一类最佳数据压缩FIR滤波器与Daubechies小波

A Class of Optimal FIR Filter-bank for Data Compression and Daubechies Wavelet

提出了一种设计数据压缩FIR滤波器的新方法．该方法在不引入信息失真的前提下以最有效分解原信号为目的设计滤波器．由此设计的滤波器可以实现数据基于压缩目的的最优分解,能够最大可能地提取信号中的有用信息同时去除冗余信息．该分解过程与具有一定正则性的Daubechies小波的离散小波变换十分相似,该滤波器也和Daubechies小波分解滤波器完全相同,其原因是Daubechies在构造小波时引入的余项应为零．

A new approach of FIR filter design for data compression is proposed, in the approach, the filters are designed to optimally decompose the data without bringing any additive distortion. In view of data compression, the filters can decompose the data into two parts in the most efficient way, which means the valuable information of the signal can be preserved and the redundant information can be ignored as far as possible. The decomposition is quite similar to discrete wavelet transform （DWT） using Daubeehies wavelet with certain regularity. The filters are also identical with the corresponding wavelet decomposition filters. The reason for this situation is that the residual term Daubechies introduced in constructing of the wavelets should be zero.