Wavelet and Discrete Transform Theory and Engineering Practice

Author: Cheng Lizhi
Publisher:
Publish Date: 2005-01-01
Features: This book adopts an intuitive approach, systematically presenting the theory of wavelets and discrete transforms, as well as the design of novel algorithms and their applications from the perspective of combining mathematics and signal processing. It enables readers to grasp the profound and intuitive engineering significance of wavelet theory by understanding the complex mathematical expressions that arise during its development process. The book is divided into two parts. Part I focuses on wavelet theory and the design of novel algorithms. It first investigates the construction methods of wavelets from the traditional perspective of multi-resolution analysis, then designs multi-band wavelets very intuitively using multi-sampling filter theory, and finally discusses the design and integer implementation of discrete transforms and wavelets using lifting schemes. Part II explores the series of applications of wavelet theory, primarily discussing the applications of wavelets and discrete transforms in fields such as image compression, digital watermarking, electromagnetic field numerical computation, signal singularity detection, radar platform motion parameter extraction, and ultra-wideband synthetic aperture radar imaging. The book is theoretically rigorous and rich in content, not only including mature theories and application results but also incorporating some of the authors' own practical work. It aims to provide inspirational insights for mathematicians to understand the engineering and physical significance of mathematical formulas, as well as for engineers to grasp the mathematical descriptions of practical problems and solve engineering challenges. This book serves as an extremely valuable reference for graduate students, teachers, and R&D personnel in fields such as signal and information processing, image processing, computer science, electronic engineering, microwave engineering, and space physics.