基于DFT和DTFT插值的正弦信号频率估计  

Frequency estimation of sinusoidal signal based on DFT and DTFT interpolation

作　　者：吴会豪 樊磊[1] 宋焕焕 兰振平[1] 李萍[1] WU Huihao;FAN Lei;SONG Huanhuan;LAN Zhenping;LI Ping(School of Information Science and Engineering,Dalian Polytechnic University,Dalian 116034,China)

机构地区：[1]大连工业大学信息科学与工程学院,辽宁大连116034

出　　处：《大连工业大学学报》2022年第6期462-468,共7页Journal of Dalian Polytechnic University

基　　金：辽宁省教育厅2021年度科学研究经费项目(LJKZ0515).

摘　　要：提出了一种基于离散傅立叶变换和离散时间傅立叶变换的三谱线插值的正弦信号频率估计算法。对接收到的正弦信号采样序列进行离散傅立叶变换,并找到离散傅立叶变换最大谱线位置,从而得到频率的粗估计值。与所有现有算法不同的是,在接下来的精估计阶段中,本算法所采用的谱线不是对称地位于离散傅立叶变换最大谱线的两侧,而是采用了离散傅立叶变换最大谱线及其同侧的两根离散时间傅立叶变换谱线来对频率进行插值。仿真结果表明,当信噪比在0~90 dB范围内变化时,均方根误差比现有算法更接近克拉美罗下限,并且运算量小于同类的基于离散傅立叶变换的算法。A sinusoidal signal frequency estimation algorithm based on three spectral line interpolation of discrete Fourier transform(DFT)and discrete time Fourier transform(DTFT)was proposed.DFT was performed on the received sinusoid sampling sequence and the coarse frequency estimate was obtained by finding the position of the maximum DFT spectral line.Different from all the existing algorithms,the spectral lines adopted by the proposed algorithm were not symmetrically located on both sides of the maximum DFT spectral line,but utilized the maximum DFT spectral line and the two DTFT spectral lines on the same side to interpolate the frequency in the following fine estimation stage.The simulation results showed that the root mean square error(RMSE)of the proposed algorithm was closer to the Cramer Rao lower bound(CRLB)than the existing algorithms when the signal-to-noise ratio varied from 0 to 90 dB.In addition,the computation amount of the proposed algorithm is less than that of the other DFT-based algorithms.

关 键 词：离散傅立叶变换 离散时间傅立叶变换 频率估计 克拉美罗下限 

分 类 号：TN911.72[电子电信—通信与信息系统]