用准同步离散Fourier变换实现高准确度谐波分析

Realization of high precision harmonics analysis with pleisiochronous DFT arithmetic

论文介绍了准同步、离散Ｆｏｕｒｉｅｒ变换（ＤＦＴ）算法，它是为解决采样周期和信号周期在不严格同步的情况下，实现高准确度谐波分析问题的方法。文中首先采用准同步算法实现周期函数非同步采样时高准确度平均值的计算，然后通过一个新构造的函数，把Ｆｏｕｒｉｅｒ变换转化为求解一个周期函数的平均值的问题，进而，将准同步算法和Ｆｏｕｒｉｅｒ变换有机结合在一起，离散后得到一个非严格同步情况下进行计算机高准确度谐波分析的计算公式。模拟测试证明，这种方法比ＤＦＴ的准确度提高一个数量级。在采样周期偏差不超过半个周期、采样点数满足采样定理的情况下，合理选择算法中参数，能够获得接近于“理想同步采样”的准确度。

This article introduced a kind of pleisiochronous Discrete Fourier Translation (DFT) algorithm to realize the high precision harmonic analysis when there would be a non synchronization between the sampling period and the signal period. First, the paper proposed the high precision equalizing value calculation process of the periodic functions by using the pleisiochronous algorithm when the sampling would be non synchronous. Then through a newly constructed function, the Fourier translation process was converted to the solution procedure of an equalizing value of a periodic function. Further more, the quasi synchronous algorithm and Fourier translation algorithm were integrated. After the discretization, the high precision harmonic analysis algorithm routine, which would be suitable for computer processing, was obtained under non synchronous condition. The simulating test shows that the accuracy of the integrated algorithm is higher than that of DFT by one order. When the deviation of the sampling periods is less than half period and the sampling number required by the sampling theorem is satisfied, after properly selecting the parameters of the algoritm, the measuring accuracy of nearly “perfect synchronized sampling” can be got.