基于样条函数的小波尺度函数计算

Computation of Wavelets Scaling Functions Based on Splines

【摘要】通过样条函数构造小波正交基是常用的方法。在用样条函数构造小波尺度函数时,对样条函数正交化,涉及样条函数的Fourier变换函数定义无穷级数的求和,导致计算很复杂。采用样条函数的性质,使无穷级数求和化为有限个整数点上的样条函数值的求和,有效地简化了计算。

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.