The generalized unified computation of multidimensional discrete orthogonal transforms

作     者：成礼智 蒋增荣 张振慧 

作者机构：1. Department of Mathematics and Systems Science National University of Defence Technology 410073 Changsha China 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2001年第44卷第6期

页      面：401-411页

学科分类：11[军事学] 0810[工学-信息与通信工程] 1105[军事学-军队指挥学] 08[工学] 081002[工学-信号与信息处理] 110503[军事学-军事通信学] 

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 69974041) 

主　　题：multidimensional signal processing fast algorithm multidimensional discrete Fourier transform multidimensional discrete cosine transform multidimensional discrete W transform. 

摘      要：By introducing a form of reorder for multidimensional data, we propose a unified fast algo-rithm that jointly employs one-dimensional W transform and multidimensional discrete polynomial trans-form to compute eleven types of multidimensional discrete orthogonal transforms, which contain three types of m-dimensional discrete cosine transforms ( m-D DCTs) ,four types of m-dimensional discrete W transforms ( m-D DWTs) ( m-dimensional Hartley transform as a special case), and four types of generalized discrete Fourier transforms ( m-D GDFTs). For real input, the number of multiplications for all eleven types of the m-D discrete orthogonal transforms needed by the proposed algorithm are only 1/m times that of the commonly used corresponding row-column methods, and for complex input, it is further reduced to 1/(2m) times. The number of additions required is also reduced considerably. Furthermore, the proposed algorithm has a simple computational structure and is also easy to be im-plemented on computer, and the numerical experiments show that the computational efficiency is con-sistent with the theoretic analysis.