离散小波分析导论（一）──小波变换的基本思想、展缩方程、展缩小波

An Introduction to The Discrete Wavelet Analysis (Ⅰ)

介绍了离散小波分析的基本理论，详细阐述了离散小波变换（ＤＷＴ）的实现方法，并指出离散小波变换的一些应用前景。本文主要内容将分５部分发表：（ｌ）小波变换的基本思想，展缩方程，展缩小波。（２）小波系数的性质，循环小波变换，离散小波变换。（３）离散小波变换的性质。（４）均方图，利用小波的卷积计算，两维小波变换。（５）调和小波，离散调和小波变换。

his paper includes enough of the basic theory of wavelet analysis to establish the background for practical calulations, explains how the discrete wavlet transform (DWT)works,and indicate some of the potential applications of the DWT. It will be published in five consecutive issues. The first part includes basic ideas of DWT, dilation equations, dilation wavelets. The second part includes properties of the wavelet coefficients, circular wavelet transforms,discrete wavelet transforms. The third includes properties of the DWT. The forth part includes mean-square maps, convolution by wavelets, two-dimentional wavelet transforms. The last part includes harmonic wavelets and discrete harmonic wavelet transform.