A class of compactly supported symmetric/antisymmetric B-spline wavelets

摘要

An algorithm for constructing a class of compactly supported symmetric/antisymmetric B-spline wavelets is presented For any mth order and kth order cardinal B-spline N_m ( x), N_k ( x) , if m + k is an even integer, the corresponding mth order B-spline wavelets phi_m~k (x) can be constructed, which are compactly supported symmetric/antisymmetric. In addition, if phi_m~k (x) , m>l is mth Bspline wavelet associated with two spline functions N_m(x) and N_K ( x ), then ( phi_m~k (x) )' ( x) is m - 1th B-spline wavelet associated with N_(m-1) (x) and N_(k+1) (x), i.e. ( phi_m~k (x) =2~2 phi_(m-1)~(k+1) ( x) Similarly, integral_0~x phi_m~k (t ) dt, k >1 is m + 1th B-spline wavelet associated with N_(m+1) (x) and N_(k-1) (x). Using this method, we recovered Chui and Wang's spline wavelets Since a class of B-spline wavelets are symmetric/antisymmetric, their linear phase property is assured Several examples are also presented.