Abstract
Wide ranges of signal-to-noise ratios would cause frequency estimation algorithm to perform unstable anti-noise characteristics, low estimation accuracy, and poor realizability in engineering experiments. To resolve such impacts, this paper proposes an improved algorithm for a two-step frequency estimation of a complex sinusoidal signal submerged in Gaussian white noise - the fixed Quinn algorithm integrates with the Aboutanios and Mulgrew algorithm to compose a hybrid high-precision and robust frequency estimation algorithm. Through simulations, the results proved that the estimator is asymptotically unbiased with its root mean square error (RMSE) and is further closed to the Cramer–Rao lower bound (CRLB). In addition, the improved algorithm possesses anti-noise characteristics, stronger algorithm robustness, and can be easily applied in various signal processing contexts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Yanping, L.: Dissertation, Harbin University of Science and Technology (2012)
Rife, D., Boorstyn, R.: Single tone parameter estimation from discrete-time observations. IEEE Trans. Inf. Theory 20, 591–598 (1974). https://doi.org/10.1109/tit.1974.1055282
Fan, L., Qi, G.: Frequency estimator of sinusoid based on interpolation of three DFT spectral lines. Sig. Process. 144, 52–60 (2018). https://doi.org/10.1016/j.sigpro.2017.09.028
Xia, Y., He, Y., Wang, K., Pei, W., Blazic, Z., Mandic, D.P.: A complex least squares enhanced smart DFT technique for power system frequency estimation. IEEE Trans. Power Deliv. 32, 1270–1278 (2015). https://doi.org/10.1109/tpwrd.2015.2418778
Seo, W.-S., Kang, S.-H.: A novel frequency estimation algorithm based on DFT and second derivative. J. Int. Counc. Electr. Eng. 7, 69–75 (2017). https://doi.org/10.1080/22348972.2017.1325079
Kang, S.H., Yoon, Y.D., Seo, W.S.: 13th International Conference on Development in Power System Protection 2016 (DPSP), pp. 1–5. Institution of Engineering and Technology, Edinburgh (2016)
Kay, S.: A fast and accurate single frequency estimator. IEEE Trans. Acoust. Speech Sig. Process. 37, 1987–1990 (1989). https://doi.org/10.1109/29.45547
Quinn, B.G.: Estimating frequency by interpolation using Fourier coefficients. IEEE Trans. Sig. Process. 42, 1264–1268 (1994). https://doi.org/10.1109/78.295186
Quinn, B.G.: Estimation of frequency, amplitude, and phase from the DFT of a time series. IEEE Trans. Sig, Process. 45, 814–817 (1997). https://doi.org/10.1109/78.558515
Liao, J.R., Chen, C.M.: Phase correction of discrete Fourier transform coefficients to reduce frequency estimation bias of single tone complex sinusoid. Sig. Process. 94, 108–117 (2014). https://doi.org/10.1016/j.sigpro.2013.05.021
Aboutanios, E., Mulgrew, B.: Iterative frequency estimation by interpolation on Fourier coefficients. IEEE Trans. Sig. Process. 53, 1237–1242 (2005). https://doi.org/10.1109/tsp.2005.843719
Candan, Ç.: A method for fine resolution frequency estimation from three DFT samples. IEEE Sig. Process. Lett. 18, 351–354 (2011). https://doi.org/10.1109/lsp.2011.2136378
Fang, L., Duan, D., Yang, L.: MILCOM 2012: Proceedings of the 2012 IEEE Military Communications Conference, pp. 1–6. IEEE, Piscataway (2012)
Lei, F., Guoqing, Q.: High accuracy frequency estimation algorithm of sinusoidal signals based on fast Fourier transform. J. Comput. Appl. 35, 3280–3283 (2015). https://doi.org/10.11772/j.issn.1001-9081.2015.11.3280
Jing, Y., Shengwen, Z., et al.: Improved Quinn algorithm for frequency estimation of sinusoid wave. J. Telem. Track. Command 38, 7–12 (2017). https://doi.org/10.13435/j.cnki.ttc.002830
Zhou, S., Shancong, Z.: Improved frequency estimation algorithm by least squares phase unwrapping. Circ. Syst. Sig. Process. 37(12), 5680–5687 (2018). https://doi.org/10.1007/s00034-018-0838-0
Qian, C., Huang, L., So, H.C., Sidiropoulos, N.D., Xie, J.: Unitary PUMA algorithm for estimating the frequency of a complex sinusoid. IEEE Trans. Sig. Process. 63, 5358–5368 (2015). https://doi.org/10.1109/tsp.2015.2454471
So, H.C., Chan, F.K.W., Lau, W.H., Chan, C.F.: An efficient approach for two-dimensional parameter estimation of a single-tone. IEEE Trans. Sig. Process. 58, 1999–2009 (2010). https://doi.org/10.1109/tsp.2009.2038962
Xu, Z., Lu, T., Huang, B.: Fast frequency estimation algorithm by least squares phase unwrapping. IEEE Sig. Process. Lett. 23, 776–779 (2016). https://doi.org/10.1109/lsp.2016.2555933
Lei, Z.: Dissertation, Harbin Engineering University (2016)
Yang, C., Wei, G.: A noniterative frequency estimator with rational combination of three spectrum lines. IEEE Trans. Sig. Process. 59, 5065–5070 (2011). https://doi.org/10.1109/tsp.2011.2160257
Serbes, A.: Fast and efficient sinusoidal frequency estimation by using the DFT coefficients. IEEE Trans. Comm. 67, 2333–2342 (2019). https://doi.org/10.1109/TCOMM.2018.2886355
Candan, C.: Analysis and further improvement of fine resolution frequency estimation method from three DFT samples. IEEE Sig. Process. Lett. 20, 913–916 (2013). https://doi.org/10.1109/lsp.2013.2273616
Oppenheim, A.V., Schafer, R.W.: Digital Signal Processing. Prentice Hall, Englewood Cliffs (1975)
Liu, Y., Nie, Z., Zhao, Z., Liu, Q.H.: Generalization of iterative Fourier interpolation algorithms for single frequency estimation. Digit. Sig. Process. 21, 141–149 (2011). https://doi.org/10.1016/j.dsp.2010.06.012
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Chen, S., Pan, M., Wang, X. (2022). An Improved Algorithm for High-Precision Frequency Estimation. In: Li, X. (eds) Advances in Intelligent Automation and Soft Computing. IASC 2021. Lecture Notes on Data Engineering and Communications Technologies, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-030-81007-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-81007-8_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-81006-1
Online ISBN: 978-3-030-81007-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)