A class of compactly supported symmetric/antisymmetric B-spline wavelets
Yang Shouzhi, Zengjian Lou · Progress in Natural Science Materials International · 2005
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 ψ m k (x) can be constructed, which are compactly supported symmetric/antisymmetric. In addition, if ψ m k (x), m > 1 is mth B-spline wavelet associated with two spline functions Nm (x) and Nk (x), then (ψ m k (x))′(x) is m − 1th B-spline wavelet associated with Nm −1(x) and Nk +1(x), i.e. (ψ m k (x))′(x) = 22ψ m −1 k +1(x). Similarly, ∫0 x ψ m k (t)dt, k > 1 is m + 1th B-spline wavelet associated with Nm +1(x) and Nk −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.