On instantaneous frequency

Advances in Adaptive Data Analysis

Volumn 1, Issue 2, 2009, Pages 177-229

  Huang, Norden E ^a   Wu, Zhaohua ^b   Long, Steven R ^c   Arnold, Kenneth C ^d   Chen, Xianyao ^e   Blank, Karin ^c  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

^b FLORIDA STATE UNIVERSITY   (United States)

^c NASA GODDARD SPACE FLIGHT CENTER   (United States)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^e FIRST INSTITUTE OF OCEANOGRAPHY   (China)

Author keywords

empirical AM FM decomposition; empirical mode decomposition; Hilbert transform; Instantaneous frequency; normalized intrinsic mode function; quadrature

Indexed keywords

EMPIRICAL AM/FM DECOMPOSITION; EMPIRICAL MODE DECOMPOSITION; HILBERT TRANSFORM; INSTANTANEOUS FREQUENCY; INTRINSIC MODE FUNCTIONS; QUADRATURE;

SIGNAL PROCESSING;

MATHEMATICAL TRANSFORMATIONS;

EID: 77951668826     PISSN: 17935369     EISSN: 17937175     Source Type: Journal    
DOI: 10.1142/S1793536909000096     Document Type: Review

References (46)

1. J. Shekel, Instantaneous frequency, Proc. IRE 41 (1953) 548.
2. Huang et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. Roy. Soc. London 454 (1998) 903-995. (Pubitemid 128733183)
3. K. Gröchenig, Foundations of Time-Frequency Analysis: Applied and Numerical Harmonic Analysis (Birkhauser, Boston, 2001).
4. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
5. E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, 1990).
6. N. E. Huang, Z. Shen and R. S. Long, A new view of nonlinear water waves - the Hilbert spectrum, Ann. Rev. Fluid Mech. 31 (1999) 417-457. (Pubitemid 36186209)
7. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 1997).
8. B. Boashash, Estimating and interpreting the instantaneous frequency of a signal. Part I: Fundamentals, Proc. IEEE 80 (1992) 520-538.
9. B. Boashash, Estimating and interpreting the instantaneous frequency of a signal. Part II: Algorithms and applications, Proc. IEEE 80 (1992) 540-568.
10. B. Boashash, Time-Frequency Signal Analysis - Methods and Applications (Longman-Cheshire, Melbourne and John Wiley Halsted Press, New York, 1992).
11. P. J. Kootsookos, B. C. Lovell and B. Boashash, A unified approach to the STFT, TFDs and instantaneous frequency, IEEE Trans. Signal Process. 40 (8) (1992) 1971-1982.
12. B. C. Lovell, R. C. Williamson and B. Boashash, The relationship between instantaneous frequency and time-frequency representations, IEEE Trans. Signal Process. 41 (3) (1993) 1458-1461. (Pubitemid 23701020)
13. L. Cohen, Time-Frequency Analysis (Prentice Hall, Englewood Cliffs, NJ, 1995).
14. P. Flandrin, Time-Frequency/Time-Scale Analysis (Academic Press, San Diego, CA, 1999).
15. P. J. Loughlin and B. Tracer, On the amplitude - and frequency-modulation decomposition of signals, J. Acoust. Soc. Am. 100 (1996) 1594-1601.
16. B. Picinbono, On instantaneous amplitude and phase signals, IEEE Trans. Signal Process. 45 (1997) 552-560.
17. S. Olhede and A. T. Walden, The Hilbert spectrum via wavelet projections, Proc. Roy. Soc. London A 460 (2004) 955-975. (Pubitemid 38406356)
18. E. Bedrosian, On the quadrature approximation to the Hilbert transform of modulated signals, Proc. IEEE 51 (1963) 868-869.
19. A. H. Nuttall, On the quadrature approximation to the Hilbert transform of modulated signals, Proc. IEEE 54 (1966) 1458-1459.
20. V. Vatchev, Intrinsic mode function and the Hilbert transform (PhD Dissertation, Industrial Mathematics Institute, Department of Mathematics, University of South Carolina, Columbia, SC, 2004).
21. N. E. Huang, M.-L. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen and K. L. Fan, A confidence limit for empirical mode decomposition and Hilbert spectral analysis, Proc. Roy. Soc. London 459 (2003) 2317-2345. (Pubitemid 38328337)
22. S. O. Rice, Mathematical analysis of random noise, Bell Syst. Tech. J. 23 (1944) 282-310.
23. S. O. Rice, Mathematical analysis of random noise, II. Power spectrum and correlation functions, Bell Syst. Tech. J. 23 (1944) 310-332.
24. S. O. Rice, Mathematical analysis of random noise, III. Statistical properties of random noise currents, Bell Syst. Tech. J. 24 (1945) 46-108.
25. S. O. Rice, Mathematical analysis of random noise, IV. Noise through nonlinear devices, Bell Syst. Tech. J. 24 (1945) 109-156.
26. W. K. Meville, Wave modulation and breakdown, J. Fluid Mech. 128 (1983) 489-506.
27. H. Goldstein, Classi cal M echanics, 2nd edn. (Addison-Wesley, Reading, MA, 1980).
28. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics: Vol. 1: Mechanics (Pergamon, Oxford, UK, 1976).
29. I. Daubechies, Ten Lectures on Wavelets (Philadelphia SIAM, 1992).
30. D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis (Cambridge University Press, Cambridge, 2000).
31. B. Van der Pol, The fundamental principles of frequency modulation, Proc. IEE 93 (1946) 153-158.
32. D. Gabor, Theory of communication, J. IEE 93 (1946) 426-457.
33. S. Hahn, Hilbert Transforms in Signal Processing (Artech House, Boston, MA, 1995).
34. T. Qian, Q. Chen and L. Li, Analytic unit quadrature signals with nonlinear phase, Physica D 203 (2005) 80-87. (Pubitemid 40538765)
35. L. W. Salvino and R. Cawley, Time-frequency dependant damping via Hilbert damping sepectrum, US Patent 6, 507, 798 granted 14 Jan. 2003.
36. N. E. Huang, M. Brenner, C.-G. Pak and L. Salvion, An application of Hilbert-Huang transform to the stability study of airfoil flutter, AIAA J. 44 (2006) 772-786.
37. J. F. Kaiser, On Teager's energy algorithm and its generalization to continuous signals, Proc. 4th IEEE Signal Processing Workshop (Mohonk, NY, 1990).
38. T. F. Quatieri, Discrete-Time Speech Signal Processing (Principles and Practice, Prentice-Hall, Upper Saddle River, NJ, 2002).
39. P. Maragos, J. F. Kaiser and T. F. Quatieri, On amplitude and frequency demodulation using energy operators, IEEE Trans. Signal Process. 41 (1993) 1532-1550.
40. P. Maragos, J. F. Kaiser and T. F. Quatieri, Energy separation in signal modulation with application to speech analysis, IEEE Trans. Signal Process. 41 (1993) 3024-3051.
41. Z. Wu and N. E. Huang, Ensemble empirical mode decomposition: A noise-assisted data analysis method, Adv. Adap. Data Anal. 1 (2009) 1-41.
42. G. Rilling and P. Flandrin, One or two frequencies? The empirical mode decomposition answers, IEEE Trans. Signal Process. 56 (1) (2008) 85-95.
43. N. E. Huang, S. R. Long and Z. Shen, The mechanism for frequency downshift in nonlinear wave evolution, Adv. Appl. Mech. 40 (1996) 59-111.
44. P. Flandrin, G. Rilling and P. Gonçalvès, Empirical mode decomposition as a filterbank, IEEE Signal Process. Lett. 11 (2004) 112-114.
45. Z. Wu and N. E. Huang, A study of the characteristics of white noise using the empirical mode decomposition method, Proc. Roy. Soc. London A 460 (2004) 1597-1611. (Pubitemid 38703409)
46. N. E. Huang, Empirical mode decomposition for analyzing acoustic signal, US Patent 10-073857, August 2003 (pending).