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High Resolution Time-Frequency Distribution Based on Short-Time Sparse Representation

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Abstract

This paper focuses on the high resolution time-frequency distribution (TFD) of multicomponent signals with amplitude and frequency modulations, and a concise method named short-time sparse representation (STSR) is proposed. In STSR, both analysis and synthesis of the discrete signal can be achieved by exploiting the signal’s sparsity in frequency domain at each time instant. In order to fasten the STSR procedure, an efficient sparse recovery algorithm named SL0 is applied, and the signal model for each sliding window is modified to form the same dictionary, which guarantees that the whole recovery procedure adapts to the matrix form. The performance of STSR is compared with other TFD techniques and assessed in various configurations. It is shown that both preferable representation and acceptable computational cost can be obtained.

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References

  1. C.D. Austin, R.L. Moses, J.N. Ash, E. Ertin, On the relation between sparse reconstruction and parameter estimation with model order selection. IEEE J. Sel. Top. Signal Process. 4(3), 560–570 (2010)

    Article  Google Scholar 

  2. M. Babaie-Zadeh, C. Jutten, On the stable recovery of the sparsest overcomplete representations in presence of noise. IEEE Trans. Signal Process. 58(10), 5396–5400 (2010)

    Article  MathSciNet  Google Scholar 

  3. B. Boashash, P. O Shea, Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra. IEEE Trans. Signal Process. 42(1), 216–220 (1994)

    Article  MathSciNet  Google Scholar 

  4. P. Borgnat, P. Flandrin. Time-frequency localization from sparsity constraints, in IEEE International Conference on Acoustics, Speech, and Signal Processing. (ICASSP08), (2008)

  5. A.M. Bruckstein, D.L. Donoho, M. Elad, From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 51(1), 34–81 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Bultan, A four-parameter atomic decomposition of chirplets. IEEE Trans. Signal Process. 47, 731–745 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. S.S. Chen, D.L. Donoho, M.A. Saunders, Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. D.L. Donoho, Y. Tsaig, Fast solution of l\(_{1}\)-norm minimization problems when the solution may be sparse. IEEE Trans. Inf. Theory 54(11), 4789–4811 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Elad, M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736–3745 (2006)

    Article  MathSciNet  Google Scholar 

  10. P. Flandrin, P. Borgnat. Sparse time-frequency distributions of chirps from a compressed sensing perspective, in 8th IMA International Conference on Mathematics in Signal Processing (2008).

  11. P. Flandrin, P. Borgnat, Time-frequency energy distributions meet compressed sensing. IEEE Trans. Signal Process. 58(6), 2974–2982 (2010)

    Article  MathSciNet  Google Scholar 

  12. D. Gabor, Theory of communication. J. Inst. Electron. Eng. 93(11), 429–457 (1946)

    Google Scholar 

  13. R. Gribonval, Fast matching pursuit with a multiscale dictionary of Gaussian chirps. IEEE Trans. Signal Process. 49(5), 994–1001 (2001)

    Article  MathSciNet  Google Scholar 

  14. J. Illingworth, J. Kittler, A survey of the Hough transform. Comput. Vis., Graph., Image Process. 44(1), 87–116 (1988)

    Article  Google Scholar 

  15. D.L. Jones, T.W. Parks, A high resolution data-adaptive time-frequency representation. IEEE Trans. Acoust., Speech, Signal Process. 38(12), 2127–2135 (1990)

    Article  Google Scholar 

  16. D.L. Jones, R.G. Baraniuk, A simple scheme for adapting time-frequency representations. IEEE Trans. Signal Process. 42(12), 3530–3535 (1994)

    Article  Google Scholar 

  17. D.L. Jones, R.G. Baraniuk, An adaptive optimal-kernel time frequency representation. IEEE Trans. Signal Process. 43(10), 2361–2371 (1995)

    Article  Google Scholar 

  18. H.K. Kwok, D.L. Jones, Improved instantaneous frequency estimation using an adaptive short-time Fourier transform. IEEE Trans. Signal Process. 48(10), 2964–2972 (2000)

    Article  MathSciNet  Google Scholar 

  19. S. Mallat, Z. Zhang, Matching pursuit with time-frequency dictionary. IEEE Trans. Signal Process. 41(12), 3397–3415 (1993)

    Article  MATH  Google Scholar 

  20. S. Mallat, A Wavelet Tour of Signal Processing-The Sparse Way, 3rd edn. (Academic Press, Boston, 2009)

    MATH  Google Scholar 

  21. F. Marvasti, A. Amini, F. Haddadi, M. Soltanolkotabi, B. Khalaj, A. Aldroubi, S. Sanei, J. Chambers, A unified approach to sparse signal processing. EURASIP J. Adv. Signal Process. 44, 1–45 (2012)

    Google Scholar 

  22. H. Mohimani, M. Babaie-Zadeh, Ch. Jutten, A fast approach for overcomplete sparse decomposition based on smoothed \(l^{0}\) norm. IEEE Trans. Signal Process. 57(1), 289–301 (2009)

    Article  MathSciNet  Google Scholar 

  23. J.C. O’Neill, P. Flandrin, Virtues and vices of quartic time-frequency distributions. IEEE Trans. Signal Process. 48(9), 2641–2650 (2000)

    Article  Google Scholar 

  24. G.E. Pfander, H. Rauhut, Sparsity in time-frequency representations. J. Fourier Anal. Appl. 11(6), 715–726 (2010)

    MathSciNet  Google Scholar 

  25. S. Qian, D. Chen, Introduction to Joint Time-Frequency Analysis-Methods and Applications (Prentice Hall, Englewood Cliffs, 1996)

    Google Scholar 

  26. L.J. Stankovic, A multitime definition of the Wigner higher order distribution: L-Wigner distribution. IEEE Signal Process. Lett. 1(7), 106–109 (1994)

    Article  Google Scholar 

  27. J.A. Tropp, S.J. Wright, Computational methods for sparse solution of linear inverse problems. Proc. IEEE 98(6), 948–958 (2010)

    Article  Google Scholar 

  28. P.J. Wolfe, S.J. Godsill, W. Ng, Bayesian variable selection and regularization for time-frequency surface estimation. J. R. Statist. Soc., B 66, 575–589 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  29. S. Yin, S.X. Ding, A. Haghani, H.Y. Hao, P. Zhang, A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process. J. Process Control 22(9), 1567–1581 (2012)

    Article  Google Scholar 

  30. S. Yin, S.X. Ding, A.H.A. Sari, H.Y. Hao, Data-driven monitoring for stochastic systems and its application on batch process. Int. J. Syst. Sci. 44(7), 1366–1376 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  31. S. Yin, H. Luo, S.X. Ding, Real-time implementation of fault-tolerant control systems with performance optimization. IEEE Trans. Ind. Electron. 61(5), 2402–2411 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the Natural Science Foundation of China (NSFC, No. 61171133 and No. 61271442) and the innovation project for excellent postgraduates of National University of Defense Technology under Grant B110404.

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Authors and Affiliations

  1. School of Electronic Science and Engineering, National University of Defense Technology, Changsha , 410073, People’s Republic of China

    Zhen Liu, Peng You, Xizhang Wei, Dongping Liao & Xiang Li

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  1. Zhen Liu
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  2. Peng You
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  3. Xizhang Wei
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  4. Dongping Liao
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  5. Xiang Li
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Correspondence to Peng You.

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Liu, Z., You, P., Wei, X. et al. High Resolution Time-Frequency Distribution Based on Short-Time Sparse Representation. Circuits Syst Signal Process 33, 3949–3965 (2014). https://doi.org/10.1007/s00034-014-9832-3

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  • DOI: https://doi.org/10.1007/s00034-014-9832-3

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