A novel method of constructing compactly supported orthogonal scaling functions from splines
Shouzhi Yang, Huiqing Huang · Journal of Inequalities and Applications · 2017
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.