【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。更多还原

【Abstract】 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.更多还原