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 Nm(x), Nk(x), if m+k is an even integer, the corresponding mth order B-spline wavelets ψkm(x) can be constructed, which are compactly supported symmetric/antisymmetric. In addition, if ψkm(x), m>1 is mth B-spline wavelet associated with two spline functions Nm(x) and Nk(x), then (ψkm(x))′(x) is m-1th B-spline wavelet associated with N m-1(x) and N k+1(x), i.e. (ψkm(x))′(x)=22ψ k+1 m-1(x). Similarly, ∫x0ψkm(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.
