Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics

• Autorzy: Borkowski J. , Kania D. , Mroczka J.

Identyfikatory

DOI

10.24425/119567

• Języki publikacji: EN

Abstrakty

EN

The paper deals with frequency estimation methods of sine-wave signals for a few signal cycles and consists of two parts. The first part contains a short overview where analytical error formulae for a signal distorted by noise and harmonics are presented. These formulae are compared with other accurate equations presented previously by the authors which are even more accurate below one cycle in the measurement window. The second part contains a comparison of eight estimation methods (ESPRIT, TLS, Prony LS, a newly developed IpDFT method and four other 3-point IpDFT methods) in respect of calculation time and accuracy for an ideal sine-wave signal, signal distorted by AWGN noise and a signal distorted by harmonics. The number of signal cycles is limited from 0.1 to 3 or 5. The results enable to select the most accurate/fastest estimation method in various measurement conditions. Parametric methods are more accurate but also much slower than IpDFT methods (up to 3000 times for the number of samples equal to 5000). The presented method is more accurate than other IpDFT methods and much faster than parametric methods, which makes it possible to use it as an alternative, especially in real-time applications.

Słowa kluczowe

EN

DFT spectrum interpolation; short-time frequency estimation; statistical analysis; Prony LS; TLS; ESPRIT

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2018
• Tom: Vol. 25, nr 2
• Strony: 283--302
• Opis fizyczny: Bibliogr. 36 poz., rys., wykr., wzory

Twórcy

autor

Borkowski J.

• Wrocław University of Science and Technology, Faculty of Electronics, B. Prusa 53/55, 50-317 Wrocław, Poland

autor

Kania D.

• Wrocław University of Science and Technology, Faculty of Electronics, B. Prusa 53/55, 50-317 Wrocław, Poland

autor

Mroczka J.

• Wrocław University of Science and Technology, Faculty of Electronics, B. Prusa 53/55, 50-317 Wrocław, Poland

Bibliografia

• [1] Kelley, K., Light, R.P., Agarwal R. (2007). Trended cosinor change model for analyzing hemodynamic rhythm patterns in hemodialysis patients. Hypertension, 50(1), 143-150.
• [2] Engels, F., Heidenreich, P., Zoubir, A.M., Jondral, F.K., Wintermantel, M. (2017). Advances in Automotive Radar: A framework on computationally efficient high-resolution frequency estimation. IEEE Signal Processing Magazine, 34(2), 36-46.
• [3] Blaira, J.J., Linnenbrinkb, T.E. (2003). Corrected rms error and effective number of bits for sine wave ADC tests. Computer Standards and Interfaces, 26(1), 43-49.
• [4] Powell, K. (2011). Estimating the impact of structural vibration on adaptive optics system performance. Journal of Applied Optics, 50, 2185-2191.
• [5] Li, X., Zhang, Y., Amin, M.G. (2009). Multifrequency-based range estimation of RFID Tags. IEEE International Conference on RFID, 147-154.
• [6] Borkowski, J., Kania, D., Mroczka, J. (2014). Interpolated DFT-based Fast and Accurate Frequency Estimation for the Control of Power. IEEE Transactions on Industrial Electronics, 61(12), 7026-7034.
• [7] Abbas, S.A., Sun, Q., Foroosh, H. (2016). Frequency estimation of sinusoids from nonuniform samples. Signal Processing, 129, 67-81.
• [8] Zygarlicki, J., Mroczka, J. (2012). Variable-frequency Prony method in the analysis of electrical power quality. Metrol. Meas. Syst., 19(1), 39-48.
• [9] Zygarlicki, J., Mroczka, J. (2012). Prony’s method used for testing harmonics and interharmonics in electrical power systems. Metrol. Meas. Syst., 19(4), 659-672.
• [10] Ahmad, A., Schlindwein, F.S., Ng, G.A. (2010). Comparison of computation time for estimation of dominant frequency of atrial electrograms: Fast fourier transform, blackman tukey, autoregressive and multiple signal classification. Journal Biomedical Science and Engineering, 3, 843-847.
• [11] Chen, H., Hou, C., Zhu, W.P., Liu, W., Dong, Y.Y., Peng, Z. (2017). ESPRIT-like two dimensional direction finding for mixed circular and strictly noncircular sources based on joint diagonalization. Signal Processing, 141, 48-56.
• [12] Wang, M., Nehorai, A. (2017). Coarrays, MUSIC, and the Cramér-Rao Bound. IEEE Transactions on Signal Processing, 65(4), 933-946.
• [13] Koglin, H.-J, Leonowicz, Z., Lobos, T. (2006). High-Resolution Spectrum Estimation Methods for Signal Analysis in Power Systems. IEEE Transactions on Instrumentation and Measurement, 55(1), 219-225.
• [14] Huckle, T. (1998). Computations with Gohberg-Semencul-type formulas for Toeplitz matrices. Linear Algebra and its Applications, 273(1), 169-198.
• [15] Agrež, D. (2002). Frequency Estimation of the Non-Stationary Signals Using Interpolated DFT. IEEE Instrumentation and Measurement Technology Conference, 2, 925-930.
• [16] Candan, C. (2013). Analysis and Further Improvement of Fine Resolution Frequency Estimation Method From Three DFT Samples. IEEE Signal Processing Letters, 20(9), 913-916.
• [17] Belega, D., Dallet, D., Eynard, G. (2010). Influence of the Noise on the Amplitude Estimation of a Sive-Wave by the Three-Point Interpolated DFT Method. 4th International Symposium on Communications, Control and Signal Processing, 1-5.
• [18] Liang, X., Liu, S., Pan, X., Zhang, Q., Chen, F. (2016). A New and Accurate Estimator With Analytical Expression for Frequency Estimation. IEEE Communications Letters, 20(1), 105-108.
• [19] Borkowski, J., Kania, D., Mroczka, J. (2014). Influence of A/D Quantization in Interpolated-DFT-Based System of Power Control with Small Delay. Metrol. Meas. Syst., 2(3), 423-432.
• [20] Kania, D. (2015). Estimation of the sinusoidal oscillation parameters in the adaptive optics system based on the example of the photovoltaic system. SPIE Optics and Optoelectronics Conference, 1-8.
• [21] Kania, D., Borkowski, J. (2016). Influence of noise on the IpDFT-based estimation of the grid frequency in Renewable Energy Systems. IEEE International Conference on Environment and Electrical Enegineering, 1-5.
• [22] Kania, D., Borkowski, J. (2017). Estimation methods of multifrequency signals with noise and harmonics for PV systems with a DSP processor. IEEE International Conference on Telecommunications and Signal Processing, 1-4.
• [23] Belega, D., Petri, D. (2017). Effect of noise and harmonics on sine-wave frequency estimation by interpolated DFT algorithms based on few observed cycles. Signal Processing, 140, 207-218.
• [24] Wang, Y., Wei, W., Xiang, J. (2017). Multipoint interpolated DFT for sine waves in short records with DC components. Signal Processing, 131, 161-170.
• [25] Lee, M., Clarke, D. (2005). A Frequency Estimation Comparison between the Modified Covariance Method and the Fourier Transform. World Scientific and Engineering Academy and Society Conference, 1-4.
• [26] Almoosawy, A.N., Hussain, Z.M., Murad, F.A. (2014). Frequency Estimation of Single-Tone Sinusoids Under Additive and Phase Noise. International Journal of Advanced Computer Science and Applications, 5(9), 102-106.
• [27] Costa, F.F., Fernandes, D.A., de Almeida, L.A.L., Naidu, S.R. (2005). Prony’s method versus FFT for analyzing power converters signals. European Conference on Power Electronics and Applications, 1-9.
• [28] Nuttall, A.H. (1981). Some Windows with Very Good Sidelobe Behavior. IEEE Transactions on Acoustics, Speech, and Signal Processing, 29(1), 84-91.
• [29] Rife, D.C., Vincent, G.A. (1970). Use of the Discrete Fourier Transform in the Measurement of Frequencies and Levels of Tones. Bell System Technical Journal, 49, 197-228.
• [30] Belega, D., Dallet, D. (2009). Multifrequency signal analysis by Interpolated DFT method with maximum sidelobe decay windows. Measurement, 42(3), 420-426.
• [31] Belega, D. (2005). The maximum sidelobe decay windows. Revue Roumaine des Sciences Techniques. Série Electrotechnique et Energetique, 3, 349-356.
• [32] Chen, K.F., Cao, X., Li, Y.F. (2009). Sine wave fitting to short records initialized with the frequency retrieved from Hanning windowed FFT spectrum. Measurement, 42(1), 127-135.
• [33] Belega, D., Dallet, D. (2009). Multifrequency signal analysis by Interpolated DFT method with maximum sidelobe decay windows. Measurement, 42, 420-426.
• [34] Handel, P. (2000). Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm. IEEE Transactions on Instrumentation and Measurement, 49(6), 1189-1193.
• [35] Dilaveroğlu, E. (1998). Nonmatrix Cramér-Rao Bound Expressions for High Resolution Frequency Estimators. IEEE Transactions on Signal Processing, 46(2), 463-474.
• [36] Voltage Characteristics in Public Distribution Systems (2010), EN 50160.

Uwagi

EN

1. This work was supported by the National Science Centre, Poland under the decision 2015/19/B/ST7/00497.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).