一种选择多小波预滤波器的方法

提出了多小波(Multiwavelet)预滤波器的选择原则—预滤波和多小波变换对原数据不引入任何形式的信息损失或失真,该原则对应于预滤波器和多小波滤波器组在频域内能谱密度恒为常数．在此基础上,得到了常用多小波预滤波器应满足的必要条件．提出了用于数据压缩的预滤波器的选择方法,该方法以数据高低频成分分离的分离效率为选择准则．以此准则,给出了常用多小波的最佳预滤波器．仿真实例证实了这种方法的有效性．

On Prefilters of Multiwavelets

In this paper,the fundamental for choosing multiwavelet prefilters is proposed,which demands that there is no infor- mation distortion or loss to the original data caused by the processes of prefiltering and multiwavelet transformation.This fundamental can be fulfilled by the fact that the energy spectral density of multiwavelet filterbanks and its prefilters is constant in frequency domain. The necessary condition of some universal multiwavelets is derived based on this fundamental.A new approach is proposed for choosing prefilters in data compression,in which the efficiency of the multiwavelet filterbanks and its prefilter in decomposing data into high-fre- quency and low-frequency portions is used as a criterion.The most appropriate prefilters for the usual multiwavelets are derived by this approach.The results of some simulation examples confirm the effectiveness of the proposed approach.