二维DWT的分裂向量基新算法

A SPLIT—VECTOR RADIX ALGORITHM FOR COMPUTING FIRST VERSION 2D-DISCRETE W TRANSFORM

本文导出了一种快速计算二维离散W变换的新算法——分裂向量基二维快速W变换算法(Split—Vector radix fast W traneform简称SVR—FWT)这种新算法具有概念清晰,结构简单及计算量少的特点。

This paper presents a split-vector radix algorithm for computingfirst version two-dimensional discrete W transform(2D-DWT-I),itis also called discrete Hartly transform,which shows that an N×N-point 2D-DWT-I can be decomposed into(N/2)×(N/2)-point 2D-DWT-I by taking vector radix-2 decomposition for which k andj are even,twelve(N/4)×(N/4)-point 2D-DWT-I by taking vec-tor radix-4 decomposition for which k and j are both odd,k isodd and j even,or k is even and j odd.We demonstrate that thesplit-vector radix algorithm saves more multiplications and additionsthan mirror row-column algorithm.