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出 处:《宁夏大学学报(自然科学版)》2007年第4期289-292,共4页Journal of Ningxia University(Natural Science Edition)
基 金:广东省自然科学基金资助项目(05008289;032038);广东省自然科学基金博士启动基金资助项目(04300917)
摘 要:设N2m+1(x)是2m+1阶B-样条尺度函数,其两尺度符号为P(x)=[(1+z)/2]^2m+1.给出了N2m+1(x)对应的一个短支撑反对称小波ψ(x)的显式构造,即ψ(x)=^2m+1∑k=0(-1)^k2^-2m(^2m+1k)N2m+1(2x-k),其对应的两尺度符号Q(z)=P(-z).所构造的小波ψ(x)与N2m+1(x)有相同的支撑区间,这方便了它的应用.另外也给出了N2m+1(x)的对偶尺度函数N^~2m+1(x)以及ψ(x)的对偶小波ψ^-(x)的构造.N^~2m+1(x)和ψ^-(ψ)也都具有对称性.特别地,如果设G(z),H(z)分别为N^~2m+1(x)和ψ^-(x)的两尺度符号,则G(z),H(z)也具有H(z)=G(-z)^——的关系.基于所构造的ψ(x)和ψ^-(x),建立了相应的小波分解与重构的算法.最后给出了一个构造算例.Suppose that N2m+1 (x) is the (2m+1)^th cardinal B-spline scaling function associated with its two-scale symbol P(z)=[(1+z)/2]^2m+1. A short compactly supported and anti-symmetric wavelet of N2m+1(x) is constructed, i.e. ψ(x) = ^2m+1∑k=0(-1)^k2^-2m(^2m+1k)N2m+1(2x-k) with Q(z)=P(-z) as its two-scale symbol. ψ(x) has the same supported interval as N2m+1(x). The dual N^~2m+1(x) of N2N+1 (x) and the other one ψ^-(x) of ψ(x) are also constructed explicitly. While N^~2m+1(x) is symmetric, ψ^-(x) is anti-symmetric. In particular,if G(z) and H(z) are the two-scale symbols of N^~2m+1(x) and ψ(x) respectively,then H(z)=G(-z)^--. The formulas of wavelet decompositions and reconstructions is concisely presented based on ψ(x) and its dual ψ^-(x). In the end, a construction example is given.
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