第一作者涂亚庆男，博士，教授，1963年生

计及负频率的DFT与DTFT相位差测量误差分析

涂亚庆，李明，沈廷鳌，张海涛

(后勤工程学院信息工程系，重庆401311)

摘要：针对噪声背景下计及负频率的DFT(Discrete Fourier Transform)与DTFT(Discrete Time Fourier Transform)相位差测量误差问题，用误差理论分别推导出高斯白噪声背景下计及负频率的DFT与DTFT相位差估计方差计算公式。对不同的泄漏误差系数、采样序列长度及信噪比，在负频率影响条件下进行计算验证。结果表明，仿真结果与计算结果一致，表明相位差测量误差分析公式的正确性。提升频率估计精度、增加采样序列长度、提高信号信噪比，可有效提升计及负频率的DFT与DTFT相位差测量方法精度。采样序列长度大于2048点或信噪比大于5 dB时，相位差测量精度提升有限，且DTFT相位差测量方法对频率估计精度更敏感。

关键词：相位差测量；误差分析；负频率；DFT；DTFT

基金项目：国家自然科学基金(61271449,61302175)；重庆市自然科学基金(CSTC2011BA2015,CSTC2012jjA0877,CSTC2013jcyjA40030)

收稿日期：2014-01-08修改稿收到日期：2014-05-14

中图分类号:TN911.7

文献标志码：A

DOI:10.13465/j.cnki.jvs.2015.20.015

Abstract:Aiming at the errors in phase difference measurement based on DFT(Discrete Fourier Transform) or DTFT (Discrete Time Fourier Transform) methods, taking into account the negative frequency contribution under white noise background, the formulas for evaluating the variance of phase difference were presented according to the error theory. With the consideration of negative frequency contribution, the different leakage error coefficients, sampling sequence lengths and signal-noise-ratios (SNR) were calculated. The results of some the simulations coincide well with those results calculated by using the presented formulas, which shows the correctness of the phase measurement error analysis method. The accuracy of DFT or DTFT based phase difference measurement methods considering the negative frequency contribution could be further improved effectively by enhancing the frequency estimation accuracy, increasing the sampling sequence length, and improving the SNR. When the sampling sequence length is more than 2048 or SNR is greater than 5dB, the further improvement of the accuracy of phase difference measurement is limited. The DTFT based phase measurement method is more sensitive to frequency estimation accuracy.

Error analysis of DFT or DTFT based phase difference measurement considering the negative frequency contribution

TUYa-qing,LIMing,SHENTing-ao,ZHANGHai-tao(Department of Information Engineering, Logistical Engineering University, Chongqing 401311, China)

Key words:phase difference measurement; error analysis; negative frequency; DFT; DTFT

正弦信号相位差测量在雷达、导航、电力系统、机械状态监测与故障诊断、工业测量等领域中广泛应用。相位差测量方法较多，而数字相关法[1-2]及频谱分析法[3-6]为研究、应用较多的两种方法。数字相关法具有良好的噪声抑制能力，但难以消除谐波干扰，且要求对周期信号实行严格整周期采样；频谱分析法对谐波及随机噪声干扰抑制能力较强，且能利用FFT快速算法取得高运算效率，便于硬件实现，因而应用较广。

然而，当信号频率较低或接近奈奎斯特频率(即采样频率一半)时负频率干扰严重，数字相关法及频谱分析法的相位差测量精度均不理想。……