基于全相位谱分析的多频内插迭代频率估计器
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摘要
为精确估计多频信号的各成分频率值,提出了基于全相位谱分析的内插迭代估计器。用全相位谱分析替代了传统FFT谱分析,从而减小了各成分之间的谱干扰;探究了全相位离散时间傅里叶变换谱的峰值谱附近的频偏估计机理;利用该机理设计出相应的内插迭代措施,从而增强了估计器的精度。仿真和实际数据分析表明:给定同样数目的多频观测样本,无论是无噪情况还是含噪情况,该估计器比Tsui估计器具有更高的估计精度,故具有较高的应用价值。
To accurately estimate the frequency components of a multiple-frequency signal,an all-phase spectral analysis-based interpolation iterative frequency estimator was proposed. Firstly,the all-phase spectral analysis was used to replace the FFT spectral analysis in this new estimator to reduce inter-spectral component interferences. Secondly,the frequency offset estimation mechanism was explored near the peak position of all-phase discrete time Fourier transformation( apDTFT) spectra. Thirdly,based on this mechanism,the corresponding interpolation and interative measures were designed to improve the accuracy of the proposed estimator. Both simulation results and actual data analysis showed that with the same number of multi-frequency signal observation samples,the proposed estimator has a higher estimation accuracy compared to Tsui estimator,so it is more valuable in application.
To accurately estimate the frequency components of a multiple-frequency signal,an all-phase spectral analysis-based interpolation iterative frequency estimator was proposed. Firstly,the all-phase spectral analysis was used to replace the FFT spectral analysis in this new estimator to reduce inter-spectral component interferences. Secondly,the frequency offset estimation mechanism was explored near the peak position of all-phase discrete time Fourier transformation( apDTFT) spectra. Thirdly,based on this mechanism,the corresponding interpolation and interative measures were designed to improve the accuracy of the proposed estimator. Both simulation results and actual data analysis showed that with the same number of multi-frequency signal observation samples,the proposed estimator has a higher estimation accuracy compared to Tsui estimator,so it is more valuable in application.
引文
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[22]黄翔东,王兆华.全相位数字谱分析方法[M].北京:科学出版社,2017.
[23]王兆华,侯正信,苏飞.全相位FFT频谱分析[J].通信学报,2003,24(B11):16-19.WANG Zhaohua,HOU Zhengxin,SU Fei.All-phase FFTspectrum analysis[J].Journal of China Institute Communicaions,2003,24(B11):16-19.
[24]屈梁生.机械故障的全息诊断原理[M].北京:科学出版社,2007.
[2]ANSARI M,ESMAILZADEH E,JALILI N.Exact frequency analysis of a rotating cantilever beam with tip mass subjected to torsional-bending bibrations[J].Journal of Vibration&Acoustics,2011,133(4):041003.
[3]SCHMIDT R.Multiple emitter location and signal parameter estimation[J].IEEE Transactions on Antennas and Propagation,1986,34(3):276-280.
[4]ROY R,KAILATH T.ESPRIT-estimation of signal parameters via rotational invariance techniques[J].IEEETransactions on Acoustics Speech&Signal Processing,1990,37(7):984-995.
[5]STOICA P,MOSES R L.Spectral analysis of signals[M].Upper Saddle River,NJ:Pearson/Prentice Hall,2005.
[6]QUINN B G.Estimation of frequency,amplitude,and phase from the DFT of a time series[J].IEEE Transactions on Signal Processing,1997,45(3):814-817.
[7]丁康,江利旗.离散频谱的能量重心校正法[J].振动工程学报,2001,14(3):354-358.DING Kang,JIANG Liqi.Energy centrobaric correction method for discrete spectrum[J].Journal of Vibration Engineering,2001,14(3):354-358.
[8]MACLEOD M D.Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones[J].IEEE Transactions on Signal Processing,1998,46(1):141-148.
[9]JACOBSEN E,KOOTSOOKOS P.Fast,accurate frequency estimators[DSP Tips&Tricks][J].Signal Processing Magazine,IEEE,2007,24(3):123-125.
[10]CANDAN C.Analysis and further improvement of fine resolution frequency estimation method from three DFTsamples[J].IEEE Signal Processing Letters,2013,20(9):913-916.
[11]HUANG X,XIA X G.A fine resolution frequency estimator based on double sub-segment phase difference[J].IEEESignal Processing Letters,2015,22(8):1055-1059.
[12]胡文彪,夏立,向东阳,等.一种改进的基于相位差法的频谱校正方法[J].振动与冲击,2012,31(1):162-166.HU Wenbiao,XIA Li,XIANG Dongyang,et al.An inproved frequency spectrum correction method based on phase difference correction method[J].Journal of Vibration and Shock,2012,31(1):162-166.
[13]齐国清.利用FFT相位差校正信号频率和初相估计的误差分析[J].数据采集与处理,2003,18(1):7-11.QI Guoqing.Error analysis of frequency and phase estimations based on phase difference of segmented FFTs[J].Journal of Data Acquisition and Processing,2003,18(1):7-11.
[14]丁康,钟舜聪.通用的离散频谱相位差校正方法[J].电子学报,2003,31(1):142-145.DING Kang,ZHONG Shuncong.A universal phase difference correcting method on discrete spectrum[J].Chinese Journal of Electronics,2003,31(1):142-145.
[15]陈奎孚,王建立,张森文.频谱校正的复比值法[J].振动工程学报,2008,21(3):314-318.CHEN Kuifu,WANG Jianli,ZHANG Senwen.Spectrum correction based on the complex ratio of discrete spectrm around the main-lobe[J].Journal of Vibration Engineering,2008,21(3):314-318.
[16]ABOUTANIOS E,MULGREW B.Iterative frequency estimation by interpolation on Fourier coefficients[J].IEEETransactions on Signal Processing,2005,53(4):1237-1242.
[17]LIANG X,LIU A,PAN X,et al.A new and accurate estimator with analytical expression for frequency estimation[J].IEEE Communications Letters,2016,20(1):105-108.
[18]TSUI J,CHENG C H.Digital techniques for wideband receivers[M].3rd ed.Stevenage:Institution of Engineering and Technology,2015.
[19]RIFE D,BOORSTYN R.Single tone parameter estimation from discrete-time observations[J].IEEE Transactions on Information Theory,1974,20(5):591-598.
[20]王兆华,黄翔东.数字信号全相位谱分析与滤波技术[M].北京:电子工业出版社,2009.
[21]黄翔东,王兆华.全相位DFT抑制谱泄漏原理及其在频谱校正中的应用[J].天津大学学报,2007,40(7):882-886.HUANG Xiangdong,WANG Zhaohua.Principle of all-phase DFT restraining spectral leakage and the application in correcting spectrum[J].Journal of Tianjin Univercity,2007,40(7):882-886.
[22]黄翔东,王兆华.全相位数字谱分析方法[M].北京:科学出版社,2017.
[23]王兆华,侯正信,苏飞.全相位FFT频谱分析[J].通信学报,2003,24(B11):16-19.WANG Zhaohua,HOU Zhengxin,SU Fei.All-phase FFTspectrum analysis[J].Journal of China Institute Communicaions,2003,24(B11):16-19.
[24]屈梁生.机械故障的全息诊断原理[M].北京:科学出版社,2007.