子波变换理论及其在信号处理中的应用

The Wavelet Transform Theory and Its Applications in Signal Processing

子波分析的形成是傅里叶分析发展史上里程碑式的进展，子波分析优于傅里叶交换的地方在于它在时域和频域同时具有良好的局部化性质，从而可以把分析的重点聚焦到任意的细节，被人们誉为数学显微镜，成为近年来在工具和方法上的重大突破。本文将子波理论中的主要定理、结论、变换特性和一些重要概念加以综述，以促进子波理论的应用。本文的重点在于介绍多分辨率分析和子波分析及其实现、子波变换及其算法、子波和滤波器组等的重要内容，并介绍其在信号处理中的应用及研究动态。

The wavelet analysis is a milestone in the development of Fourier analysis history. It is superior to the Fourier transforms due to its possession of good localization performances in both time and frequency fields. Since it can focus the analysis to any details, the wavelet analysis, known as mathematical microscope, is an important break--through inmethods and tools of signal analysis and processing. The paper summarizes the main theorems, conclusions, transform properties and important concepts of the wavelet theory. Thefocal points of the paper are to introduce the multiresolution and wavelet analysis with theirrealization, the wavelet transforms and their algorithms, the wavelet and filter banks etc.The paper also presents the applications of the wavelet theory on signal processing.