Extraction of intrawave signals using the sparse time-frequency representation method

Multiscale Modeling and Simulation

Volumn 12, Issue 4, 2014, Pages 1458-1493

  Tavallali, Peyman ^a   Hou, Thomas Y ^a   Shi, Zuoqiang ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Instantaneous frequency; Intrawave frequency modulation; Sparse time frequency representation

Indexed keywords

DYNAMICAL SYSTEMS; EXTRACTION; FREQUENCY MODULATION; TIME VARYING NETWORKS;

DATA ANALYSIS METHODS; EMPIRICAL MODE DECOMPOSITION; FREQUENCY MODULATED SIGNAL; INSTANTANEOUS FREQUENCY; MECHANICAL SYSTEMS; NOISE PERTURBATION; SYSTEM IDENTIFICATION PROBLEMS; TIME-FREQUENCY REPRESENTATIONS;

SIGNAL PROCESSING;

EID: 84920000800     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/140957767     Document Type: Article

References (21)

1. C. Blatter, Wavelets: A Primer, Universities Press, New Delhi, 2003.
2. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, 2004.
3. E. Brevdo, Synchrosqueezing Wavelet Transform, https://web.math.princeton.edu/-ebrevdo/ synsq/, 2012.
4. E.J. Candes and T. Tao, Near-optimal signal recovery from random projections: Universal encoding strategies?, IEEE Trans. Inform. Theory, 52 (2006), pp. 5406-5425.
5. S.S. Chen, D.L. Donoho, and M.A. Saunders, Atomic decomposition by basis pursuit, SIAM J. Sci. Comput., 20 (1998), pp. 33-61.
6. I. Daubechies, J. Lu, and H. Wu, Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool, Appl. Comput. Harmon. Anal., 30 (2011), pp. 243-261.
7. T.Y. Hou and Z. Shi, Adaptive data analysis via sparse time-frequency representation, Adv. Adapt. Data Anal., 3 (2011), pp. 1-28.
8. T.Y. Hou and Z. Shi, Data-driven time-frequency analysis, Appl. Comput. Harmon. Anal., 35 (2013), pp. 284-308.
9. T.Y. Hou, Z. Shi, and P. Tavallali, Convergence of a data-driven time-frequency analysis method, Appl. Comput. Harmon. Anal., 37 (2014), pp. 235-270.
10. B. Huang and A. Kunoth, An optimization based empirical mode decomposition scheme, J. Comput. Appl. Math., 240 (2013), pp. 174-183.
11. C. Huang, L. Yang, and Y. Wang, Convergence of a convolution-filtering-based algorithm for empirical mode decomposition, Adv. Adapt. Data Anal., 1 (2009), pp. 561-571.
12. N.E. Huang and S.S. Shen, Hilbert-Huang Transform and Its Applications, Interdiscip. Math. Sci. 5, World Scientific, Hackensack, NJ, 2005.
13. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung, and H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), pp. 903-995.
14. N.E. Huang, Z. Wu, S.R. Long, K.C. Arnold, X. Chen, and K. Blank, On instantaneous frequency, Adv. Adapt. Data Anal., 1 (2009), pp. 177-229.
15. S.G. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA, 1999.
16. S.G. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Trans. Signal Process., 41 (1993), pp. 3397-3415.
17. G. Thakur, E. Brevdo, N.S. Fučkar, and H. Wu, The synchrosqueezing algorithm for timevarying spectral analysis: Robustness properties and new paleoclimate applications, Signal Process., 93 (2013), pp. 1079-1094.
18. B. van der Pol, Frequency modulation, Proc. Inst. Radio Eng., 18 (1930), pp. 1194-1205.
19. H. Wu, Instantaneous frequency and wave shape functions (I), Appl. Comput. Harmon. Anal., 35 (2013), pp. 181-199.
20. Z. Wu and N.E. Huang, A study of the characteristics of white noise using the empirical mode decomposition method, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 460 (2004), pp. 1597-1611.
21. Z. Wu and N.E. Huang, Ensemble empirical mode decomposition: A noise-assisted data analysis method, Adv. Adapt. Data Anal., 1 (2009), pp. 1-41.