基于采样逼近的准同步改进算法研究

Study on the improved quasi-synchronization algorithm based on sample approximation

准同步算法在和离散傅里叶变换结合求取周期信号的幅值和相位时,由于被测信号频率未知或仅知道被测信号的频率变化范围,在求解傅里叶系数时只能将采样频率作为被测信号频率带入造成傅里叶系数计算产生理论近似,尤其是在求解各次谐波初相角时频偏越大,求解相位误差相应增大。本文首先基于准同步测频差原理求出被测信号的实际频率,重新选取采样点使其逼近整周期采样点数,再将计算频率代入傅立叶变换中的基函数频率,最后迭代求取傅里叶系数。计算结果表明这种基于频率代入并采样逼近的改进准同步算法可以极大地提高准同步谐波算法的准确度。

When quasi-synchronization algorithm and discrete Fourier transform are combined to determine the amplitude and phase of periodic signals,because the frequency of the signal under test is unknown or only the frequency range of the signal under test is known,only the sampling frequency can be used as the frequency of the signal under test to calculate the Fourier coefficients,which results in theoretical approximation in solving Fourier coefficients. Especially,in solving the initial phase angles of the harmonics,the larger the frequency deviation is,the larger the calculated phase error becomes correspondingly. This paper firstly obtains the actual frequency of the measured signal based on the quasi-synchronization frequency deviation measurement principle,then the sampling points are reselected and made to approach the number of sampling points of integral period; and the calculated frequency is used to replace the base function frequency in Fourier transform. Finally,the Fourier coefficients are calculated using iteration method. The calculation result shows that the improved quasi-synchronization algorithm based on frequency deviation and sampling approximation proposed in this paper can significantly improve the accuracy of quasi-synchronization harmonic algorithm.