Ripples in Mathematics
This introduction to the discrete wavelet transform and its applications is based on a novel approach to discrete wavelets called lifting. After an elementary introduction, connections of filter theory are presented, and wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals, problems with finite length signals are detailed, and MATLAB is used for examples and implementation of transforms.
Why Read This Book
You should read this book if you want a practical, implementation‑oriented introduction to the discrete wavelet transform using the lifting scheme: you will learn how wavelets arise from filter banks, how to implement transforms efficiently, and how to handle finite‑length signals in real systems. The book balances intuition and algorithms and includes MATLAB examples so you can quickly prototype and test DWT-based processing.
Who Will Benefit
DSP engineers, graduate students, and practitioners who need a hands‑on guide to discrete wavelets, lifting, and practical DWT implementations in MATLAB.
Level: Intermediate — Prerequisites: Basic signals and systems (discrete‑time signals), familiarity with Fourier transforms and digital filter concepts, and working knowledge of MATLAB.
Key Takeaways
- Implement the discrete wavelet transform efficiently using the lifting scheme.
- Understand the connection between wavelets and perfect‑reconstruction filter banks.
- Design and use wavelet packet transforms for alternate time–frequency tilings.
- Handle finite‑length signals and boundary effects in practical DWT implementations.
- Apply MATLAB code and examples to prototype wavelet‑based signal processing algorithms.
- Compare and construct biorthogonal wavelet filters and analyze their properties.
Topics Covered
- 1. Introduction and motivation
- 2. Time–frequency intuition and signal representations
- 3. Filter‑bank view of the wavelet transform
- 4. The lifting scheme: construction and factorization
- 5. Biorthogonal wavelets and filter design
- 6. Wavelet packet transforms and adaptive tilings
- 7. Finite‑length signals and boundary handling
- 8. Implementation issues and efficient algorithms
- 9. MATLAB examples and code
- 10. Applications and case studies
- 11. Further reading and mathematical appendices
Languages, Platforms & Tools
How It Compares
More hands‑on and implementation focused than Mallat's 'A Wavelet Tour of Signal Processing' (which is more comprehensive/theoretical), and more approachable on lifting than Strang & Nguyen's 'Wavelets and Filter Banks', which is more mathematically rigorous.
