离散傅立叶变换(DFT)计算中一些问题的论证  

Some Discussion On the Calculation of the Discrete Fourier Transform(DFT)

作　　者：钟佑明[1] 汤宝平[1] 秦树人[1] 

机构地区：[1]重庆大学机械学院测试中心,重庆400044

出　　处：《重庆大学学报（自然科学版）》2001年第3期1-4,共4页Journal of Chongqing University

基　　金：国家自然科学资金资助项目 !(5 9875 0 90 )

摘　　要：在时频信号分析领域中 ,DFT是一个常见的术语 ,尤其是在它的高效算法FFT出现以后 ,信号分析中的其他运算也常常尽可能转化为DFT以提高运算速度。但作者在开发虚拟频谱分析仪中了解到 ,对DFT及其逆变换 (IDFT)的计算存在着两套公式 ,导致不同信号分析人员 ,或不同时频信号分析仪计算出的DFT结果不一致 ,其物理意义也不分明。作者首先阐述了以前文献中定义DFT时所依据的周期延拓原理 ,然后分别用待定系数法和类比演变法论证了在周期延拓原理的认识下 ,DFT的计算公式采用式 ( 3)更具合理性 ,指出并纠正了以前诸多文献中定义DFT计算公式时 ,推导过程中存在的一个不当之处 ,对以前认为DFT及其IDFT的计算存在两套公式是一种习惯的不恰当观点加以了澄清 ,最后以三个算例直观地验证了作者观点的正确性。In the field of signal analyies for time frequency, the DFT is a familiar term. Especially,when its efficient algorithm FFT given, the other operations in signal analyses are also usually translated to DFT as soon as possible so as to enhance the calculating speed. But in our exploning the virtual instrument for time frequency analyzing, two sorts of formulas to calculate DFT and its inverse transform (IDFT) are found. These results are in different value of operation from different signal analysts or from different instruments for time frequency analyzing, their physical meaning are also not clear enough.The period extent theory some previous document based on when defined DFT is firstly expatiated. Then, separately with future defining coefficient method and analogy evolvement method, the authors argue that, based on the period extent theory, it is more rational to calculate DFT with the formula given. A shortage is pointed out and corrected is appeared in some previous documents when having given the formula of DFT. The improper view is also clarified that the reason why there are two sorts of formulas is make by custom.The rationality of the authors view with three examples is visually verified in the end.

关 键 词：离散傅立叶变换 有限长数字信号 周期延拓 原理 DFT 时频信号分析 

分 类 号：O174.22[理学—数学] TN911.6[理学—基础数学]