Multirate Systems and Filter Banks
Presenting general principles without bias towards specific application-oriented detail, this text offers a thorough, unified, and in-depth treatment of the techniques of multirate signal processing. It is the first book to cover the topics of digital filter banks, multidimensional multirate systems, and wavelet representations under one cover. This manual will be valuable to engineers working with applications of speech and image compression, digital audio, and statistical and adaptive signal processing.
Why Read This Book
You should read this book if you need a rigorous, unified foundation in multirate signal processing and filter-bank theory; it shows how polyphase representations, perfect-reconstruction conditions, and paraunitary structures fit together and how they connect to wavelets. The text gives deep theoretical results and design tools that you'll use when building subband coders, QMF/analysis-synthesis systems, or wavelet-based transforms for audio, speech, and image applications.
Who Will Benefit
Graduate students, researchers, and practicing DSP engineers who design filter banks, subband coders, or wavelet transforms and want mathematically sound design and analysis tools.
Level: Advanced — Prerequisites: Basic signals & systems, z-transform/DTFT, linear systems, linear algebra (matrix factorization, orthogonality), and familiarity with digital filter design fundamentals.
Key Takeaways
- Analyze multirate operations using polyphase representations and commutation identities.
- Design perfect-reconstruction (PR) filter banks and understand conditions for alias cancellation and distortionless reconstruction.
- Construct and analyze paraunitary and orthogonal filter-bank structures and their lattice realizations.
- Relate multirate filter banks to wavelet bases and derive wavelet filter design from multirate principles.
- Extend multirate and filter-bank concepts to M-channel and multidimensional systems for image and multidimensional signal processing.
Topics Covered
- Introduction and Motivation for Multirate Processing
- Decimation, Interpolation and Multirate Identities
- Polyphase Representation and Noble Identities
- Two-Channel Filter Banks and Quadrature Mirror Filters (QMF)
- M-Channel Filter Banks and Perfect-Reconstruction Conditions
- Paraunitary Filter Banks and Orthogonal/Perfect-Reconstruction Structures
- Lattice and State-Space Realizations of Filter Banks
- Design Methods for PR and Near-PR Filter Banks
- Multidimensional Multirate Systems and Filter Banks
- Connection to Wavelet Bases and Multiresolution Analysis
- Applications: Subband Coding, Audio/Speech and Image Compression
- Advanced Topics and Research Directions (extensions and open problems)
Languages, Platforms & Tools
How It Compares
More rigorous and comprehensive than Crochiere & Rabiner's Multirate Digital Signal Processing (which is more tutorial/practical), and it complements Strang & Nguyen's Wavelets and Filter Banks by providing deeper multirate algebra and paraunitary theory.
