快速变换算法三十年的发展  

The 30 Year's Development of Fast Transform Algorithms

作　　者：马维祯[1] 

机构地区：[1]华南理工大学

出　　处：《信号处理》1995年第4期225-236,244,共13页Journal of Signal Processing

基　　金：国家自然科学基金!NFSC-68972023

摘　　要：傅里叶变换快速算法发展已三十年，本文综述了高散变换快速算法的发展，特别是近几年的发展，其中包括传统的基2、基4、基8、分裂基算法的发展以及多维离散傅里叶变换、多维离散余（正）弦变换、多维离散W变换（哈特莱变换）的快速算法．阐述各种算法是如何将多维变换转换为一维变换的计算，并讨论了在有理数域上计算上述各种变换所需最小实数乘法的次数。The publication of Cooley-Tukey Fast Fourier Transform in 1965 has past 30 years,The recent developments of major discrete transform fast algorithms are reviewed.These algorithms are reviewed.These traditional radix-2,radix-4 radix-8,split-radix discrete fourier transforms,multi-dimensional discrete fourier transtorms,multi-Dimensional discrete cosine transional descrete Hartley transforms(discrete W transform).In the paper, we demonstrate that the multi-dimensional discrete ransforms can be computed by one-dimensional transform and discuss the minimal number of real multiplication required to compute various discrete transforms over the rational number field.

关 键 词：付里叶变换 信号处理 算法 

分 类 号：TN911.7[电子电信—通信与信息系统]