Compactly Supported B-spline Wavelets with Orthonormal Scaling Functions

Abstract

Polynomial spline wavelets have played a momentous role in the enlargement of wavelet theory. Due to their attractive properties like compact support, good smoothness property, interpolation property, they are now provide powerful tools for many scientific and practical problems. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. Except for the case of order one, the orthogonality condition vanishes. Here we give a simple procedure to generate the compactly supported orthogonal scaling function for higher order B-splines. We multiply the mask of the B-spline with a polynomial function which satisfies all the conditions as the mask of B-spline. The existence and construction of such function is also given.