一种新的细分加权小波  

A Novel Weighted Wavelet with Subdivision

作　　者：侯霞[1] 胡寿松[1] 

机构地区：[1]南京航空航天大学自动化学院,南京210016

出　　处：《自动化学报》2004年第6期1017-1020,共4页Acta Automatica Sinica

基　　金：国家自然科学基金(60234010)高校博士点基金(20040287005)资助~~

摘　　要：利用细分方案和递推平均插值方法构造了一类新的具有加权性质的小波，并证明了它的常用性质：紧支撑性，光滑性，消失矩，正交性.与采用常见的 Fourier 变换得到的正交小波相比，加权小波系数的衰减性比正交小波的系数衰减性快，而且计算过程简单，复杂度低，易于应用．仿真结果显示，当加权函数跳跃性很大时，加权小波具有非常好的光滑性，同时加权小波能准确地逼近函数，并且逼近收敛率要快于一般小波．A novel weighted wavelet is constructed by using the subdivision scheme andrecursive average interpolated method.Its characteristics is respectively proved to be compactsupported,smooth,vanishing moment,and orthogonal.Cornpared with the common waveletby the Fourier transform,the decay of weighted wavelet coefficient is faster than that of thecommon wavelet.Furthermore,the method is simple and easily applied.Its computationalcomplexity is greatly reduced.The simulation demonstrate that the weighted wavelet issufficiently smooth even though the weighted function has a large jump,and that it canapproximate functions exactly and the approximated convergence is faster.

关 键 词：加权小波 尺度函数 对偶小波 紧支撑性 细分法 

分 类 号：O241[理学—计算数学]