ConceFT: Concentration of frequency and time via a multitapered synchrosqueezed transform

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 374, Issue 2065, 2016, Pages

  Daubechies, Ingrid ^a   Wang, Yi ^b   Wu, Hau Tieng ^c  

^a DUKE UNIVERSITY   (United States)

^b SYRACUSE UNIVERSITY   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

ConceFT; Instantaneous frequency; Multitaper; Reassignment method; Synchrosqueezing transform

Indexed keywords

CONCEFT; INSTANTANEOUS FREQUENCY; MULTITAPER; REASSIGNMENT METHOD; SYNCHROSQUEEZING;

ENGINEERING;

EID: 84960371692     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2015.0193     Document Type: Article

References (73)

1. Golombek D, Rosenstein R. 2010 Physiology of circadian entrainment. Physiol. Rev. 90, 1063-1102. (doi:10.1152/physrev.00009.2009)
2. Takeda N, Maemura K. 2011 Circadian clock and cardiovascular disease. J. Cardiol. 57, 249-256. (doi:10.1016/j.jjcc.2011.02.006)
3. Wang X. 2010 Neurophysiological and computational principles of cortical rhythms in cognition. Physiol. Rev. 90, 1195-1268. (doi:10.1152/physrev.00035.2008)
4. Lewis GF, Furman SA, McCool M.F., Porges SW. 2012 Statistical strategies to quantify respiratory sinus arrhythmia: are commonly used metrics equivalent? Biol. Psychol. 89, 349-364. (doi:10.1016/j.biopsycho.2011.11.009)
5. Lin YT, Wu HT, Tsao J, Yien H.W., Hseu SS. 2014 Time-varying spectral analysis revealing differential effects of sevoflurane anaesthesia: non-rhythmic-to-rhythmic ratio. Acta Anaesthesiol. Scand. 58, 157-167. (doi:10.1111/aas.12251)
6. Wu HT, Hseu SS, Bien M.Y., Kou YR, Daubechies I. 2013 Evaluating physiological dynamics via synchrosqueezing: prediction of ventilator weaning. IEEE Trans. Biomed. Eng. 61, 736-744. (doi:10.1109/TBME.2013.2288497)
7. Baudin F, Wu HT, Bordessoule A, Beck J., Jouvet P, Frasch M, Emeriaud G. 2014 Impact of ventilatory modes on the breathing variability in mechanically ventilated infants. Front. Pediatr. Sect. Neonatol. 2, 132. (doi:10.3389/fped.2014.00132)
8. Flandrin P. 1999 Time-frequency/time-scale analysis. San Diego, CA: Academic Press.
9. Thakur G, Wu HT 2011 Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples. SIAM J. Math. Anal. 43, 2078-2095. (doi:10.1137/100798818)
10. Huang NE, Shen Z, Long S.R., Wu M., Shih H, Zheng Q, Yen N.C., Tung CC, Liu HH. 1998 The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903-995. (doi:10.1098/rspa.1998.0193)
11. Wu Z, Huang NE 2009 Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv. Adapt. Data Anal. 1, 1-41. (doi:10.1142/S1793536909000047)
12. Tavallali P, Hou T, Shi Z. 2014 Extraction of intrawave signals using the sparse time-frequency representation method. Multiscale Model. Simul. 12, 1458-1493. (doi:10.1137/140957767)
13. Lin L, Wang Y, Zhou H. 2009 Iterative filtering as an alternative for empirical mode decomposition. Adv. Adapt. Data Anal. 1, 543-560. (doi:10.1142/S179353690900028X)
14. Huang C, Wang Y, Yang L. 2009 Convergence of a convolution-filtering-based algorithm for empirical mode decomposition. Adv. Adapt. Data Anal. 1, 561-571. (doi:10.1142/S17935 36909000205)
15. Chui CK, Mhaskar H. 2016 Signal decomposition and analysis via extraction of frequencies. Appl. Comput. Harmon. Anal. 40, 97-136. (doi:10.1016/j.acha.2015.01.003)
16. Galiano G, Velasco J. 2014 On a non-local spectrogram for denoising one-dimensional signals. Appl. Math. Comput. 244, 1-13. (doi:10.1016/j.amc.2014.06.092)
17. De Livera A.M., Hyndman RJ, Snyder RD 2011 Forecasting time series with complex seasonal patterns using exponential smoothing. J. Am. Stat. Assoc. 106, 1513-1527. (doi:10.1198/jasa.2011.tm09771)
18. Daubechies I, Maes S. 1996 A nonlinear squeezing of the continuous wavelet transform based on auditory nerve models. In Wavelets in medicine and biology(eds A Aldroubi, M Unser), pp. 527-546. Boca Raton, FL: CRC Press.
19. Daubechies I, Lu J, Wu HT 2011 Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl. Comput. Harmon. Anal. 30, 243-261. (doi:10.1016/j. acha.2010.08.002)
20. Wu HT, Flandrin P, Daubechies I. 2011 One or two frequencies? The synchrosqueezing answers. Adv. Adapt. Data Anal. 3, 29-39. (doi:10.1142/S179353691100074X)
21. Wu HT. 2011 Adaptive analysis of complex data sets. PhD thesis, Princeton University. See https://sites.google.com/site/hautiengwu/home.
22. Kodera K, Gendrin R, Villedary C. 1978 Analysis of time-varying signals with small BT values. IEEE Trans. Acoust. Speech, Signal Process. 26, 64-76. (doi:10.1109/TASSp.1978.1163047)
23. Auger F, Flandrin P. 1995 Improving the readability of time-frequency and time-scale representations by the reassignment method. IEEE Trans. Signal Process. 43, 1068-1089. (doi:10.1109/78.382394)
24. Chassande-Mottin E., Auger F, Flandrin P. 2003 Time-frequency/time-scale reassignment. In Wavelets and signal processing(ed. L Debnath), pp. 233-267. Applied and Numerical Harmonic Analysis Series. Cham, Switzerland: Springer International. (doi:10.1007/978-1-4612-0025-3-8)
25. Auger F, Chassande-Mottin E, Flandrin P. 2012 Making reassignment adjustable: the Levenberg-Marquardt approach. In 2012 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Kyoto, Japan, 25-30 March, pp. 3889-3892. Piscataway, NJ: IEEE. (doi:10.1109/ICASSp.2012.6288767)
26. Thakur G. 2014 The synchrosqueezing transform for instantaneous spectral analysis. In Excursions in harmonic analysis, Vol. 4 (eds R Balan, M Begué, JJ Benedetto, W Czaja, KA Okoudjou), pp. 397-406. Applied and Numerical Harmonic Analysis Series. Cham, Switzerland: Springer International. (doi:10.1007/978-3-319-20188-7-15)
27. Chui CK, Lin YT, Wu HT In press. Real-time dynamics acquisition from irregular samples - with application to anesthesia evaluation. Anal. Appl. (doi:10.1142/S0219530515500165)
28. Chen YC, Cheng MY, Wu HT 2014 Nonparametric and adaptive modeling of dynamic seasonality and trend with heteroscedastic and dependent errors. J. R. Stat. Soc. B 76, 651-682. (doi:10.1111/rssb.12039)
29. Maes S. 1995 Synchrosqueezed representation yields a new reading of the wavelet transform. In Wavelet Applications II, Orlando, FL, 17-21 April, Proc. SPIE, Vol. 2491, p. 532. Bellingham, WA: SPIE. (doi:10.1117/12.205417)
30. Wu HT. 2013 Instantaneous frequency and wave shape functions (I). Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)
31. Meignen S, Oberlin T, McLaughlin S. 2012 A new algorithm for multicomponent signals analysis based on synchrosqueezing: with an application to signal sampling and denoising. IEEE Trans. Signal Process. 60, 5787-5798. (doi:10.1109/TSp.2012.2212891)
32. Lin YT, Flandrin P, Wu HT In press. When interpolation-induced reflection artifact meets time-frequency analysis. IEEE Trans. Biomed. Eng. (doi:10.1109/TBME.2015.2510580)
33. Thakur G, Brevdo E, Fuckar N.S., Wu HT. 2013 The synchrosqueezing algorithm for timevarying spectral analysis: robustness properties and new paleoclimate applications. Signal Process. 93, 1079-1094. (doi:10.1016/j.sigpro.2012.11.029)
34. Li C, Liang M. 2012 A generalized synchrosqueezing transform for enhancing signal time-frequency representation. Signal Process. 92, 2264-2274. (doi:10.1016/j.sigpro.2012.02.019)
35. Yang H. 2015 Synchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1D general mode decompositions. Appl. Comput. Harmon. Anal. 39, 33-66. (doi:10.1016/j.acha.2014.08.004)
36. Oberlin T, Meignen S, Perrier V. 2015 Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations. IEEE Trans. Signal Process. 63, 1335-1344. (doi:10.1109/TSp.2015.2391077)
37. Xi S, Cao H, Chen X., Zhang X, Jin X. 2015 A frequency-shift synchrosqueezing method for instantaneous speed estimation of rotating machinery. ASME. J. Manuf. Sci. Eng. 137, 031012. (doi:10.1115/1.4029824)
38. Huang Z, Zhang J, Zhao T., Sun Y. 2016 Synchrosqueezing S-transform and its application in seismic spectral decomposition. Geosci. Remote Sensing, IEEE Trans. 54, 817-825. (doi:10.1109/TGRS.2015.2466660)
39. Yang H, Ying L. 2013 Synchrosqueezed wave packet transform for 2D mode decomposition. SIAM J. Imaging Sci. 6, 1979-2009. (doi:10.1137/120891113)
40. Yang H, Ying L. 2014 Synchrosqueezed curvelet transform for two-dimensional mode decomposition. SIAM J. Math. Anal. 46, 2052-2083. (doi:10.1137/130939912)
41. Iatsenko D, Bernjak A, Stankovski T., Shiogai Y, Owen-Lynch PJ, Clarkson PBM, McClintock PVE, Stefanovska A. 2013 Evolution of cardiorespiratory interactions with age. Phil. Trans. R. Soc. A 371, 20110622. (doi:10.1098/rsta.2011.0622)
42. Wu HT, Chan YH, Lin Y.T., Yeh YH. 2014 Using synchrosqueezing transform to discover breathing dynamics from ECG signals. Appl. Comput. Harmon. Anal. 36, 354-359. (doi:10.1016/j.acha.2013.07.003)
43. Wu HT, Talmon R, Lo YL 2015 Assess sleep stage by modern signal processing techniques. IEEE Trans. Biomed. Eng. 62, 1159-1168. (doi:10.1109/TBME.2014.2375292)
44. Lin Y-T. 2015 The modeling and quantification of rhythmic to non-rhythmic phenomenon in electrocardiography during anesthesia. PhD thesis, National Taiwan University. (http://arxiv.org/abs/1502.02764)
45. Li C, Liang M. 2012 Time-frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform. Mech. Syst. Signal Process. 26, 205-217. (doi:10.1016/j.ymssp.2011.07.001)
46. Feng Z, Chen X, Liang M. 2015 Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions. Mech. Syst. Signal Process. 52-53, 360-375. (doi:10.1016/j.ymssp.2014.07.009)
47. Guharay S, Thakur G, Goodman F., Rosen S, Houser D. 2013 Analysis of non-stationary dynamics in the financial system. Econ. Lett. 121, 454-457. (doi:10.1016/j.econlet.2013.09.026)
48. Vatter T, Wu HT, Chavez-Demoulin V, Yu B. 2015 Non-parametric estimation of intraday spot volatility: disentangling instantaneous trend and seasonality. Econometrics3 (4), 864-887. (doi:10.3390/econometrics3040864)
49. Wang P, Gao J, Wang Z. 2014 Time-frequency analysis of seismic data using synchrosqueezing transform. Geosci. Remote Sensing Lett. IEEE 11, 2042-2044. (doi:10.1109/LGRS.2014. 2317578)
50. Herrera RH, Han J, van der Baan M. 2014 Applications of the synchrosqueezing transform in seismic time-frequency analysis. Geophysics 79, V55-V64. (doi:10.1190/geo2013-0204.1)
51. Tary JB, Herrera RH, Han J, van der Baan M. 2014 Spectral estimation - What is new? What is next? Rev. Geophys. 52, 723-749. (doi:10.1002/2014RG000461)
52. Li PC, Sheu YL, Laughlin C, Chu SI 2013 Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms. Phy. Rev. A 90, 041401(R). (doi:10.1103/PhysRevA.90.041401)
53. Sheu YL, Hsu LY, Wu H.T., Li PC, Chu SI. 2014 A new time-frequency method to reveal quantum dynamics of atomic hydrogen in intense laser pulses: synchrosqueezing transform. AIP Adv. 4, 117138. (doi:10.1063/1.4903164)
54. Li PC, Sheu YL, Laughlin C, Chu SI 2015 Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field. Nat. Commun. 6, 7178. (doi:10.1038/ncomms8178)
55. Yang H, Lu J, Ying L. 2015 Crystal image analysis using 2D synchrosqueezed transforms. Multiscale Model. Simul.13 (4), 1542-1572. (doi:10.1137/140955872)
56. Yang H, Lu J, Brown W.P., Daubechies I., Ying L. 2015 Quantitative canvas weave analysis using 2-D synchrosqueezed transforms: application of time-frequency analysis to art investigation. Signal Process. Mag., IEEE32 (4), 55-63. (doi:10.1109/MSp.2015.2406882)
57. Thomson DJ. 1982 Spectrum estimation and harmonic analysis. Proc. IEEE 70, 1055-1096. (doi:10.1109/PROC.1982.12433)
58. Percival DB, Walden AT 1993 Spectral analysis for physical applications: multitaper and conventional univariate techniques. Cambridge, UK: Cambridge University Press.
59. Babadi B, Brown EN 2014 A review of multitaper spectral analysis. IEEE Trans. Biomed. Eng. 61, 1555-1564. (doi:10.1109/TBME.2014.2311996)
60. Fraser G, Boashash B. 1994 Multiple window spectrogram and time-frequency distributions. In 1994 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Adelaide, Australia, 19-22 April, Vol. 4, IV/293-IV/296. Piscataway, NJ: IEEE. (doi:10.1109/ICASSp.1994.389818)
61. Farry KA, Baraniuk RG, Walker ID 1995 Nonparametric, low bias, and low variance time-frequency analysis of myoelectric signals. In 1995 IEEE 17th Annu. Conf. Engineering in Medicine and Biology Society, Montreal, Canada, 20-23 September, Vol. 2, pp. 993-994. Piscataway, NJ: IEEE. (doi:10.1109/IEMBS.1995.579397)
62. Bayram M, Baraniuk RG 1996 Multiple window time-frequency and time-scale analysis. In Advanced Signal Processing Algorithms, Architectures, and Implementations VI, Denver, CO, 4 August, Proc. SPIE, Vol. 2846, p. 174. Bellingham, WA: SPIE. (doi:10.1117/12.255431)
63. Xu Y, Haykin S, Racine RJ 1999 Multiple window time-frequency distribution and coherence of EEG using Slepian sequences and Hermite functions. IEEE Trans. Biomed. Eng. 46, 861-866. (doi:10.1109/10.771197)
64. Xiao J, Flandrin P. 2007 Multitaper time-frequency reassignment for nonstationary spectrum estimation and chirp enhancement. IEEE Trans. Signal Process. 55, 2851-2860. (doi:10.1109/TSp.2007.893961)
65. Lin YT, Hseu SS, Yien H.W., Tsao J. 2011 Analyzing autonomic activity in electrocardiography about general anesthesia by spectrogram with multitaper time-frequency reassignment. In 2011 4th Int. Conf. on Biomedical Engineering and Informatics (BMEI), Shanghai, China, 15-17 October, Vol. 2, pp. 630-634. Piscataway, NJ: IEEE. (doi:10.1109/BMEI.2011.6098432)
66. Orini M, Bailón R, Mainardi L.T., Laguna P., Flandrin P. 2012 Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence. IEEE Trans. Biomed. Eng. 59, 663-673. (doi:10.1109/TBME.2011.2171959)
67. Daubechies I. 1992 Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, No. 61. Philadelphia, PA: SIAM. (doi:10.1137/1.9781611970104)
68. Kowalski M, Meynard A, Wu HT 2015 Convex optimization approach to signals with fast varying instantaneous frequency. (http://arxiv.org/abs/1503.07591)
69. Gallager R. 2008 Circularly-symmetric Gaussian random vectors. See http://www.rle.mit.edu/rgallager/documents/CircSymGauss.pdf.
70. Daubechies I. 1988 Time-frequency localization operators: a geometric phase space approach. IEEE Trans. Inform. Theory 34, 605-612. (doi:10.1109/18.9761)
71. Daubechies I, Paul T. 1988 Time-frequency localization operators: a geometric phase space approach: II. The use of dilations. Inverse Probl. 4, 661-680. (doi:10.1088/0266-5611/4/3/009)
72. Olhede SC, Walden AT 2002 Generalized morse wavelets. IEEE Trans. Signal Process. 50, 2661-2671. (doi:10.1109/TSp.2002.804066)
73. Lin YT, Wu HT Submitted. ConceFT for time-varying heart rate variability analysis as a measure of noxious stimulation during general anesthesia.