关于DFT中的延拓原理及计算结果物理意义的一些讨论

SOME DISCUSSION ON THE EXTENSION PRINCIPLE IN THE DFT AND THE PHYSICAL MEANING OF ITS VALUE

在信号分析领域 ,DFT(离散傅立叶变换 )是一个常见术语。但关于DFT中的延拓原理及计算结果的物理意义作者始终感到有些迷惑。而且 ,关于DFT及其逆变换IDFT的计算目前存在两套公式 ,这两套公式并存的原因是什么 ,它们的物理意义区别在哪里 ,作者始终未在文献中得到明确和满意的答案。本文在查阅了较多文献的基础上 ,对这些问题作了深入的研究 ,分析和澄清了以前对这些问题的一些模糊认识 ,对DFT中的延拓提出了一种新的见解 (零延拓观点 ) 。

In the field of signal analysis, the DFT (Discrete Fourier Transform) is a well known term. However about the extension principle in the DFT and the physical meaning of its value, some engineers are often feeling puzzled. Furthermore, presently there exist two sorts of formulas to calculate DFT and its inverse IDFT, while the physical meanings of the two sorts of formulas are rarely explained clearly and satisfactorily in references. In the paper some on these problems, are made and some previous fuzzy cognitions to them are analyzed and clarified. A new point of view (the view of Zero Extend) on the extension problem in the DFT is presented and the definitive physical meanings of the operating results of the two formulas of the DFT are described.