Hermite Cubic Spline Wavelets With High Order Vanishing Moments

Because vanishing moments are important in wavelets and applications,this paper constructs two Hermite spline waveletsψ₁(x) andψ₂(x) with compact supports on[-2,2].They have vanishing moments of order 6 and 7 respectively,as well as symmetric and antisymmentric properties.In addition,it is proved that the integer translations of wavelets are L₂((?)) stable.All these work are motivated by Jia's paper.Firstly,we show that all symmetric and antisymmetric wavelets with compact supports on[-1,1]are essentially the wavelets given by Jia in some sense; Secondly,we try to find wavelets with vanishing moments of higher order and compact supports on[-2,2],according to Jia's standard.However,the stability of the integer translations is a problem.Finally,we receive the desired result by changing the standard.