A New Definition of the Intrinsic Mode Function

This paper makes a detailed analysis regarding the definition of the intrinsic mode function and proves that Condition 1 of the intrinsic mode function can really be deduced from Condition 2. Finally, an improved definition of the intrinsic mode function is given.

• Zhihua Yang
• Lihua Yang

• Empirical Mode Decomposition (EMD)
• Hilbert-Huang transform(HHT)
• Intrinsic Mode Function(IMF).

[1] L. Cohen, Time-frequency analysis: theory and applications Prentice-
Hall, Inc., Upper saddle River, NJ, 1995.
[2] S. Mallat. Wavelet tour of signal processing. Academic Press, San Diego,
USA, 1999.
[3] B. Boashash. Estimating and interpreting the instantaneous frequency of
a signal: Part I Fundamentals. Proc. IEEE 80, 417-430, 1992.
[4] L. Cohen. Time-Frequency distributions-A review. Proc. IEEE, 77:941-
981, 1989.
[5] N. E. Huang, Z. Shen, and S. R. Long et al. The empirical mode
decomposition and the Hilbert spectrum for nonlinear and non-stationary
time series analysis. Proceedings of the Royal Society of London,
A(454):903-995, 1998.
[6] P. Flandrin, G. Rilling, and P. Goncalves. Empirical mode decomposition
as a filter bank. IEEE Signal Processing Letters, 11(2): 112-114, 2004.
[7] G. Rilling, and P. Flandrin. One or two frequencies? The empirical mode
decomposition answers. IEEE Trans. Signal Processing, 56(1): 85-95,
2007.
[8] S. Meignen, and V. Perrier. A new formulation for empirical mode decomposition
based on constrained optimization. IEEE Signal Processing
Letters, 14(12): 932-935, 2007.
[9] Z. H. Yang, D. X. Qi, and L. H. Yang. Signal period analysis based
on Hilbert-Huang transform and its application to texture analysis.
Proceedings of Third International Conference on Image and Graphics,
Hong Kong, China, 430-433, 2004.
[10] A. Boudraa, and J. Cexus. EMD-Based signal filtering. IEEE Trans.
Instrumentation and Measurement, 56(6): 2196-2202, 2007.
[11] C. H. Loh, T. C. Wu, and N. E. Huang. Application of emd+hht
method to identify near-fault ground motion characteristics and structural
responses. BSSA, Special Issue of Chi-Chi Earthquake, 91(5):1339-1357,
2001.
[12] N. E. Huang, Z. Shen, and S. R. Long. A new view of nonlinear water
waves: the Hilbert spectrum. Annu. Rev. Fluid Mech, 31:417-57, 1999.
[13] B. Liu, S. Riemenschneider, and Y. Xu. Gearbox fault diagnosis using
empirical mode decomposition and Hilbert spectrum. Mechanical
Systems and Signal Processing, 20(3): 718-734, 2006.
[14] D. F. Chen, and X. L. Wu. Recovery of signal from transient scattered
response contaminated by Gaussian white noise based on EMD method.
Chinese Journal of Electronics, 32(3): 496-498, 2004.
[15] N. Bi, Q. Y. Sun, D. R. Huang, Z. H. Yang, and J. W. Huang. Robust
image watermarking based on multiband wavelets and empirical mode
decomposition. IEEE Trans. Image Processing, 16(8): 1956-1966, 2007.
[16] Z. X. Liu, and S. L. Peng. Directional EMD and its application to texture
segmentation. Science in China(F), 35(2):113-123, 2005.
[17] Z. H. Yang, L. H. Yang, and D. X. Qi. Detection of spindles in sleep
EEGs using a novel algorithm based on the Hilbert-Huang transform.
Applied and Numerical Harmonic Analysis, 543-559, 2006.
[18] M. K. Molla, and K. Hirose. Single-Mixture audio source separation by
subspace decomposition of Hilbert spectrum. IEEE Trans. Audio, Speech,
and Language Processing, 15(3): 893-900, 2007.
[19] Z. H. Yang, D. X. Qi, and L. H. Yang. Chinese font recognition based
on EMD. Pattern Recognition Letters, 27(14):1692-1701, 2006.
[20] Y. J. Deng, W. Wang, C. C. Qian, and D. J. Dai. Boundary-processingtechnique
in EMD method and Hilbert transform. Chinese Science
Bulletin, 46(3):954-961, 2001.
[21] E. Delechelle, J. Lemoine, and O. Niang. Empirical mode decomposition:
An analytical approach for sifting process. IEEE Signal Processing
Letters, 12: 764-767, 2005.
[22] Q. H. Chen, N. E. Huang, D. Riemenschneider, and Y. S. Xu. A B-spline
approach for empirical mode decomposition. Advances in Computational
Mathematics, 24: 171-195, 2006.
[23] P. G. Drazin. Nonlinear systems. Cambridge University Press, Cambridge,
1992.