基于加窗傅里叶变换的相位误差研究

Study on phase error based on windowed fourier transform

为了在已知相位精度要求的前提下提高谐波测量的速度,定量分析了基于WFFT的相位误差,分别推导出相位误差与窗口周期数、采样信号频率、初相位之间的解析式。在此基础上提出通过工程中相位所需要的精确度来找到最合适的窗口长度的方法,拟合出了采样频率/窗口长度和相位误差之间的关系公式,可由相位误差精度确定最小窗口长度,从而提高谐波测量的速度。存在固定的旁瓣衰减率值使得相位误差范围最准确。仿真实验表明,在已知初始条件和误差精度要求的前提下,可以找到一个最短的窗口长度及最合适的旁瓣衰减率,使谐波测量速度最快。

In order to improve the speed of harmonic measurement on the premise of known phase accuracy require- ment, quantitative analysis of phase error based on WFFF, the formula between phase error and window period num- ber, sampling signal frequency, and initial phase is deduced. On this basis, a method which finds the optimal window length according to the accuracy demand in actual phase measurement is proposed. The formula of the relationship be- tween the sampling frequency / window length and the phase error is fitted, and the minimum window length can be determined by the phase error precision, so as to improve the speed of harmonic measurement. The fixed side lobe at- tenuation rate makes the phase error range the most accurate. Simulation results show that the known initial conditions and error accuracy requirements of the premise, a window of the length of the shortest and most suitable side lobe de- cay rate can be found, so that the fastest harmonic measurement can be achieved.