广义Battle-Lemarié子波

The Generalized Battle-Lemarié Wavelets

从Haar尺度函数入手 ,提出尺度系数函数概念 ,引入时移因子 ,将Battle Lemari啨子波基拓展而构造出广义Battle Lemari啨多分辨分析基 .然后从理论上论证这种拓展的合理性与广义Battle Lemari啨基的一些基本性质 .研究结果表明 :所有广义Battle Lemari啨基继承了 (原始 )Battle Lemari啨基的许多优点 ,比如标准正交性 ,时、频局域化特征和指数衰减性等 ,同时还得到一系列新的对称基 ,广义Battle Lemari啨基的正则性优于相应的 (原始 )Battle

Starting with investigating the Haar scaling function,the scaling coefficient function is first presented.Then the Battle Lemarié basis is extended to the generalized Battle Lemarié basis by introducing time shift factor to the scaling coefficient function of the Battle Lemarié.The rationality of the extending method,which is used in this paper,is theoretically proved.Some basic properties of the generalized Battle Lemarié basis are also discussed.Our research results show that all the Battle Lemarié bases inherit many good properties of the original Battle Lemarié bases,such as orthonormality,time frequency localization,exponential decay and so on.Meanwhile a series of neoteric symmetric multiresolution analysis basis are generated.The generalized Battle Lemarié wavelets are better than the corresponding original Battle Lemarié wavelets in regularity.