二维离散W变换的快速算法

A fast algorithm for 2D discrete W transform

离散Ｗ变换（ＤＷＴ）是在Ｈａｒｔｌｅｙ变换的基础上提出的。从ＤＷＴ提出之后已研究出了不少快速算法，但大多数算法都局限于长度为２的幂的一维ＤＷＴ。二维ＤＷＴ的核是不可分离的，因而不能简单地利用一维ＤＷＴ构造二维ＤＷＴ的算法。本文给出了一种将二维ＤＷＴ转化为一种可分离的二维变换，然后用一维ＤＷＴ计算这种二维变换，并给出了其各种应用及运行时间与二维离散付里叶变换运行时间的比较结果。

A 2D discrete W transform is turned to another discrete transform method are proposed in this paper. The Kernel of the resulting transform is separable, Therefore, it can be computed by the row-column algorithm. So that, a fast algorithm is obtained for 2DDWT with arbitrary length. Methods are also given in the paper for computing 2D cyclic convolutions, 2D skew-cyclic convolutions and 2D generalized discrete Fourier transform by using 2D discrete W transform. Furthermore, running time of the algorithm on a micro computer is given, and we compare the algorithm with that algorithm of 2D discrete Fourier transform.