Wavelets and Filter Banks
This text has had an overwhelming response from readers. Lauded by some as a marriage between math and engineering, the text features useful and balanced explanations of wavelets for both engineers and mathematicians. The explanations of difficult topics are informal and very approachable, yet rigor is not sacrificed in the process. Also included in Wavelets and Filter Banks are many examples from the MATLAB Wavelet® Toolbox.
Why Read This Book
You should read this book if you want a clear, balanced presentation that connects the mathematical foundations of wavelets with the engineering practice of filter-bank design and fast algorithms. You will get rigor where it matters and practical insight (including MATLAB examples) for implementing wavelet transforms and perfect-reconstruction filter banks.
Who Will Benefit
Practicing DSP engineers, graduate students, and researchers who want a compact but rigorous treatment of wavelets, multirate systems, and filter-bank design to apply in signal processing, compression, or analysis tasks.
Level: Intermediate — Prerequisites: Linear algebra and basic Fourier analysis, familiarity with discrete-time signals and basic digital filter concepts; MATLAB familiarity helpful but not required.
Key Takeaways
- Explain the connection between multiresolution analysis and two-channel filter banks
- Design and analyze perfect-reconstruction two-channel and paraunitary filter banks
- Construct orthogonal and biorthogonal compactly supported wavelets from filter coefficients
- Implement the discrete wavelet transform and fast wavelet algorithms via filter banks
- Apply wavelet concepts to practical problems using worked MATLAB examples
- Analyze time-frequency and scaling properties of wavelets for signal representation
Topics Covered
- Introduction and overview: wavelets versus classical Fourier methods
- Background: Fourier transforms, sampling, and basic filter theory
- Multiresolution analysis and scaling functions
- Two-channel filter banks and perfect reconstruction
- Orthogonality, paraunitary conditions, and polyphase representations
- Construction of compactly supported orthogonal wavelets
- Biorthogonal wavelets and symmetric filters
- Fast wavelet transform and implementation issues
- Wavelet packets and extensions
- Applications and MATLAB examples
- Mathematical appendices (z-transform, linear algebra, proofs)
Languages, Platforms & Tools
How It Compares
More engineering-oriented and filter-bank focused than Daubechies' Ten Lectures (which is more mathematical) and more concise and construction-focused than Mallat's A Wavelet Tour, which provides broader application coverage.
