| 离散傅里叶变换的定义研究 |
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| 引用本文： | 熊元新,陈允平. 离散傅里叶变换的定义研究[J]. 武汉大学学报(工学版), 2006, 39(1): 89-91,142 |
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| 作者姓名： | 熊元新 陈允平 |
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| 作者单位： | 武汉大学电气工程学院,湖北,武汉,430072 |
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| 摘 要： | 提出了将序列信号分解成正交序列集表示,证明了正交序列集{ej2πNkn(n=0,1,…,N-1),(k=0,1,…,N-1)}是完备正交序列集,将周期序列信号x(n)分解成完备正交序列集{ej2πkNn(n=0,1,…,N-1),(k=0,1,…,N-1)}表示而定义为离散傅里叶级数,由离散傅里叶级数导出离散傅里叶变换定义.
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| 关 键 词： | 正交序列集 离散傅里叶变换 定义 |
| 文章编号： | 1671-8844（2006）01-089-03 |
| 收稿时间： | 2004-11-20 |
| 修稿时间： | 2004-11-20 |
Research on definition of discrete Fourier transform |
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| XIONG Yuanxin,CHEN Yunping. Research on definition of discrete Fourier transform[J]. Engineering Journal of Wuhan University, 2006, 39(1): 89-91,142 |
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| Authors: | XIONG Yuanxin CHEN Yunping |
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| Affiliation: | School of Electrical Engineering, Wuhan University, Wuhan 430072, China |
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| Abstract: | It is presented that the sequence signal is expressed by orthogonal sequence set.It is proved that the orthogonal sequence set {e~(j2πknN)(n=0,1,...,N-1),(k=0,1,...,N-1)} is a complete set of orthogonal sequence set.The periodic sequence signal x(n) is decomposed to a complete orthogonal sequence set {e~(j2πknN)(n=0,1,...,N-1),(k=0,1,...,N-1)} to define it as discrete Fourier series.And then,the definition of discrete Fourier transform is derived from discrete Fourier series. |
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| Keywords: | orthogonal sequence set discrete Fourier transform definition |
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