Abstract:In order to solve the problem of unhomogeneities of estimation error and expensive computing of existing algorithms, an iterative frequency estimation algorithm based on interpolated zoom spectrum is proposed. Firstly, fast Fourier transform algorithm is applied to get the frequency corresponding to the peak spectral amplitude of the half-length signal. The unbiased estimation of frequency of the signal is then given based on the zoom spectra, which are calculated with the half-length signal. The zoom spectra are updated with the complete signal and the frequency is estimated with the updated zoom spectra, lastly. Computing cost analysis proves the superiority of the algorithms when length of signal is long compared with the algorithms in the references. Simulation result verifies good performance of distribution of estimation error and estimation error of the proposed algorithm is closer to the Cramer-Rao lower bound at the circumstance of high signal to noise ratio.
崔维嘉,鲁航,巴斌. 基于细化频谱的频率迭代插值估计算法[J]. 电子与信息学报, 2017, 39(9): 2141-2147.
CUI Weijia, LU Hang, BA Bin. Iterative Frequency Estimation Algorithm Based on Interpolated Zoom Spectrum. JEIT, 2017, 39(9): 2141-2147.
SHEN Yanlin, TU Yaqing, CHEN Linjun, et al. A phase match based frequency estimation method for sinusoidal signals[J]. Review of Scientific Instruments, 2015, 86(4): 721-726. doi: 10.1063/1.4916365.
[2]
DJUKANOVIC S. An accurate method for frequency estimation of a real sinusoid[J]. IEEE Signal Processing Letters, 2016, 23(7): 915-918. doi: 10.1109/LSP.2016. 2564102.
[3]
SYED A A, SUN Q, and FOROOSH H. Frequency estimation of sinusoids from nonuniform samples[J]. Signal Processing, 2016, 129: 67-81. doi: 10.1016/j.sigpro.2016.05. 024.
[4]
LUO Jiufei, XIE Zhijiang, and XIE Ming. Frequency estimation of the weighted real tones or resolved multiple tones by iterative interpolation DFT algorithm[J]. Digital Signal Processing, 2015, 41(6): 118-129. doi: 10.1016/j.dsp. 2015.03.002.
HUANG Xiangdong, WANG Yuedong, JIN Xukang, et al. No-windowed apFFT/FFT phase difference frequency estimator based on frequency-shift & compensation[J]. Journal of Electronics & Information Technology, 2016, 38(5): 1135-1142. doi: 10.11999/JEIT151041.
[6]
RIFE D C and VINCENT G A. Use of the discrete fourier transform in the measurement of frequencies and levels of tones[J]. Bell Labs Technical Journal, 1970, 49(2): 197-228. doi: 10.1002/j.1538-7305.1970.tb01766.x.
DENG Zhenmiao, LIU Yu, and WANG Zhizhong. Modified Rife algorithm for frequency estimation of sinusoid wave[J]. Journal of Data Acquisition and Processing, 2006, 21(4): 473-477. doi: 10.3969/j.issn.1004-9037.2006.04.020.
XU Jiajia, LIU Yu, DENG Zhenmiao, et al. A research of fast and accurate recursive algorithm for frequency estimation of sinusoid signal[J]. Journal of Electronics & Information Technology, 2009, 31(4): 865-869. doi: 10.3724/SP.J.1146. 2008.00075.
[9]
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. doi: 10.1109/78. 558515.
[10]
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. doi: 10.1109/78.651200.
[11]
MAO X H and TING H. Estimation of complex single-tone parameters in the DFT domain[J]. IEEE Transactions on Signal Processing, 2010, 58(7): 3879-3883. doi: 10.1109/TSP. 2010.2046693.
[12]
CANDAN C. A method for fine resolution frequency estimation from three DFT samples[J]. IEEE Signal Processing Letters, 2011, 18(6): 351-354. doi: 10.1109/LSP. 2011.2136378.
[13]
CANDAN C. Analysis and further improvement of fine resolution frequency estimation method from three DFT samples[J]. IEEE Signal Processing Letters, 2013, 20(9): 913-916. doi: 10.1109/LSP.2013.2273616.
[14]
JAN-RAY L and SHYING L. Analytical solutions for frequency estimators by interpolation of DFT coefficients[J]. Signal Processing, 2014, 100: 93-100. doi: 10.1016/j.sigpro. 2014.01.012.
[15]
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. doi: 10.1109/LCOMM.2015.2496149.
QI Guoqing and JIA Xinle. Accuracy analysis of frequency estimation of sinusoid based on interpolated FFT[J]. Acta Electronica Sinica, 2004, 32(4): 625-629. doi: 10.3321/j.issn: 0372-2112.2004.04.022.
HUANG Xiangdong, MENG Tianwei, DING Daoxian, et al. A novel phase difference frequency estimator based on forward and backward sub-segmenting[J]. Acta Physica Sinica, 2014, 63(21): 202-208. doi: 10.7498/aps.63.214304.