Multirate and Wavelet Signal Processing (Volume 8) (Wavelet Analysis and Its Applications, Volume 8)
This innovative and in-depth book integrates the well-developed theory and practical applications of one dimensional and multidimensional multirate signal processing. Using a rigorous mathematical framework, it carefully examines the fundamentals of this rapidly growing field. Areas covered include: basic building blocks of multirate signal processing; fundamentals of multidimensional multirate signal processing; multirate filter banks; lossless lattice structures; introduction to wavelet signal processing.
Multirate and Wavelet Signal Processing forms the basis for a graduate course in multirate signal processing. It includes an introduction to wavelet signal processing and emphasizes topics of ever-increasing importance for a wide range of applications. Concise and easy-to-read, this book is also a useful primer for professional engineers.
Key Features
* Integrates the well-developed theory and practical applications of one-dimensional and multidimensional multirate signal processing
* Emphasizes topics of ever-increasing importance for a wide range of applications
* Written in a concise, easy-to-read style
* Uses relevant examples
* General mathematical formulation permits extensions of concepts to diverse applications, such as speech, imaging, video, and synthetic aperture radar
* Emphasizes key topics of the field, allowing the reader to make the most efficient use of time in learning the fundamentals of multirate
* Designed to be completely covered in a single semester or quarter
Why Read This Book
You should read this book if you want a mathematically rigorous, unified treatment of multirate systems, filter banks and how they lead to wavelet transforms. It gives both the theoretical foundations and the structural tools (polyphase, paraunitary, lossless lattices) you need to design perfect-reconstruction subband systems and practical wavelet implementations.
Who Will Benefit
Graduate students and practicing DSP engineers working on subband coding, filter-bank design, multidimensional signal processing, or implementing wavelet transforms will get the most value.
Level: Advanced — Prerequisites: Undergraduate signals & systems (Fourier and Z-transforms), linear algebra, discrete-time filter basics, and familiarity with sampling and basic DSP concepts.
Key Takeaways
- Analyze and manipulate multirate building blocks (decimators, interpolators, rate converters) using polyphase representations.
- Design and evaluate analysis/synthesis filter banks with conditions for perfect reconstruction and near-perfect reconstruction.
- Construct paraunitary and lossless lattice structures for stable, numerically robust filter-bank implementations.
- Derive and implement discrete wavelet transforms from filter-bank designs and understand their multiresolution interpretation.
- Extend multirate and wavelet concepts to multidimensional signals and apply them to image and multidimensional data processing.
Topics Covered
- Introduction and motivation: multirate systems and applications
- Basic building blocks: decimation, interpolation, and sampling-rate conversion
- Multirate identities and noble relations
- Polyphase decomposition and matrix representations
- Two-channel and M-channel filter banks: analysis and synthesis
- Perfect reconstruction conditions and aliasing cancellation
- Paraunitary systems and orthogonal filter banks
- Lossless factorization and lattice structures
- Introduction to wavelet signal processing and multiresolution analysis
- Construction of wavelet bases from filter banks
- Multidimensional multirate signal processing
- Applications and implementation issues (subband coding, denoising, etc.)
- Appendices: mathematical tools and proofs
Languages, Platforms & Tools
How It Compares
Covers similar foundational ground to Vaidyanathan's 'Multirate Systems and Filter Banks' but places more emphasis on linking multirate theory to wavelet constructions; complements Vetterli & Kovacevic's 'Wavelets and Subband Coding', which is more focused on wavelets and applications.
