The Generalized Battle-Lemarié Wavelets
Yuan Ming Xiao · Dianzi xuebao · 2003
Starting with investigating the Haar scaling function,the scaling coefficient function is first presented.Then the Battle Lemarie basis is extended to the generalized Battle Lemarie basis by introducing time shift factor to the scaling coefficient function of the Battle Lemarie.The rationality of the extending method,which is used in this paper,is theoretically proved.Some basic properties of the generalized Battle Lemarie basis are also discussed.Our research results show that all the Battle Lemarie bases inherit many good properties of the original Battle Lemarie 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 Lemarie wavelets are better than the corresponding original Battle Lemarie wavelets in regularity.