周期测量误差对周期信号时域平均处理结果的影响

Influence of the Error in Periodic Measurement on Time Domain Average Results of a Periodic Signal

时域平均处理是从混有噪声的复杂周期信号中提取简谐分量的有效方法之一。本文从时域平均处理的基本原理出发，探讨了时域平均处理中周期测量误差对简谐分量幅值和相位的影响，并给出了时域平均处理后信号各阶简谐分量幅值衰减量和相位变化与周期测量误差、平均次数以及分量阶次之间的关系式。该关系式较复杂不便于工程应用，本文进一步用简单函数线性组合逼近的方法，得出了简化关系式。仿真和工程实例表明。

Time domain averaging (TDA) is one of effective methods for extracting a periodic signal from a complex periodic signal mixed with noise. On the basic principle of the TDA, a discussion is made about the influence of an error in the period measurement of a sinusoidal component on its amplitude and phase angle, extracted from the periodic signal by the TDA method. A formula is given for describing the relationship between the errors in the amplitude and phase angle of each harmonic component estimated by the method and some parameters including the number of averages, the order of harmonic component and the error in period measurement. The formula, however, is too complicated for practical use. Therefore, a simplified expression approximate to the formula by the linear combinatioin of simple functioins is also given in the paper. Simulation and practical example results show that the expression is suitable for engineering applicatioins.