Computation of Wavelets Scaling Functions Based on Splines

Constructing orthonormal wavelet bases from splines is a method used often. But when wavelet scaling functions are constructed by splines,first step is orthogonalization,in which an infinite series defined by Fourier transform of splines is summed.The approaches used currently to sum the infinite series are complicated.In this paper,the summation of the infinite series defined by Fourier transform of splines is turned to sum a finite series defined by splines over integer by means of spline properties,therefore computation of the summation is efficiently simplified.