Wavelet Analysis and Its Applications (Computer Textbook for Key Universities)

Author: Sun Yankui
Publisher:
Publish Date: 2005-03-01
Features: Based on the lecture notes of the author's course "Wavelet Analysis and Its Engineering Applications" at Tsinghua University, this book explains the fundamental theory and application techniques of wavelets in an accessible manner. While striving to maintain the mathematical rigor of wavelet theory, it emphasizes the exposition of wavelet technology and its applications from an engineering perspective. The aim is to overcome the mathematical barriers of wavelet analysis and reveal its practical essence. Just like Fourier analysis, wavelet analysis methods are intended to become a fundamental, widely accessible, and easily understandable mathematical tool for a broad readership. The main contents include: the 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 can also be used as a reference for professionals engaged in related research and applications.