三进制双正交对称小波的设计

On the Construction of Triadic Symmetric Bi-Orthogonal Wavelets with Pre-Assigned Fundamental Scaling Function

本文给出了一种三进制双正交对称小波的设计方法.在给定插值紧支撑对称尺度函数的情况下,指出了如果对偶尺度函数同为紧支撑插值的,则它们同为1-型对称.并且给出了对偶尺度函数为紧支撑插值和非插值情况下的通解计算公式.还提出了频率优化方法设计对偶尺度函数和小波函数,把双正交条件归结为线性约束的二次规划问题,最后通过线性方程组来求解.对于小波函数本文也给出了一组特解公式.

In this paper, a design method of triadic bi-orthogonal symmetric wavelets is proposed. If both dual scaling function and scaling function are compact support, symmetric and interpolatory, then they are type-1 symmetric. And the general for-mulas of compact support dual scaling functions are given. The method of frequency optimization is brought forward to design scaling function and wavelet functions. It can be formulated as linear constrained minimization problem, which can be solved through Lagrange's method of multipliers.