience is helpful but not required.
Key Takeaways
- Design perfect-reconstruction two-channel and M-channel filter banks for analysis/synthesis systems.
- Construct orthogonal and biorthogonal wavelets from discrete-time filter-bank prototypes.
- Implement fast discrete wavelet transform algorithms and understand their multirate foundations.
- Analyze aliasing, distortion, and stability in subband coding systems and derive conditions for perfect reconstruction.
- Apply wavelet/subband techniques to signal compression and quantify rate–distortion tradeoffs.
Topics Covered
- Introduction and Motivation: Signals, Compression, and Subband Coding
- Basics of Multirate Signal Processing
- Two-Channel Filter Banks: Analysis, Synthesis and PR Conditions
- M-Channel Filter Banks and Polyphase Representations
- Paraunitary and Perfect-Reconstruction Filter Banks
- Wavelets from Filter Banks: Multiresolution Analysis
- Orthogonal and Biorthogonal Wavelets; Compact Support
- Continuous Wavelet and Local Fourier Transforms
- Fast Algorithms for Wavelet and Filter-Bank Computations
- Design of Filters with Vanishing Moments and Regularity
- Subband Coding and Compression Applications
- Extensions, Implementation Issues, and Applications
Languages, Platforms & Tools
How It Compares
Compared with Mallat's 'A Wavelet Tour of Signal Processing', Vetterli's book is more focused on discrete-time filter-bank interpretations and subband coding; compared with Strang & Nguyen's 'Wavelets and Filter Banks', it provides a broader, DSP-oriented treatment linking theory to coding and algorithms.
