[0,3]上所有实系数紧支撑正交小波的构造

The Construction of all Real Coefficient Binary Waveletes with Ompact Supports over

给出了构造所有实系数紧支撑二进制正交小波的方法,并进一步从消失距方面给予了讨论,提出此类小波的最高消失矩定理,从而得到了这一类小波的数量和简洁的构造方法.并得到所有[0,3]上紧支撑正交小波的分布情况,这个集合涵盖了著名的Haar小波和Daubechies紧支撑小波,并给出关于这类小波的一个最高消失矩定理及完整的证明.

It is a special important work to construct wavelet in wavelet analysis.The paper presents means of constructing all real coefficient binary waveletes with compact supports,and discusses vanishing moment,and gives uppermost vanishing moment theorem of the wavelets,and gives all binary waveletes with compact supports on ,Furthermore,the set contains famous Haar wavelets and Daubechies waveletes with compact supports.Finally,an uppermost vanishing moment theorem of the wavelets and its proof are given.