计及负频率的DFT与DTFT相位差测量误差分析  

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

作　　者：涂亚庆[1] 李明[1] 沈廷鳌[1] 张海涛[1] 

机构地区：[1]后勤工程学院信息工程系,重庆401311

出　　处：《振动与冲击》2015年第20期85-91,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(61271449;61302175);重庆市自然科学基金(CSTC2011BA2015;CSTC2012jj A0877;CSTC2013jcyj A40030)

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 d B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。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 5d B,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.

关 键 词：相位差测量 误差分析 负频率 DFT DTFT 

分 类 号：TN911.7[电子电信—通信与信息系统]