On Orthogonality Condition of Bubble 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 inL2(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.