Wavelet Analysis and Its Applications: A Textbook for Key Universities

Author: Sun Yankui
Publisher:
Publish Date: 2005-03-01
Features: The author has been engaged in research on wavelet analysis and its applications for ten years. This book is based on the lecture notes of the "Wavelet Analysis and Its Engineering Applications" course he taught at Tsinghua University, supplemented and refined. It is particularly suitable as a fundamental textbook for wavelet analysis.
Key Features of the Book:
- Combines fundamental and practical content: It selects the construction of wavelets, various common wavelet transforms, and their fast algorithms as the theoretical foundation, while focusing on typical applications and representative algorithms in data compression, signal singularity detection, image multi-scale edge extraction, signal denoising, and multi-resolution modeling as the application part.
- Rich examples, practical algorithms: The described algorithms are highly operational.
- Strong readability and broad applicability: It simplifies the mathematical derivation process and omits some complex mathematical proofs, making it accessible to readers with a basic knowledge of advanced mathematics. The content progresses from simple to complex, interweaving theory and application with numerous examples to illustrate the principles, algorithms, and applications of wavelet technology, facilitating self-study.
- Suitable for senior undergraduate and graduate students in science and engineering, as well as teachers, researchers, and engineering professionals interested in wavelets.
Based on the lecture notes of the "Wavelet Analysis and Its Engineering Applications" course taught by the author at Tsinghua University, this book explains the fundamental theory and application techniques of wavelets in an accessible manner. While maintaining the mathematical rigor of wavelet theory, it emphasizes the engineering perspective of wavelet technology and its applications. The goal is to overcome the mathematical barriers of wavelet analysis and reveal its practical essence, making wavelet analysis methods, like Fourier analysis, a fundamental, widely accessible, and easily mastered mathematical tool.
Main Content Includes:
- Construction of discrete wavelets, discrete wavelet transform, fast implementation algorithms, and their applications in image compression and signal denoising;
- Continuous wavelet transform and its localization time-frequency analysis techniques;
- Dyadic wavelet transform, fast algorithms, and their applications in signal singularity detection, signal representation, image multi-scale edge extraction, and signal denoising;
- Wavelet packet transform and its applications in signal denoising, feature extraction, and non-stationary signal fault diagnosis;
- B-spline semi-orthogonal wavelets on intervals and their applications in curve multi-resolution representation and editing.
This book can serve as a textbook for senior undergraduate and graduate courses on "Wavelet Analysis and Its Applications" and also as a reference for professionals engaged in related research and applications.