{"title":"A New Definition of the Intrinsic Mode Function","authors":"Zhihua Yang, Lihua Yang","volume":36,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1144,"pagesEnd":1148,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14995","abstract":"
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.<\/p>\r\n","references":"[1] L. Cohen, Time-frequency analysis: theory and applications Prentice-\r\nHall, Inc., Upper saddle River, NJ, 1995.\r\n[2] S. Mallat. Wavelet tour of signal processing. Academic Press, San Diego,\r\nUSA, 1999.\r\n[3] B. Boashash. Estimating and interpreting the instantaneous frequency of\r\na signal: Part I Fundamentals. Proc. IEEE 80, 417-430, 1992.\r\n[4] L. Cohen. Time-Frequency distributions-A review. Proc. IEEE, 77:941-\r\n981, 1989.\r\n[5] N. E. Huang, Z. Shen, and S. R. Long et al. The empirical mode\r\ndecomposition and the Hilbert spectrum for nonlinear and non-stationary\r\ntime series analysis. Proceedings of the Royal Society of London,\r\nA(454):903-995, 1998.\r\n[6] P. Flandrin, G. Rilling, and P. Goncalves. Empirical mode decomposition\r\nas a filter bank. IEEE Signal Processing Letters, 11(2): 112-114, 2004.\r\n[7] G. Rilling, and P. Flandrin. One or two frequencies? The empirical mode\r\ndecomposition answers. IEEE Trans. Signal Processing, 56(1): 85-95,\r\n2007.\r\n[8] S. Meignen, and V. Perrier. A new formulation for empirical mode decomposition\r\nbased on constrained optimization. IEEE Signal Processing\r\nLetters, 14(12): 932-935, 2007.\r\n[9] Z. H. Yang, D. X. Qi, and L. H. Yang. Signal period analysis based\r\non Hilbert-Huang transform and its application to texture analysis.\r\nProceedings of Third International Conference on Image and Graphics,\r\nHong Kong, China, 430-433, 2004.\r\n[10] A. Boudraa, and J. Cexus. EMD-Based signal filtering. IEEE Trans.\r\nInstrumentation and Measurement, 56(6): 2196-2202, 2007.\r\n[11] C. H. Loh, T. C. Wu, and N. E. Huang. Application of emd+hht\r\nmethod to identify near-fault ground motion characteristics and structural\r\nresponses. BSSA, Special Issue of Chi-Chi Earthquake, 91(5):1339-1357,\r\n2001.\r\n[12] N. E. Huang, Z. Shen, and S. R. Long. A new view of nonlinear water\r\nwaves: the Hilbert spectrum. Annu. Rev. Fluid Mech, 31:417-57, 1999.\r\n[13] B. Liu, S. Riemenschneider, and Y. Xu. Gearbox fault diagnosis using\r\nempirical mode decomposition and Hilbert spectrum. Mechanical\r\nSystems and Signal Processing, 20(3): 718-734, 2006.\r\n[14] D. F. Chen, and X. L. Wu. Recovery of signal from transient scattered\r\nresponse contaminated by Gaussian white noise based on EMD method.\r\nChinese Journal of Electronics, 32(3): 496-498, 2004.\r\n[15] N. Bi, Q. Y. Sun, D. R. Huang, Z. H. Yang, and J. W. Huang. Robust\r\nimage watermarking based on multiband wavelets and empirical mode\r\ndecomposition. IEEE Trans. Image Processing, 16(8): 1956-1966, 2007.\r\n[16] Z. X. Liu, and S. L. Peng. Directional EMD and its application to texture\r\nsegmentation. Science in China(F), 35(2):113-123, 2005.\r\n[17] Z. H. Yang, L. H. Yang, and D. X. Qi. Detection of spindles in sleep\r\nEEGs using a novel algorithm based on the Hilbert-Huang transform.\r\nApplied and Numerical Harmonic Analysis, 543-559, 2006.\r\n[18] M. K. Molla, and K. Hirose. Single-Mixture audio source separation by\r\nsubspace decomposition of Hilbert spectrum. IEEE Trans. Audio, Speech,\r\nand Language Processing, 15(3): 893-900, 2007.\r\n[19] Z. H. Yang, D. X. Qi, and L. H. Yang. Chinese font recognition based\r\non EMD. Pattern Recognition Letters, 27(14):1692-1701, 2006.\r\n[20] Y. J. Deng, W. Wang, C. C. Qian, and D. J. Dai. Boundary-processingtechnique\r\nin EMD method and Hilbert transform. Chinese Science\r\nBulletin, 46(3):954-961, 2001.\r\n[21] E. Delechelle, J. Lemoine, and O. Niang. Empirical mode decomposition:\r\nAn analytical approach for sifting process. IEEE Signal Processing\r\nLetters, 12: 764-767, 2005.\r\n[22] Q. H. Chen, N. E. Huang, D. Riemenschneider, and Y. S. Xu. A B-spline\r\napproach for empirical mode decomposition. Advances in Computational\r\nMathematics, 24: 171-195, 2006.\r\n[23] P. G. Drazin. Nonlinear systems. Cambridge University Press, Cambridge,\r\n1992.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 36, 2009"}