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快速变换算法三十年的发展
The 30 Year’s Development of Fast Transform Algorithms
【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。
【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.
【Key words】 Discrete transforms; Algorithm; Fast Fourier transform; Computational complexity; Discrete Fourier transform; Discrete cosine transform; Discrete Hartley transform;
- 【文献出处】 信号处理 ,Signal Processing , 编辑部邮箱 ,1995年04期
- 【分类号】TN911
- 【被引频次】4
- 【下载频次】262