小波基的解析结构研究

The Research about Analysis Structure of Wavelet Base

小波分析与应用已十分深入，特别是紧支集上的小波变换已广泛应用在信号处理、图象压缩等 领域．但小波基的构造却是一年十分艰苦的工和，本文给出了紧支集上正交小波基对Ｎ＝２^(ｋ－１)时 （ｋ个参数角）的解析结构，它是三角函数ｓｉｎｘ、ｃｏｓｘ合角公式的多重分解系，它能直接构造出无 穷多种小波滤波系数，并部分验证了包含著名数学家Ｄａｕｂｅｃｈｉｅｓ的小波滤波系数．它使得在小波

Wavelet analysis have been used to many fields deeply, especially, the wavelet transforms on compact support sets have been applied to signal processing and image compression, etc. However the constructing of wavelet base is a hard work yet. In this paper, for N= 2^(k-1). the analysis structure of walvelet base on compact support sets are found successfully! That is the general solutions structure of equations which fits to the wavelet base ortho gonal conditions, such as: the multi-dissolve formulas of sinx, cosx which x is the plus of parameter angles. Those formulas make it enable to construct many filters of wavelet base. At the same time, some formulas have been tested which includes the Daubechies's filters. With the aid of our formulas. it is very easy to choose the wavelet bases match to questions by dynamically.