基于DFT相位的正弦波频率和初相的高精度估计方法

提出一种新的基于DFT相位的正弦波信号频率和初相的高精度估计方法.利用分段DFT频谱的相位差消除了初相对频率估计的影响且避免了相位测量模糊问题.给出了频率和初相估计的均方根误差计算公式.理论分析和Monte Carlo模拟结果显示频率估计均方根误差接近Cramer-Rao(CR)下限,初相估计均方根误差略高于CR下限的2倍.阈值信噪比远远低于基于时域瞬时相位的频率和初相估计方法.在信噪比为6dB、采样点数为1024的情况下,频率估计均方根误差约为DFT频率分辨率的1%,初相估计均方根误差约为2度.该方法已用于FMCW液位测量雷达并取得1mm距离测量精度.

High-Accuracy Frequency and Phase Estimation of Single-Tone Based on Phase of DFT

A fast and accurate estimation technique of frequency and initial phase of singl e tone signal based on the phase of the DFT spectrum is proposed.To eliminate t he ambiguity in DFT phase measurement,the sampled data are divided into two segments and the DFT is applied on them individually,then the frequency and initial phase of the signal are estimated with the phase difference of the two DFT spectra at their maximum amplitude position.Computer simulation results show that the variance of frequency estimation is close to the Cramer Rao bound,and the SN R threshold is much lower than that of the ML estimators for moderate N (l ength of DFT).For SNR =6dB and N =1024,the RMS error of frequency estimati on is about 1% of the frequency resolution of the DFT,and the RMS error of the i nitial phase estimation is about 2 degrees.Formulas for evaluating the RMS error s of frequency and phase estimation in white Gaussian noise for different SNR and N are also presented,which fit well with computer simulation results. This technique has been used in FMCW level radar and 1mm range measurement accuracy has been achieved.