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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.Abstract: A novel weighted wavelet is constructed by using the subdivision scheme and recursive average interpolated method. Its characteristics is respectively proved to be compact supported, smooth, vanishing moment, and orthogonal. Compared with the common wavelet by the Fourier transform, the decay of weighted wavelet coefficient is faster than that of the common wavelet. Furthermore, the method is simple and easily applied. Its computational complexity is greatly reduced. The simulation demonstrate that the weighted wavelet is sufficiently smooth even though the weighted function has a large jump, and that it can approximate functions exactly and the approximated convergence is faster.
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Key words:
- Weighted wavelet /
- scaling function /
- dual wavelet /
- compactly supported /
- subdivision
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