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Novel Method for Non-stationary Signals Via High-Concentration Time–Frequency Analysis Using SSTFrFT

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Abstract

The short-time fractional Fourier transform (STFrFT) is beneficial for addressing non-stationary signals in many application settings. However, the STFrFT algorithm fails to obtain a high time–frequency (TF) concentration because of the uncertainty principle. To resolve these problems, we introduce a new algorithm that is referred to as the SSTFrFT, which is a combination of the synchroextracting transform and STFrFT. The main principle of this algorithm is to establish a synchroextracting operator based on the STFrFT and then to extract the TF coefficient of the ridgeline position in the TF distribution to improve the concentration. Using numerical simulations with two examples (linear frequency modulation signal and nonlinear frequency modulation signal), we illustrate how the algorithm can be useful in improving concentration. The instantaneous frequency estimation and energy distribution description are more accurate than traditional methods, such as the short-time Fourier transform, Wigner Ville distribution, synchrosqueezed transform, and STFrFT. Furthermore, we apply the algorithm to identify the frequency curve generated by the target’s motion from Ice Multiparameter Imaging X-Band radar echo data from the sea clutter background. The test results of the SSTFrFT method that we developed can accurately distinguish moving targets and sea clutter, which suggest the possible utility of this approach for detection and motion characteristics of marine moving targets.

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References

  1. F. Auger, P. Flandrin, Y.T. Lin et al., Time-frequency reassignment and synchrosqueezing: an overview. IEEE Signal Process. Mag. 30(6), 32–41 (2013)

    Article  Google Scholar 

  2. M.A. Awal, S. Ouelha, S. Dong et al., A robust high-resolution TF representation based on the local optimization of the short-time fractional Fourier transform. Digit. Signal Process. 70, 125–144 (2017)

    Article  Google Scholar 

  3. C. Capus, K. Brown, Short-time fractional Fourier methods for the TF representation of chirp signals. J. Acoust. Soc. Am. 113(6), 3253–3263 (2003)

    Article  Google Scholar 

  4. A.T. Catherall, D.P. Williams, High-resolution spectrograms using a component optimized short-term fractional Fourier transform. Signal Process. 90(5), 1591–1596 (2010)

    Article  Google Scholar 

  5. Z.Z. Che, TF Method for Target Detection in Sea Clutter (Xidian University, Xi’an, 2014)

    Google Scholar 

  6. X.L. Chen, J. Guan, X.H. Yu et al., Extraction and detection of radar target micro-motion based on short-time sparse TF distribution. J. Electron. Inf. Technol. 39(5), 1017–1023 (2017)

    Google Scholar 

  7. I. Daubechies, J.F. Lu, H.T. Wu, Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl. Computat. Harmon. Anal. 30(2), 243–261 (2011)

    Article  MathSciNet  Google Scholar 

  8. I. Daubechies, Y. Wang, H.T. Wu, F.T. Conce, Concentration of frequency and time via a multi tapered synchrosqueezed transform. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. (2016). https://doi.org/10.1098/rsta.2015.0193

    Article  Google Scholar 

  9. G.C. Hao, Y.X. Bai, H. Liu et al., The Earth’s natural pulse electromagnetic field for earthquake time–frequency characteristics: insights from the EEMD–WVD method. Island Arc (2018). https://doi.org/10.1111/iar.12256

    Article  Google Scholar 

  10. G.C. Hao, Y.X. Bai, M. Wu et al., Time-frequency analysis of the Earth’s natural pulse electromagnetic field before earthquake based on BSWT-DDTFA method. Chin. J. Geophys. 61(10), 4063–4074 (2018)

    Google Scholar 

  11. G.C. Hao, F. Li, Y.X. Bai et al., Time-frequency analysis algorithm of non-stationary signal based on NDSST. Geomat. Inf. Sci. Wuhan Univ. 44(6), 941–948 (2019)

    Google Scholar 

  12. G.C. Hao, F. Tan, Z. Cheng et al., Time-frequency analysis of BGabor-NSPWVD algorithm with strong robustness and high sharpening concentration. Acta Autom. Sin. 45(3), 566–576 (2019)

    Google Scholar 

  13. G.C. Hao, F. Tan, X.Y. Hu et al., A matching pursuit-based method for cross-term suppression in WVD and its application to the ENPEMF. IEEE Geosci. Remote Sens. Lett. 16(8), 1304–1308 (2019)

    Article  Google Scholar 

  14. S. Haykin, T.K. Bhattacharya, Modular learning strategy for signal detection in a nonstationary environment. IEEE Trans. Signal Process. 45(6), 1619–1637 (1997)

    Article  Google Scholar 

  15. N.E. Huang, Z. Shen, S.R. Long et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A Math. Phys. Eng. Sci. (1998). https://doi.org/10.1098/rspa.1998.0193

    Article  MATH  Google Scholar 

  16. Y. Long, B.B. Xu, D.Y. Chen et al., Dynamic characteristics for a hydro-turbine governing system with viscoelastic materials described by fractional calculus. Appl. Math. Model. 58, 128–139 (2018)

    Article  MathSciNet  Google Scholar 

  17. Y. Long, R. Zhou, Z.D. Zhang et al., On the fractional-order 3D 3D Δ × n memristor-LC circuit network model. Electric Power Compon. Syst. 1, 1–14 (2019)

    Google Scholar 

  18. J.B. Luan, B. Deng, TF resolving capability of frequency modulated signals by short-time fractional Fourier transform. Telecommun. Eng. 55(7), 773–778 (2015)

    Google Scholar 

  19. C. Pang, Y. Han, H. Hou et al., Micro-doppler signal TF algorithm based on STFRFT. Sensors 16(10), 1559–1576 (2016)

    Article  Google Scholar 

  20. D.F. Ping, X.Z. Liu, P.H. Zhao, Basic properties of short-time fractional Fourier transform. J. Data Acquis. Process. 24(S1), 39–42 (2009)

    Google Scholar 

  21. I. Shafi, J. Ahmad, S.I. Shah et al., Quantitative evaluation of concentrated TF distributions, in 17th European Signal Processing Conference (EUSIPCO 2009), Glasgow, Scotland, pp. 1176–1180 (2009)

  22. R. Tao, Y. Li, Y. Wang, Short-time fractional Fourier transform and its applications. IEEE Trans. Signal Process. 58(5), 2568–2580 (2010)

    Article  MathSciNet  Google Scholar 

  23. J. Wang, H. Du, M. Guo et al., Feature extraction using HHT-based locally optimized short-time fractional Fourier transform for speaker recognition, in IEEE International Conference on Imaging, Vision & Pattern Recognition, Dhaka, Bangladesh, pp. 1–5 (2017)

  24. P. Wang, Processing and Analysis of Polarized IPIX Radar Echo Data (Harbin Institute of Technology, Harbin, 2016)

    Google Scholar 

  25. C. Wei, Research on TF Analysis Method Based on Measured Sea Clutter Data (Xidian University, Xi’an, 2013)

    Google Scholar 

  26. H.T. Wu, Y.H. Chan, Y.T. Lin et al., Using synchrosqueezing transform to discover breathing dynamics from ECG signals. Appl. Comput. Harmon. Anal. 36(2), 354–359 (2014)

    Article  Google Scholar 

  27. H.Z. Yan, J. Chen, F. Wang et al., Nonlinear FM-like signal detection based on short-time fractional Fourier transform. J. Guangxi Normal Univ. (Nat. Sci. Ed.) 33(4), 30–37 (2015)

    MATH  Google Scholar 

  28. Y.P. Yi, D.Y. Chen, Q. Xie, Controllability of nonlinear fractional order integrodifferential system with input delay. Math. Methods Appl. Sci. (2019). https://doi.org/10.1002/mma.5613

    Article  MathSciNet  MATH  Google Scholar 

  29. G. Yu, M.J. Yu, C.Y. Xu, Synchroextracting transform. IEEE Trans. Ind. Electron. 64(10), 8042–8054 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Key Projects of the National Natural Science Foundation of China (61733016), Open Research Foundation of the State Key Laboratory of Geodesy and Earth’s Dynamics (SKLGED2018-5-4-E), Open Research Project of the Hubei Key Laboratory of Intelligent Geo-Information Processing (KLIGIP-2017A02), and the Foundation of the Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems (ACIA2017002).

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Authors and Affiliations

  1. School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, 430074, China

    Guocheng Hao, Juan Guo, Yuxiao Bai & Songyuan Tan

  2. Department of Mathematics, Duke University, Durham, NC, 27708, USA

    Guocheng Hao

  3. School of Automation, China University of Geosciences, Wuhan, 430074, China

    Min Wu

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  1. Guocheng Hao
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Correspondence to Guocheng Hao.

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Hao, G., Guo, J., Bai, Y. et al. Novel Method for Non-stationary Signals Via High-Concentration Time–Frequency Analysis Using SSTFrFT. Circuits Syst Signal Process 39, 5710–5728 (2020). https://doi.org/10.1007/s00034-020-01430-w

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