Discrete Wavelet Transform: A Signal Processing Approach
Provides easy learning and understanding of DWT from a signal processing point of view
- Presents DWT from a digital signal processing point of view, in contrast to the usual mathematical approach, making it highly accessible
- Offers a comprehensive coverage of related topics, including convolution and correlation, Fourier transform, FIR filter, orthogonal and biorthogonal filters
- Organized systematically, starting from the fundamentals of signal processing to the more advanced topics of DWT and Discrete Wavelet Packet Transform.
- Written in a clear and concise manner with abundant examples, figures and detailed explanations
- Features a companion website that has several MATLAB programs for the implementation of the DWT with commonly used filters
“This well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing.”
-- Prof. Dr. Manfred Tasche - Institut für Mathematik, Uni Rostock
Full review at https://zbmath.org/?q=an:06492561
Why Read This Book
You will get a signal‑processing–first explanation of the discrete wavelet transform that emphasizes filter‑bank intuition and practical implementation rather than abstract functional analysis. The book includes clear examples, figures and MATLAB code so you can quickly move from theory to working DWT implementations.
Who Will Benefit
Engineers and graduate students with a background in DSP who need a hands‑on, implementation‑oriented treatment of DWT and wavelet packet techniques for analysis, denoising or compression.
Level: Intermediate — Prerequisites: Basic signals & systems and discrete‑time Fourier transform knowledge, familiarity with FIR filters and multirate concepts, and basic MATLAB skills.
Key Takeaways
- Explain the DWT using filter‑bank and multirate DSP concepts rather than pure functional analysis
- Design and analyze orthogonal and biorthogonal wavelet filter banks for practical use
- Implement DWT and Discrete Wavelet Packet Transform algorithms in MATLAB
- Apply wavelet transforms to common tasks such as denoising, compression and time–frequency analysis
- Evaluate time‑frequency tradeoffs and select appropriate wavelet bases for engineering problems
Topics Covered
- 1. Introduction to Discrete‑Time Signal Processing Fundamentals
- 2. Convolution, Correlation and the Discrete Fourier Transform Review
- 3. FIR Filters and Basic Filter Design Concepts
- 4. Multirate Signal Processing and Decimation/Interpolation
- 5. Two‑Channel Filter Banks and Perfect Reconstruction Conditions
- 6. Theory of the Discrete Wavelet Transform (DWT)
- 7. Orthogonal and Biorthogonal Wavelet Filters and Construction
- 8. Discrete Wavelet Packet Transform and Best‑Basis Selection
- 9. Implementation Details and MATLAB Algorithms
- 10. Applications: Denoising, Compression and Time–Frequency Analysis
- 11. Examples, Exercises and Worked MATLAB Programs
- Appendices: Mathematical Background and Reference Tables
Languages, Platforms & Tools
How It Compares
More implementation‑focused than Mallat's A Wavelet Tour of Signal Processing and less mathematically abstract than Strang & Nguyen's Wavelets and Filter Banks; it sits between practical MATLAB tutorials and theoretical references.
