中文摘要：

现有基于DFT频谱分析的相位差测量方法在测量低频振动信号的相位差时，精度明显下降，甚至无法测量，其主要原因之一是忽略了频谱中的负频率成分贡献。基于离散时问傅里叶变换（DTFT），提出了一种计及负频率影响的低频振动信号相位差测量方法，分别给出了加矩形窗和加汉宁窗对应的相位差计算公式。仿真及实测结果表明，在无噪声背景下，该方法具有很高的精度，误差接近双精度运算的下限；在噪声背景下，其测量精度仍高于传统的DFT频谱分析方法。提出的测量方案简单实用，特别适用于频率很低或接近奈奎斯特频率的振动信号的相位差测量。

英文摘要：

For the phase difference measurement of the vibration signals with a low frequency, the traditional methods based on DFT spectrum analysis bring about significant errors and even become ineffective. The reason exists in the neglect of the contribution of negative frequency in the models. A new method for phase difference measurement for low-frequency vibration signals is proposed based on discrete time Fourier transform （DTFT）, for which the negative frequency contribution is counted. New formulas for the phase difference calculation are presented respectively for both the cases of rectangular window and Hanning one. Simulation and field test results show that the precision of the new method under noiseless background is so high that it almost approaches the lower limit of double precision arithmetic. Furthermore, under noise background, the precision of the new method is also higher than those of the traditional ones. The new method has the virtue of simplicity and practicability, and is expected to be suitable especially for vibration signals with a quite low frequency or with a frequency close to the Nyquist frequency.