基于提升方法的滤波器组因子分解

讨论了FIR滤波器组的分解.2通道完全重构FIR 子波变换分解可为有限步的提升步骤,使用Laurent多项式的辗转相除法给出了这种分解的一个代数方法的证明;证明了二通道子波变换的分解定理不能平行推广到2M通道滤波器组.提出使用M-通道滤波器组构造2M-通道滤波器组,它由多相矩阵的分块化和提升方法实现,这种方法易于构造非线性滤波器组,如整数变换.

Factorization of Filter Banks Through Lifting Scheme

The decomposition of the multi channel filter banks has been discussed.It is known that any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple lifting steps.The proof of this decomposition is provided using an algebraic method.It is also proved that multi channel filter does not have this decomposition.It proposes using lifting scheme and block factorization of the polyphase matrix to construct 2M channel FIR filter banks from M channel FIR filter banks. This method is easy to build non linear filter banks, such as integer-integer transforms.