数字介损测量离散付立叶变换的理论误差分析

Error Analysis of DFT in Digital tanδ Measurement

数字介损测量的基础是离散付立叶变换,为分析介损测量离散付立叶变换的误差对介损测量准确度的影响。从数字介损测量的数学模型出发,给出从采样到时窗处理过程对应的数学公式,分析了离散付立叶变换、半离散付立叶变换与信号频谱的关系以及误差来源,并针对常用的时窗函数说明误差的计算方法和控制误差的方法。同时指出准同步采样信号包含的信息与同步采样并无区别,使用半离散付立叶变换方法用准同步数字采样信息计算得到的信号相位与在相同的频率精度下的同步采样信息得到的信号相位具有相同的准确度。

The digital tanδ measurement is based on DFT, and consequently the error of DFT causes great influence on the accuracy of the tanδ measurement, e.g. the sampling frequency deflection will cause non-integer period sampling and spectral leakage; and fence effect will lead to measuring error of dielectric loss angle. Since most of the errors resuh from asynchronous sampling, it is claimed that the sampling frequency must be synchronous with the signal in order to reduce the error. However, this paper proposes that the imposition is not necessary; actually the information conveyed by the sample signals will not be influenced by the synchronization of the sampling frequency. This proposition is supported by mathematical resuhs derived from the Fourier transformation, models of digital tanδ measurement and the equations deal with the samplings and time-windows. In the digital tanδ measurement, this paper focuses on the quasi-synchronous sampling, and chooses the phases that are close to the actual frequency grids, and reduces the side effects of negative components and harmonic components using the Hamming window and Biackman window. Finally, the conclusions are drawn that the same accuracy can be achieved within the quasisynchronous sampling. The synchronous sampling devices are more complex than the quasi-synchronous sampling ones, and thus we can anticipate a simplification of both hardware and software for the sarnpling process. In addition, this paper points ot,t that higher accuracy can be achieved using a more accurate approximation of the actual frequency, for instance the computational result of the fundamental wave frequency, which can be based on the relation between the signal shift and the correspondent Change in phases.