基于解析插值离散时间傅里叶变换的精确频率估计

doi:10.19595/j.cnki.1000-6753.tces.201667

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摘要短时波动周期下,来自负频率的频谱泄漏是频域插值算法估计误差的主要来源。为消除频谱泄漏影响以实现任意波动周期下实正弦信号频率的精确估计,该文提出一种基于广义离散时间傅里叶变换（DTFT）插值解析的频率估计算法。该算法利用位于频谱主瓣范围内的任意DTFT谱线构建对应实/虚部的线性方程组,进而通过方程组求解得到基于解析插值DTFT的无偏频率估计公式。此外,考虑实际中加性白噪声的影响,根据频率估计的统计特性分析给出一种简单且有效的迭代方法,从而确保频率估计的方均误差（MSE）在任意波动周期下能够一致逼近无偏频率估计的克拉美罗下届（CRLB）。仿真和实验结果验证了所提算法优于现有的DFT插值算法。

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关键词 ：短时波动周期, 频谱泄漏, 解析插值DTFT, 迭代方法, 克拉美罗下届（CRLB）

Abstract：When the cycles in record (CiR) of the signal is small, the spectral leakage from the image component is the main source of estimation errors in the frequency-domain interpolation. To eliminate the influence of spectral leakage and accurately estimate the frequency of a real sinusoidal signal with any CiR, an analytic interpolation algorithm based on generalized DTFT is proposed. The algorithm uses any DTFT spectral lines located in the main lobe of the spectrum to construct a linear equation set corresponding to the real and imaginary parts, and then an unbiased frequency estimator based on analytic interpolated DTFT is obtained. Besides, considering the influence of additive white noise in practice, a simple and effective iterative method is presented based on the analysis of the statistical characteristics of the frequency estimator. The iterative method ensures that the mean square errors (MSE) of the frequency estimation can consistently achieve the Cramer-Rao lower bound (CRLB) of the unbiased frequency estimation under any CiR. Simulation and experimental results confirm that the proposed algorithm is superior to other existing interpolated DFT algorithms.

Key words： Small cycles in record spectral leakage analytically interpolated discrete time fourier transform (DTFT) iterative method Cramer-Rao lower bound (CRLB)

收稿日期: 2020-12-20

PACS:

TM935

基金资助:国家重点研发计划课题（2018YFC0406904）和重庆市重点产业共性关键技术创新专项（重点研发项目）（CSTC2017ZDCY-ZDYFX0045）资助

通讯作者: 杨超男,1986年生,博士,研究方向为数字信号处理及其在精密测量、电能计量与电能质量分析中的深度应用。E-mail: 328383369@qq.com

作者简介: 李波男,1982年生,硕士,高级工程师,主要从事电气测量以及智能电网测控研究工作。E-mail: libo2010@163.com

引用本文:

杨超, 李波, 胡绪权, 付志红. 基于解析插值离散时间傅里叶变换的精确频率估计[J]. 电工技术学报, 2022, 37(6): 1338-1350. Yang Chao, Li Bo, Hu Xuquan, Fu Zhihong. Accurate Frequency Estimation Based on Analytical Interpolated Discrete Time Fourier Transform. Transactions of China Electrotechnical Society, 2022, 37(6): 1338-1350.

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