Wavelets: A Tutorial in Theory and Applications (Wavelet Analysis and Its Applications)
Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume.
Key Features
* Covers several of the most important areas in wavelets, ranging from the development of the basic theory, such as:
* Construction and analysis of wavelet bases, and
* Introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding
* Extensive bibliography is also included in this volume
* Companion to the first volume in this series, An Introduction to Wavelets, and can be used as supplementary instructional material for a two-semester course on wavelet analysis
Why Read This Book
You should read this book if you want a rigorous, tutorial-style bridge between wavelet theory and practical signal applications: you will learn how multiresolution analysis leads to concrete constructions of wavelet bases and how those bases connect to filter-bank implementations. The book also introduces key applied techniques (for example, Mallat's local wavelet maxima for image coding), giving you both the math and pointers to real DSP uses.
Who Will Benefit
Ideal for advanced undergraduates, graduate students, and practicing signal engineers or researchers who need a solid theoretical foundation in wavelets to support applications in audio/speech, radar, communications, and image processing.
Level: Advanced — Prerequisites: Undergraduate-level calculus and linear algebra, familiarity with Fourier analysis and basic digital signal processing (filters, sampling, transforms); some exposure to functional analysis or operator theory is helpful but not strictly required.
Key Takeaways
- Construct rigorous multiresolution analyses and derive orthonormal and biorthogonal wavelet bases
- Implement the discrete wavelet transform via filter-bank structures and understand the role of scaling functions
- Design and analyze compactly supported wavelets (including spline-based constructions)
- Apply Mallat’s local wavelet maxima and related techniques for signal and image coding/detection
- Analyze time–frequency and spectral properties of signals using wavelet-based methods
- Interpret theoretical results (convergence, regularity, vanishing moments) to guide practical algorithm choices
Topics Covered
- 1. Introduction and Historical Context of Wavelets
- 2. Mathematical Preliminaries: Function Spaces and Fourier Analysis
- 3. Multiresolution Analysis (MRA) and Scaling Functions
- 4. Construction of Wavelet Bases: Orthogonal and Biorthogonal Cases
- 5. Compactly Supported and Spline Wavelets
- 6. Filter Banks and the Discrete Wavelet Transform
- 7. Wavelet Packets and Time–Frequency Tilings
- 8. Mallat’s Local Wavelet Maxima and Image Coding
- 9. Selected Applications: Audio, Speech, Radar, and Communications
- 10. Numerical Considerations and Implementation Notes
- 11. Bibliography and Further Reading
Languages, Platforms & Tools
How It Compares
Complementary to Ingrid Daubechies' Ten Lectures on Wavelets (more construction-oriented and tutorial in style) and to Mallat's later signal-processing perspective — Chui emphasizes mathematical construction and selected applications rather than broad algorithmic coverage.
