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Single-tone frequency estimation based on reformed covariance for half-length autocorrelation

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Języki publikacji
EN
Abstrakty
EN
This paper presents a new simple and accurate frequency estimator of a sinusoidal signal based on the signal autocorrelation function (ACF). Such an estimator was termed as the reformed covariance for half-length autocorrelation (RC-HLA). The designed estimator was compared with frequency estimators well-known from the literature, such as the modified covariance for half-length autocorrelation (MC-HLA), reformed Pisarenko harmonic decomposition for half-length autocorrelation (RPHD-HLA), modified Pisarenko harmonic decomposition for half-length autocorrelation (MPHD-HLA), zero-crossing (ZC), and iterative interpolated DFT (IpDFT-IR) estimators. We determined the samples of the ACF of a sinusoidal signal disturbed by Gaussian noise (simulations studies) and the samples of the ACF of a sinusoidal voltage (experimental studies), calculated estimators based on the obtained samples, and computed the mean squared error (MSE) to compare the estimators. The errors were juxtaposed with the Cramér-Rao lower bound (CRLB). The research results have shown that the proposed estimator is one of the most accurate, especially for SNR>25dB. Then the RC-HLA estimator errors are comparable to the MPHD-HLA estimator errors. However, the biggest advantage of the developed estimator is the ability to quickly and accurately determine the frequency based on samples collected from no more than five signal periods. In this case, the RC-HLA estimator is the most accurate of the estimators tested.
Rocznik
Strony
473--493
Opis fizyczny
Bibliogr. 31 poz., rys., tab., wykr., wzory
Twórcy
  • University of Zielona Góra, Institute of Metrology, Electronics and Computer Science, Szafrana 2, 65-516 Zielona Góra, Poland, s.sienkowski@imei.uz.zgora.pl
  • University of Zielona Góra, Institute of Metrology, Electronics and Computer Science, Szafrana 2, 65-516 Zielona Góra, Poland, m.krajewski@imei.uz.zgora.pl
Bibliografia
  • [1] Al-Qudsi, B., El-Shennawy, M., Joram, N., Ellinger, F. (2017). Enhanced zero crossing frequency estimation for FMCW radar systems. Proc. of the 13th Conference on Ph. D. Research in Microelectronics and Electronics (PRIME), Giardini Naxos, Italy, 53-56.
  • [2] Hague, D.A., Buck, J.R. (2019). An experimental evaluation of the generalized sinusoidal frequency modulated waveform for active sonar systems. Journal of the Acoustical Society of America, 145(6), 3741-3755.
  • [3] Rice, F., Cowley, B., Moran, B., Rice, M. (2001). Cramér-Rao lower bounds for QAM phase and frequency estimation. IEEE Transactions on Communications, 49(9) 1582-1591.
  • [4] Toth, L., Kocsor, A. (2003). Harmonic alternatives to sine-wave speech. Proc. of the 8th European Conference on Speech Communication and Technology, Geneva, Switzerland, 2073-2076.
  • [5] Adelson, R.M. (1997). Frequency estimation from few measurements. Digital Signal Processing, 7(1), 47-54.
  • [6] Vizireanu, D.N. (2012). A fast, simple and accurate time-varying frequency estimation method for single-phase electric power systems. Measurement, 45(5), 1331-1333.
  • [7] Pan, X., Zhao, H., Zou, W., Zhou, Y., Ma, J., Wang, J., Hu, F. (2016). Frequency estimation of discrete time signals based on fast iterative algorithm. Measurement, 82, 461-465.
  • [8] Pei, D., Xia, Y. (2019). Robust power system frequency estimation based on a sliding window approach. Mathematical Problems in Engineering, 2019, 3254258.
  • [9] Sienkowski, S., Krajewski, M. (2018). Simple, fast and accurate four-point estimators of sinusoidal signal frequency. Metrology and Measurement Systems, 25(2), 359-376.
  • [10] Elasmi-Ksibi, R., Besbes, H., López-Valcarce, R., Cherif, S. (2010). Frequency estimation of real-valued single-tone in colored noise using multiple autocorrelation lags. Signal Processing, 90(7), 2303-2307.
  • [11] Cao, Y., Wei, G., Chen, F.J. (2012). An exact analysis of modified covariance frequency estimation algorithm based on correlation of single-tone. Signal processing, 92(11), 785-2790.
  • [12] Martinez, M.A., Ashrafi, A. (2018). Real-valued single-tone frequency estimation using half-length autocorrelation. Digital Signal Processing, 83, 98-106.
  • [13] So, H.C. (2002). A closed form frequency estimator for a noisy sinusoid. Proc. of the 45th Midwest Symposium on Circuits and Systems (MWSCAS-2002), 2, Tulsa, USA, 160-163.
  • [14] Lui, K.W.K., So, H.C. (2008). Modified Pisarenko harmonic decomposition for single-tone frequency estimation. IEEE Transactions on Signal Processing, 56(7), 3351-3356.
  • [15] Elasmi-Ksibi, R., López-Valcarce, R., Besbes, H., Cherif, S. (2008). A family of real single-tone frequency estimators using higher-order sample covariance lags. Proc. of the 16th European Signal Processing Conference, Lausanne, Switzerland.
  • [16] Tu, Y.Q., Shen, Y.L. (2017). Phase correction autocorrelation-based frequency estimation method for sinusoidal signal. Signal Processing, 130, 183-189.
  • [17] Duda, K., Zielinski, T.P. (2013). Efficacy of the frequency and damping estimation of a real-value sinusoid Part 44 in a series of tutorials on instrumentation and measurement. IEEE Instrumentation & Measurement Magazine, 16(2), 48-58.
  • [18] Eriksson, A., Stoica, P. (1993). On statistical analysis of Pisarenko tone frequency estimator. Signal Processing, 31(3), 349-353.
  • [19] Phadke, A.G., Thorp, J.S., Adamiak, M.G. (1983). A new measurement technique for tracking voltage phasors, local system frequency, and rate of change of frequency. IEEE Transactions on Power Apparatus and Systems, PAS-102(5), 1025-1038.
  • [20] Borkowski, J., Kania, D., Mroczka, J. (2018). Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics. Metrology and Measurement Systems, 25(2), 283-302
  • [21] Duda, K. (2012). Interpolation Algorithms of DFT for parameters estimation of sinusoidal and damped sinusoidal signals. Fourier Transform-Signal Processing. InTech - Open Access Publisher.
  • [22] Serbes, A. (2018). Fast and efficient sinusoidal frequency estimation by using the DFT coefficients. IEEE Transactions on Communications, 67(3), 2333-2342.
  • [23] Ye, S., Sun, J., Aboutanios, E. (2017). On the estimation of the parameters of a real sinusoid in noise. IEEE Signal Processing Letters, 24(5), 638-642.
  • [24] Djukanović, S., Popović-Bugarin, V. (2019). Efficient and accurate detection and frequency estimation of multiple sinusoids. IEEE Access, 7, 1118-1125.
  • [25] Candan, Ç. (2015). Fine resolution frequency estimation from three DFT samples: Case of windowed data. Signal Processing, 114, 245-250.
  • [26] Belega, D., Petri, D., Dallet, D. (2018). Accurate frequency estimation of a noisy sine-wave by means of an interpolated discrete-time Fourier transform algorithm. Measurement, 116, 685-691.
  • [27] Bendat, J.S., Piersol, A.G. (2010). Random Data: Analysis and Measurement Procedures. 4th ed. USA: John Wiley& Sons.
  • [28] Lal-Jadziak, J., Sienkowski, S. (2009). Variance of random signal mean square value digital estimator. Metrology and Measurement Systems, 16(2), 267-278.
  • [29] Benaroya, H., Mi Han, S., Nagurka, M. (2005). Probability Models in Engineering and Science. CRC Press.
  • [30] Fessler, J. (2015). Chapter 23 Mean and Variance Analysis. In Image reconstruction: Algorithms and analysis, Book draft, https://web.eecs.umich.edu/~fessler/book/c-mav.pdf (accessed on Aug. 2020).
  • [31] Kay, S.M. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory, Englewood Cliffs. New Jersey: Prentice-Hall.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0cce1bec-dd5a-440d-b07e-29184b16df47
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