同时计算实序列的DFT和实序列的DFT的IDFT的新公式

上海交通大学学报（自然版）

同时计算实序列的DFT和实序列的
DFT的IDFT的新公式

范安东

（成都理工大学信息管理学院，成都 610059）

收稿日期:2007-11-27 修回日期:1900-01-01 出版日期:2008-12-28 发布日期:2008-12-28

The New Formulas of Simultaneously Calculating DFT of
Real Sequence and IDFT of the DFT of Real Sequence

FAN An-dong

(Information Management College, Chengdu University of Technology, Chengdu 610059, China)

Received:2007-11-27 Revised:1900-01-01 Online:2008-12-28 Published:2008-12-28

摘要/Abstract

摘要： 通过对离散傅里叶变换(DFT)的一些性质的分析，利用DFT的对称性和将一个复序列分解为4个奇偶序列之和的方法，改正了Gunther关于直接计算双实序列的DFT和实序列的DFT和逆离散傅里叶变换（IDFT）的公式中的少数错误，给出了新的同时计算实序列的DFT和实序列的DFT的IDFT的直接公式，并给出了证明.

关键词: 对称性, 离散傅里叶变换, 逆离散傅里叶变换

Abstract: By analyzing some properties of discrete Fourier transform (DFT), exploiting the symmetries of DFT and decomposing a complex sequence into four sequences, a few mistakes in the direct formulas for simultaneously calculating the DFTs of two real sequences and the DFT & inverse discrete Fourier transform (IDFT) of real sequences which were proposed by Gunther were corrected, the new direct formulas of simultaneously calculating DFT of a real sequence and IDFT of the DFT of another real sequence were proposed and proved.

中图分类号:

O 157.4

范安东. 同时计算实序列的DFT和实序列的
DFT的IDFT的新公式[J]. 上海交通大学学报（自然版）.

FAN An-dong. The New Formulas of Simultaneously Calculating DFT of
Real Sequence and IDFT of the DFT of Real Sequence[J]. Journal of Shanghai Jiaotong University.

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