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According to the equivalent expression theorem about the orthogonality of wavelets and the equivalent expression theorem about the Riesz bounds of integral shifting basis of a function in L2(R),the orthogonality condition of Bubble wavelets is analysed and discussed systematically from three respects.The results show that the orthogonal and almost orthogonal Bubble wavelet can be constructed by selecting appropriately the shape parameter of Bubble functions,but the Mexicanhat wavelet (a special Bubble wavelet) can not be regarded as an almost orthogonal wavelets....

According to the equivalent expression theorem about the orthogonality of wavelets and the equivalent expression theorem about the Riesz bounds of integral shifting basis of a function in L2(R),the orthogonality condition of Bubble wavelets is analysed and discussed systematically from three respects.The results show that the orthogonal and almost orthogonal Bubble wavelet can be constructed by selecting appropriately the shape parameter of Bubble functions,but the Mexicanhat wavelet (a special Bubble wavelet) can not be regarded as an almost orthogonal wavelets.

根据小波正交性的等价叙述定理和L2(R)中函数整数平移系的Riesz界等价叙述定理,从三个方面系统地分析讨论Bubble小波的正交条件。适当选择Bubble函数的形状参数,可以得到正交和几乎正交的Bubble小波,并指出墨西哥帽函数不能当成几乎正交的小波函数使用。

The princciples and methods of constructing wavelets based on Bubble function are investigated sys- tematically through coorperating the integral shifting basis of Gaussian functions and Bubble functions. Th wavelets with different lateral inhibitation propetis can be constructed by changing the shape parameter of Gaussian and Bubble functions. Some wavelets with lateral inhibition performnace can be incorporated into Bubble wavelets, or represental approximately by uses of a special Bubble wavelet. Finally,...

The princciples and methods of constructing wavelets based on Bubble function are investigated sys- tematically through coorperating the integral shifting basis of Gaussian functions and Bubble functions. Th wavelets with different lateral inhibitation propetis can be constructed by changing the shape parameter of Gaussian and Bubble functions. Some wavelets with lateral inhibition performnace can be incorporated into Bubble wavelets, or represental approximately by uses of a special Bubble wavelet. Finally, the coefficients of Mallat's pyramidal decomposition filter banks of a few special wavelets are given.

本文首次系统地探讨基于 Bubble函数的子波构造原理和方法。通过选取不同形状参数和时移因子,可以得到许多具有不同侧抑制性能的子波函数.文中给出了相应的Mallat塔式分解快速算法所用的滤波器组系数计算公式与设计条件。

 
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