DFT理论及其新算法研究

本文给出了有限离散点或周期离散点的新的傅氏变换计算法。它与经典的用周期性Diracδ抽样理论之纯离散变换的算法不同,而是根据抽样点的原曲线情况,采用任意幂多项式甚至无限幂（理想光滑化）曲线来模拟的新算法。它计算简便,只要在原FFT计算结果上乘上一个本文导出的简单的β_n或β_∞因子即可。 文中给出算例,阐述了该算法之优点。在理论上它不仅给出全频域的连续变换值,并且也避免了过去DFT计算中在高频处出现的混迭误差。这对信息的合理抽样,提高计算精度等方面,具有理论和实际意义。

THE INVESTIGATIONS OF DFT THEORY AND ITS NEW COMPUTING METHOD

In this paper a new computing method of the Fourier transform for finite or periodic discrete samples is developed, i.e. a new general numerical formula for Fourier integral is provided. In this computing formula that is on the basis of the general computational result of FFT, according to the type of any n-th power polynomial or infinite power （purely smooth） analogy curve through this set of discrete samples, it is multiplied correspondingly by a simple factor β_n or β_∞. Theoretically, it can obtain a more accurate continuous transform curve in the full frequency domain. This computation is concise.The paper gives calculating examples, and elucidates in detail the superiority of this computing method.