科研之友
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摘要
A novel construction of compactly supported orthogonal scaling functions and wavelets with spline functions is presented in this paper. Let M-n be the center B-spline of order n, except for the case of order one, we know M-n is not orthogonal. But by the formula of orthonormalization procedure, we can construct an orthogonal scaling function corresponding to M-n. However, unlike M-n itself, this scaling function no longer has compact support. To induce the orthogonality while keeping the compact support of M-n, we put forward a simple, yet efficient construction method that uses the formula of orthonormalization procedure and the weighted average method to construct the two-scale symbol of some compactly supported orthogonal scaling functions.
