适合于硬件高效执行的新型无乘法小波变换  

New Multiplication-free Wavelet Transforms for Efficient VLSI Implementation

作　　者：武守远[1] 陈祥训[1] 赵波[1] 刘兵[1] 

机构地区：[1]中国电力科学研究院输配电及节电技术国家工程研究中心,北京市海淀区100192

出　　处：《中国电机工程学报》2008年第4期94-101,共8页Proceedings of the CSEE

基　　金：国家自然科学基金项目(50577059)~~

摘　　要：消除小波变换中的乘法运算,能大大节省超大规模集成电路(very large-scale integration,VLSI)执行小波变换的时间,降低VLSI的复杂度。实现无乘法运算小波变换(multiplication-free wavelet transform,MFWT)的捷径是利用移位小波,即对应的小波滤波器是滤波系数为±1乘2的整数次幂的移位滤波器或移位滤波器序列。该文提出的实现MFWT的途径是:小波变换采用提升方式(lifting wavelettransform),小波滤波器在Lazy小波的基础上用提升法(liftingscheme)生成,每个提升滤波器都设计成简单的移位滤波器;这样,提升WT的每个预测(Predict)与改正(Update)步骤都只是计算当前数据与移位滤波器的相关系数的过程,可用移位加实现,避免了乘法运算。这种方案的关键是设计移位小波滤波器。该文详细研究了线性相位、非线性相位移位小波滤波器生成方法,内容包括如何根据对小波相频特性的要求选择提升滤波器形式,如何根据对小波幅频特性的要求确定提升滤波器参数等,并给出了一大批这样生成的移位小波滤波器的参数,以及部分这种小波的特性曲线。For VLSI-based wavelet transform （WT） eliminating multiplication operation can greatly reduce operation time and architecture complexity. A reasonable way for multiplication-free WT （MFWT） is recourse to shift wavelets, for which the associated filters are single or cascade shift filters. Shift filters are a class of filters with filtering coefficients being ±1×power of two. The suggested MFWT approach is to take lifting-based WT, and to design wavelet filters by lifting scheme from lazy filter with restricting lifting filters each to be simple shift one. By this way each predict and update stage in the tiffing WT just is to calculate correlation coefficients of the current data and shift filter. It can be done by shift-and-add operation instead of multiplication. The key point for the proposed approach is to design shift wavelet filters with linear or nonlinear phases. The design method has been studied thoroughly, such as how to choose the type of lifting filters and how to determine the pendent parameters in lifting filters according to desired properties of the shift wavelet. A lot of designed shift wavelet filters and a part of wavelet waveforms are given.

关 键 词：无乘法小波变换 提升法 提升法小波变换 移位小波滤波器 移位型小波变换 硬件执行 

分 类 号：O177[理学—数学] TN911[理学—基础数学]