Mapping from One- to Multi-dimension for DFT and Circular Convolution Algorithms

Zhang Gong-li

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Mapping from One- to Multi-dimension for DFT and Circular Convolution Algorithms

更新时间：2025-12-08

- Mapping from One- to Multi-dimension for DFT and Circular Convolution Algorithms
- Acta Electronica Sinica Issue 3, Pages: 81-88(1987)
- 作者机构：
  
  西北电讯工程学院,西安
- 作者简介：
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- Published：1987
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[1]张公礼.DFT和卷积计算中的一维到多维映射[J].电子学报,1987(03):81-88.

Zhang Gong-li. Mapping from One- to Multi-dimension for DFT and Circular Convolution Algorithms[J]. Acta Electronica Sinica, 1987, (3): 81-88.
[1]张公礼.DFT和卷积计算中的一维到多维映射[J].电子学报,1987(03):81-88. DOI：

Zhang Gong-li. Mapping from One- to Multi-dimension for DFT and Circular Convolution Algorithms[J]. Acta Electronica Sinica, 1987, (3): 81-88. DOI：

摘要

本文利用有限交换环的基本概念和性质讨论了DFT和卷积计算中的一维化多维问题。文中论述了DFT一维化多维同Levy-Walsh变换的关系

论证了利用多维技术计算一维DFT和循环卷积时序号变换的充要条件

并给出了一种序号重排快速算法。

Abstract

The mapping from one- to multi-dimensions for DFT and circular convolution algorithms are discussed from the viewpoint of finite commutative rings. The relation between multidimensional DFTs mapped from one-dimensional DFT and Levy-Walsh transforms is described. The necessary and sufficient conditions for a one-dimensional DFT or circular convolution to be expressed as a multidimensional DFT are given

and then a fast algorithm for index mappings is presented.

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