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

QI Guo-qing; JIA Xin-le

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

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- High-Accuracy Frequency and Phase Estimation of Single-Tone Based on Phase of DFT
- Acta Electronica Sinica Vol. 29, Issue 9, Pages: 1164-1167(2001)
- 作者机构：
  
  1. 大连海事大学电子信息与通信工程学院,辽宁,大连,116026
  2. 大连海事大学轮机工程研究所,辽宁,大连,116026
  3. 大连海事大学电子信息与通信工程学院辽宁大连,116026
  4. 大连海事大学轮机工程研究所辽宁大连,116026
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN911.72
- Published：2001
- 稿件说明：
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QI Guo-qing, JIA Xin-le. High-Accuracy Frequency and Phase Estimation of Single-Tone Based on Phase of DFT[J]. Acta Electronica Sinica, 2001, 29(9): 1164-1167.
DOI：

QI Guo-qing, JIA Xin-le. High-Accuracy Frequency and Phase Estimation of Single-Tone Based on Phase of DFT[J]. Acta Electronica Sinica, 2001, 29(9): 1164-1167. DOI：

摘要

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.

Abstract

A fast and accurate estimation technique of frequency and initial phase of single-tone signal based on the phase of the DFT spectrum is proposed.To eliminate the 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

SNR

threshold is much lower than that of the ML estimators for moderate

(length of DFT).For

SNR

=6dB and

=1024

the RMS error of frequency estimation is about 1% of the frequency resolution of the DFT

and the RMS error o

f the initial phase estimation is about 2 degrees.Formulas for evaluating the RMS errors of frequency and phase estimation in white Gaussian noise for different

SNR

and

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.

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