基于B样条函数的移不变双正交滤波器设计

B-Spline Function Based Shift Invariant Bi-Orthogonal Filter Design

给出了1～7阶B样条半延迟算子的显式表达式，在B样条函数构造的半延迟算子和传统的双正交小波变换的基础上，构造了一种移不变双正交滤波器．针对4阶以上B样条函数构造的小波函数和尺度函数过程中出现的不可逆和不稳定问题，采用因子分解和逆序滤波的方法解决．以4阶B样条半延迟算子为例，给出移不变双正交滤波器的构造方法．

Explicit expressions of half delay operator including order 1 to 7 are presented. According to the B-spline based half delay operator, a class of shift invariant bi-orthogonal filter design method is formulated. Factor decomposition and inverse filtering methods are utilized to solve the non-inverse and instable problems existing in the wavelet function constructed from t3- spline function whose order is equal to or greater than 4. An example of shift invariant bi-orthogonal filter is given to overcome the problem occurring in 4 order B-spline half delay operator .