基于 Bessel 函数的小波基的构造与性质

Construction and Characterization of Wavelet Bases Expressed by Bessel Function

从特殊函数中的Ｂｅｓｓｅｌ函数出发，利用ＭＲＡ方法构造了一种新的小波母函数Ψ（ｘ），并证明了当Ｎ≥２时它具有良好的局部性、光滑性（Ψ（ｘ）＝Ｏ（｜ｘ｜－Ｎ））、某种对称性以及具有Ｎ－２阶消失矩．最后，给出了Ｎ＝３时的相应结论．

A new mother wavelet function which is based on the Bessel function of the special functions has been constructed by using the MultiResolution Analysis(MRA) method.It is proved that the function,when N is a positive integer and N≥2,has many good properties such as localization,smoothness(Ψ(x)=O(|x|-N)),certain symmetrization and an (N-2) order vanishing moment.As an example,a corresponding conclusion is given when N=3.