Bi-orthogonal Wavelets Related to Butterworth Filters
Youming Liu · Advances in Mathematics · 2007
Butterworth filters are related to some bi-orthogonal wavelets,called Butter- worth wavelets.Those wavelets have nice properties which include symmetry,the interpolation and vanishing moments.In this paper,a general concept for bi-orthogonal wavelet bases in L~2(Z)is introduced and an easily checked sufficient condition is given,by which the Butter- worth wavelets are derived;then a family of bi-orthogonal wavelets are constructed,which have all properties of the Butterworth wavelets;Moreover,our wavelets have the shortest possible supports.