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 deep, unified theoretical foundation in multirate signal processing, polyphase representations, and filter-bank theory that underpins high-performance DSP on FPGAs. It explains the key principles (perfect reconstruction, paraunitary structures, wavelet relationships) with proofs and design guidance so you can translate rigorous results into efficient hardware designs.
Who Will Benefit
Graduate students, DSP engineers, and FPGA designers who implement subband processing, wavelets, or high-throughput filter banks and need a rigorous theoretical basis for design and optimization.
Level: Advanced — Prerequisites: Undergraduate/graduate-level signals and systems (z-transform, discrete-time Fourier transform), basic linear algebra, and familiarity with FIR/IIR filters and sampling-rate concepts.
Key Takeaways
- Analyze polyphase decompositions and use Noble identities to simplify multimodal sampling-rate structures.
- Design and verify perfect-reconstruction and near-perfect-reconstruction filter banks (uniform and nonuniform).
- Construct and factor paraunitary matrices and use lattice structures for stable, orthogonal filter-bank realizations.
- Relate two-channel filter-bank theory to wavelet constructions and derive orthonormal/biorthogonal wavelet filters.
- Evaluate aliasing, amplitude/phase distortion, and implement techniques for alias-cancellation and bandwidth-efficient sampling.
- Apply multirate concepts to multidimensional systems and understand their implications for image and multidimensional signal processing.
Topics Covered
- Introduction and Overview of Multirate Systems
- Sampling-Rate Conversion and Basic Multirate Identities
- Polyphase Decomposition and Noble Identities
- Two-Channel Filter Banks and Perfect Reconstruction Theory
- Paraunitary Filter Banks, Lattice Structures, and Factorizations
- Modulated Filter Banks and DFT Filter Banks
- Design Methods for Perfect- and Near-Perfect-Reconstruction Filter Banks
- Multidimensional Multirate Systems and Filter Banks
- Wavelet Representations and Connections to Filter-Bank Theory
- Adaptive and Statistical Considerations in Filter Banks
- Applications: Subband Coding, Speech, Image Processing, and Audio
- Appendices: Mathematical Background and Design Examples
How It Compares
Closely related to Crochiere & Rabiner's Multirate Digital Signal Processing (more application-oriented), Vaidyanathan is more rigorous and comprehensive on paraunitary matrices, lattice structures, and wavelet ties.
