A New Algorithm for DFT （p<sup>n</sup>;k） Using Local Ring Structure

Ma Weizheng & Yang Dekun

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A New Algorithm for DFT （pⁿ;k） Using Local Ring Structure

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- A New Algorithm for DFT （pⁿ;k） Using Local Ring Structure
- Acta Electronica Sinica Issue 7, Pages: 72-79(1992)
- 作者机构：
  
  1. 华南理工大学无线电系
  2. 华南理工大学无线电系广州 510641
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：1992
- 稿件说明：
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[1]马维祯,杨德坤.用局部环构造DFT(p~n;k)新算法[J].电子学报,1992(07):72-79.

Ma Weizheng & Yang Dekun. A New Algorithm for DFT （pⁿ;k） Using Local Ring Structure[J]. Acta Electronica Sinica, 1992, (7): 72-79.
[1]马维祯,杨德坤.用局部环构造DFT(p~n;k)新算法[J].电子学报,1992(07):72-79. DOI：

Ma Weizheng & Yang Dekun. A New Algorithm for DFT （pⁿ;k） Using Local Ring Structure[J]. Acta Electronica Sinica, 1992, (7): 72-79. DOI：

摘要

本文介绍用局部环结构构造DFT（p

;k）算法

算法首先利用一种新局部环的划分方法将DFT（p

;k）变换矩阵排成具有循环矩阵块的块结构矩阵;其次将各循环矩阵块分解成一系列DFT（p

）核CFT（p

）

s=1

……

n.文中给出了本算法的乘法复杂性

并论证了当n=1

k≠1或n≠1

k=1时本算法和具有理论上最小乘法次数的算法相同。

Abstract

This paper introduces the construction of algorithm for computing DFT（pn;k）. The construction of algorithm contains two steps: first

to permute the transform matrix of DFT（pn; k） into a block-structured matrix which contains circulant matrices by use of the partition of local ring; second

to decompose the circulant matrices into a series of CFT（p3）

the core of DFT（p3）

s = 1

…… n. We also give the multiplicative complexity of the algorithm and prove that the algorithm is one with the minimum number of multiplications when n=1

k≠1

or n≠1

k=1.

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A New Algorithm for DFT （pn;k） Using Local Ring Structure

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摘要

Abstract

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Keywords

references

A New Algorithm for DFT （pⁿ;k） Using Local Ring Structure