中文摘要：

首先根据Parseval能量积分公式，推导了离散信号经离散傅里叶变换（DFT）后时频域能量的表达公式，并且分析指出，将Hanning窗函数应用于国际电工委员会（IEC）标准框架下的集合概念，其前提条件是保证加窗前的时域能量与加窗（并DFT）后的频域能量相等，同时提出引入“能量损失修正系数”来达到该条件。而后，利用能量损失修正系数，得出了加Hanning窗时集合概念的表达公式，该公式与IEC标准框架下的集合概念完全兼容。接着，对IEC推荐的谐波和间谐波检测方法进行了扩展，扩展方法将谐波和间谐波的检测细化为4种测量环境和5个衡量指标。最后，详细分析了每种测量环境下影响测量精度的因素，并且多方位比较与该测量环境相对应的5个衡量指标的综合性能，从5个指标中选出性能最优的一个作为该测量环境下的最优衡量指标。在实际测量时，根据具体的测量环境，选择对应的最优衡量指标，可以得到最精确的测量结果。

英文摘要：

According to Parseval＇ s relation, the formulas which accurately represent the signal energy expressed in the time domain and frequency domain are acquired under the circumstances that the sampled signal is processed by discrete Fourier transform （DFT）. In order to make the Hanning window compatible with the group concept recommended by International Eleetrotechnical Commission （IEC） standard, the prerequisite that the energy sum contributed by all spectral lines in the frequency domain must be equivalent to the energy of the sampled signal within the window has to be reached, and an ＂energy- loss correction factor＂ is proposed to achieve the prerequisite. By use of the energy-loss correction factor, an expression of the group concept related to Hanning window is obtained and completely compatible with the IEC technique. The method recommended by IEC to measure harmonics and interharmonies is extended, which can be completely expressed by using four measurement conditions and five measurement indices. For each measurement condition, the factors that may affect the measuring accuracy are carefully analyzed, and the measurement index which has the best overall performance in certain measurement condition is selected as the specific optimal measurement index. The most accurate results can be obtained in practical measurement through the application of the specific optimal measurement index.