Advertisement

Journal of Medical Systems

, Volume 34, Issue 2, pp 195–212 | Cite as

EEG Signal Analysis: A Survey

  • D. Puthankattil Subha
  • Paul K. Joseph
  • Rajendra Acharya U
  • Choo Min Lim
Original Paper

Abstract

The EEG (Electroencephalogram) signal indicates the electrical activity of the brain. They are highly random in nature and may contain useful information about the brain state. However, it is very difficult to get useful information from these signals directly in the time domain just by observing them. They are basically non-linear and nonstationary in nature. Hence, important features can be extracted for the diagnosis of different diseases using advanced signal processing techniques. In this paper the effect of different events on the EEG signal, and different signal processing methods used to extract the hidden information from the signal are discussed in detail. Linear, Frequency domain, time - frequency and non-linear techniques like correlation dimension (CD), largest Lyapunov exponent (LLE), Hurst exponent (H), different entropies, fractal dimension(FD), Higher Order Spectra (HOS), phase space plots and recurrence plots are discussed in detail using a typical normal EEG signal.

Keywords

EEG Correlation dimension Fractal dimension Entropy Recurrence plot 

References

  1. 1.
    Abarbanel, H. D. I., Analysis of observed Chaotic data. Springer-Verlag:New York, 1996.MATHGoogle Scholar
  2. 2.
    Acharya, U. R., Faust, O., Kannathal, N., Chua, T. J., and Laxminarayan, S., Dynamical analysis of EEG signals at various sleep stages. Comput. Methods Programs Biomed. 80(1):37–45, 2005 doi: 10.1016/j.cmpb.2005.06.011.CrossRefGoogle Scholar
  3. 3.
    Acharya, U. R., Joseph, P. K., Kannathal, N., Min, L. C., and Suri, J. S., Heart rate Variability: a review. Med. Biol. Eng. Comput. 44(12):1031–1051, 2006 doi: 10.1007/s11517-006-0119-0.CrossRefGoogle Scholar
  4. 4.
    Akaike, H., Fitting autoregressive models for prediction. Ann. Inst. Stat. Math. 21:243–247, 1969 doi: 10.1007/BF02532251.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Akaike, H., A new look at statistical model identification. IEEE Trans. Automat. Contr. 19:716–723, 1974 doi: 10.1109/TAC.1974.1100705.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bai, D., and Li Qiu, T., The sample entropy and its application in EEG based epilepsy detection. J. Biomed. Eng. 24(1):200–205, 2007.Google Scholar
  7. 7.
    Bhattacharya, J., and Petsche, H., Phase synchrony analysis of EEG during music perception reveals changes in functional connectivity due to musical expertise.. Signal processing. 85(11):2161–2177, 2005 doi: 10.1016/j.sigpro.2005.07.007.MATHCrossRefGoogle Scholar
  8. 8.
    Bruhn, J., and Ropcke, H., Approximate entropy as an electroencephalographic measure of anesthetic drug effect during desflurane anesthesia.. Anesthesilogy. 92(3):715–726, 2000 doi: 10.1097/00000542-200003000-00016.CrossRefGoogle Scholar
  9. 9.
    Bullock, T. H., Achimowicz, J. Z., Duckrow, R. B., Spencer, S. S., and Iragui-Madoz, V. J., Bicoherence of intracranial EEG in sleep, wakefulness and seizures. Electroencephalogr. Clin. Neurophysiol. 103:661–678, 1997 doi: 10.1016/S0013-4694(97)00087-4.CrossRefGoogle Scholar
  10. 10.
    Carthy, RAMc., and Warrington, E. K., Cognitive Neuropsychology: A clinical Introduction. Academic Press:San Diego, LA, 1990.Google Scholar
  11. 11.
    Chandran, V., and Elgar, S., Pattern recognition using invariants defined from higher order spectra- one dimensional inputs. IEEE Trans. Signal Process. 41(1):205–212, 1993 doi: 10.1109/TSP.1993.193139.MATHCrossRefGoogle Scholar
  12. 12.
    Charles, W. A., James, N. K., O’Connor, T., Michael, J. K., and Artem, S., Geometric subspace methods and time-delay embedding for EEG artifact removal and classification. IEEE Trans. Neural Syst. Rehabil. Eng. 14(2):142–146, 2006 doi: 10.1109/TNSRE.2006.875527.CrossRefGoogle Scholar
  13. 13.
    Chua, K. C., Chandran, V., Acharya, U. R., and Lim, C. M., Analysis of epileptic EEG signals using higher order spectra. J. Med. Eng. Technol. (2007) (in press).Google Scholar
  14. 14.
    Claesen, S., and Kitney, R. I., Estimation of the Largest Lyapunov Exponent of an RR Interval and its use as an Indicator of Decreased Autonomic Heart Rate Control. Comput. Cardiol. ▪▪▪, 133–136, (1994).Google Scholar
  15. 15.
    Dangel, S., Meier, P.F., Moser, H.R., Plibersek, S., and Shen, Y., Time series analysis of sleep EEG. Computer assisted. Physics ▪▪▪, 93–95, 1999.Google Scholar
  16. 16.
    Das, A., Das, P., and Roy, A.B., Applicability of Lyapunov Exponent in EEG data analysis. Complexity International. 2002.Google Scholar
  17. 17.
    Dias-Tosta, E., Kuckeihaus, G. S., Amaral, K., Sinha, J., Kurup, A., Paleti, A., et al., Decrease of non-linear structure in the EEG of Alzheimer patients compared to healthy controls. Clin. Neurophysiol. 110(7):1159–1167, 1999 doi: 10.1016/S1388-2457(99)00013-9.CrossRefGoogle Scholar
  18. 18.
    Ding, M., Grebogi, E., Ott, E., Sauer, T., and Yorke, J. A., Estimating correlation dimension from a chaotic time series:when a plateau occurs? Physica. D. 69:404–424, 1993 doi: 10.1016/0167-2789(93)90103-8.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Durka, P. J., Klekowicz, H., Blinowska, K. J., Szelenberger, W., and Niemcewicz, S. Z., Simple system for detection of EEG artifacts in polysomnographic recordings. IEEE Trans. Biomed. Eng. 50(4):526–528, 2003 doi: 10.1109/TBME.2003.809476.CrossRefGoogle Scholar
  20. 20.
    Eckmann, J. P., Kamphorst, S. O., and Ruelle, D., Recurrence Plots of Dynamical Systems. Europhys. Lett. 4:973–977, 1987 doi: 10.1209/0295-5075/4/9/004.CrossRefGoogle Scholar
  21. 21.
    Faust, O., Acharya, U. R., Alen, A., and Lim, C. M., Analysis of EEG signals during epileptic and alcoholic states using AR modeling techniques. Innovations and Technology in Biology and Medicine (ITBM-RBM). 29(1):44–52, 2008.Google Scholar
  22. 22.
    Fell, J., and Roschke, J., A Comparison between spectral and nonlinear EEG measures. Electroencephalogr. Clin. Neurophysiol. 98(5):401–410, 1996 doi: 10.1016/0013-4694(96)95636-9.CrossRefGoogle Scholar
  23. 23.
    Fraser, A. M., Information and entropy in strange attractors. IEEE Trans. Inf. Theory. 35:245–262, 1989 doi: 10.1109/18.32121.MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Fraser, A. M., and Swinney, H. L., Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33:1134–1140, 1986 doi: 10.1103/PhysRevA.33.1134.CrossRefMathSciNetGoogle Scholar
  25. 25.
    Gigola, S., Ortiz, F., D’Attellis, C. E., Silva, W., and Kochen, S., Prediction of epileptic seizures using accumulated energy in a multiresolution framework. J. Neurosci. Methods. 138(1–2):107–111, 2004 doi: 10.1016/j.jneumeth.2004.03.016.CrossRefGoogle Scholar
  26. 26.
    Grassberger, P., and Procassia, I., Measuring the strangeness of strange attractors. Physica D 9:189–208, 1983 doi: 10.1016/0167-2789(83)90298-1.MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Grassberger, P., and Procaccia, I., Characterization of strange attractors. Phys. Rev. Lett. 50(5):346–349, 1983 doi: 10.1103/PhysRevLett.50.346.CrossRefMathSciNetGoogle Scholar
  28. 28.
    Grassberger, P., and Schrieber, T., Nonlinear time sequence analysis. Int. J. Bifurcat. Chaos. 1(3):512–547, 1991 doi: 10.1142/S0218127491000403.Google Scholar
  29. 29.
    Haselsteiner, E., and Pfurtscheller, G., Using time-dependent neural networks for EEG classification. IEEE Trans. Rehabil. Eng. 8:457–463, 2000 doi: 10.1109/86.895948.CrossRefGoogle Scholar
  30. 30.
    Hebert, R., Lehmann, D., Tan, G., Travis, F., and Arenander, A., Enhanced EEG alpha time-domain phase synchrony during Transcendental Meditation: Implications for cortical integration theory. J. Signal Process. 85(11):2213–2232, 2005 doi: 10.1016/j.sigpro.2005.07.009.MATHCrossRefGoogle Scholar
  31. 31.
    Higuchi, T., Approach to an irregular time series on the basis of the fractal theory. Physica. D 31:277–283, 1988 doi: 10.1016/0167-2789(88)90081-4.MATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Hubert, P., Lutzenberger, W., Pulvermüller, F., and Birbaumer, N., Fractal dimensions of short EEG time series in humans. Neurosci. Lett. 225(2):77–80, 1997 doi: 10.1016/S0304-3940(97)00192-4.CrossRefGoogle Scholar
  33. 33.
    Hudson, D. L., Cohen, M. E., Kramer, M., Szeri, A., and Chang, F. L., Diagnostic Implications of EEG Analysis in Patients with Dementia. Proceedings of 2nd International IEEE EMBS Conference on Neural Engineering. 629–632, 2005Google Scholar
  34. 34.
    Inoye, K., Quantification of EEG irregularity by use of the entropy of the power spectrum. Electroencephalogr. Clin. Neurophysiol. 79:204–210, 1991 doi: 10.1016/0013-4694(91)90138-T.CrossRefGoogle Scholar
  35. 35.
    Jahankhani, P., Kodogiannis, V., and Revett, K., EEG Signal Classification Using Wavelet Feature Extraction and Neural Networks. IEEE International Symposium on Modern Computing John Vincent Atanasoff. 120–124, 2006Google Scholar
  36. 36.
    Jiayi, G., Peng, Z., Xin, Z., and Mingshi, W., Sample Entropy Analysis of Sleep EEG under Different Stages. IEEE/ICME Int. Conference on Complex Medical Engineering. 1499–1502, 2007Google Scholar
  37. 37.
    Joseph, P., Kannathal, N., and Acharya, U. R., Complex Encephalogram Dynamics during Meditation. Journal of Chinese clinical medicine. 2(4):220–230, 2007.Google Scholar
  38. 38.
    Kang-ming, C., and Pei-chen, L., Meditation EEG interpretation based on novel fuzzy-merging strategies and wavelet features. Biomedical Engineering Applications. Basis Commun. 17(4):167–175, 2005.CrossRefGoogle Scholar
  39. 39.
    Kannathal, N., Acharya, U. R., Fadilah, A., Tibelong, T., and Sadasivan, P. K., Nonlinear analysis of EEG signals at different mental states. Biomed. Online J. 3:7, 2004 doi: 10.1186/1475-925X-3-7.CrossRefGoogle Scholar
  40. 40.
    Kannathal, N., Acharya, U. R., Joseph, P., and Ng, E. Y. K. Analysis of EEG signals with and without reflexology using FFT and auto regressive modeling techniques. J. Chin. Clin. Med. 1(1):12–20, 2006.Google Scholar
  41. 41.
    Kannathal, N., Choo, M., Acharya, U. R., and Sadasivan, P., Entropies for detection of epilepsy in EEG. Comput. Methods Programs Biomed. 80(3):187–194, 2005 doi: 10.1016/j.cmpb.2005.06.012.CrossRefGoogle Scholar
  42. 42.
    Kantz, H., and Schreiber, T., Nonlinear lime series analysis. Cambridge University Press:New York. 1997Google Scholar
  43. 43.
    Katz, M., Fractals and the analysis of waveforms. Comput. Biol. Med. 18(3):145–156, 1988 doi: 10.1016/0010-4825(88)90041-8.CrossRefGoogle Scholar
  44. 44.
    Kemal, M. K., Guler, I., Alper, D., and Mehmet, A., Comparison of STFT and Wavelet Transform methods in determining epileptic seizure activity in EEG signals for real time application. Comput. Biol. Med. 35:603–616, 2005 doi: 10.1016/j.compbiomed.2004.05.001.CrossRefGoogle Scholar
  45. 45.
    Kennel, M. B., Brown, R., and Abarbanel, H. D. I., etermining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45:3403, 1992 doi: 10.1103/PhysRevA.45.3403.CrossRefGoogle Scholar
  46. 46.
    Kiymik, M. K., Akin, M., and Subasi, A., Automatic recognition of alertness level by using wavelet transform and artificial neural network. J. Neurosci. Methods. 139(2):231–240, 2004 doi: 10.1016/j.jneumeth.2004.04.027.CrossRefGoogle Scholar
  47. 47.
    Kobayashi, T., Misaki, K., Nakagawa, H., Madokoro, S., Ihara, H., Tsuda, K., et al., Non-linear analysis of the sleep EEG. Psychiatry Clin. Neurosci. 53(2):159–161, 1999 doi: 10.1046/j.1440-1819.1999.00540.x.CrossRefGoogle Scholar
  48. 48.
    Ktonas, P.Y., Golemati, S., Tsekou, H., Paparrigopoulos, T., Soldatos, C.,R., Xanthopoulos, P., et al., Potential dementia biomarkers based on the time-varying microstructure of sleep EEG spindles. 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 2464–2467, 2007.Google Scholar
  49. 49.
    Lee, J., Kim, D., Kim, I., Suk Park, K., and Kim, S., onlinear-analysis of human sleep EEG using detrended fluctuation analysis. Med. Eng. Phys. 26(9):773–776, 2004 doi: 10.1016/j.medengphy.2004.07.002.CrossRefGoogle Scholar
  50. 50.
    Li, X., Sleigh, J. W., Voss, L. J., and Ouyang, G., Measure of the electroencephalographic effects of sevoflurane using recurrence dynamics. Neurosci. Lett. 424(1):47–50, 2007 doi: 10.1016/j.neulet.2007.07.041.CrossRefGoogle Scholar
  51. 51.
    Lin, R., Ren-Guey, L., Chwan-Lu, T., Heng-Kuan, Z., Chih-Feng, C., and Joe-Air, J. A., New Approach For Identifying Sleep Apnea Syndrome Using Wavelet Transform and Neural Networks. Biomedical Engineering Applications-Basis & Communications. 18(3):138–144, 2006.CrossRefGoogle Scholar
  52. 52.
    Liu, J. Z., Yang, Q., Yao, B., Brown, R. W., and Yue, G. H., Linear correlation between fractal dimension of EEG signal and handgrip force. Biol. Cybern. 93(2):131–140, 2005 doi: 10.1007/s00422-005-0561-3.MATHCrossRefGoogle Scholar
  53. 53.
    Lu, H., Wang, M., and Yu, H., EEG Model and Location in Brain when Enjoying MusicProceedings of the 27th Annual IEEE Engineering in Medicine and Biology Conference Shanghai:China. 2695–2698, 2005.Google Scholar
  54. 54.
    Mahgoub, Y. A., and Dansereau, R. M.,Voicing-state classification of co-channel speech using nonlinear state-space reconstruction. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing. 409–412, 2005.Google Scholar
  55. 55.
    Mandelbrot, B. B., Geometry of nature. Freeman:Sanfrancisco, 1983Google Scholar
  56. 56.
    Marple, S. L., Digital Spectral Analysis. Englewood Cliffs NJ, Prentice-Hall, 1987, Chapter 7.Google Scholar
  57. 57.
    Martin, B., Milos, M., Ake, E., Katerina, C., and Vladimir, K., Objective assessment of the degree of dementia by means of EEG. Neuropsychobiology. 48:19–26, 2003 doi: 10.1159/000071824.CrossRefGoogle Scholar
  58. 58.
    Nikias, C. L., and Raghuveer, M. R., Bispectrum Estimation:A Digital Signal Processing Framework. Proc. IEEE. 75(7):869–891, 1987 doi: 10.1109/PROC.1987.13824.CrossRefGoogle Scholar
  59. 59.
    Nunes, R. R., de Almeida, M. P., and Sleigh, J. W., Spectral entropy: a new method for anesthetic adequacy. Rev. Bras. Anestesiol. 54(3):403–422, 2004.Google Scholar
  60. 60.
    Oppenheim, A. V., and Lim, J. S., The importance of phase in signals. Proc. IEEE. 69:529–550, 1981 doi: 10.1109/PROC.1981.12022.CrossRefGoogle Scholar
  61. 61.
    Packard, N. H., Crutchfield, J. P., Farmer, J. D., and Shaw, R. S., Geometry from a time series. Phys. Rev. Lett. 45:712–716, 1980 doi: 10.1103/PhysRevLett.45.712.CrossRefGoogle Scholar
  62. 62.
    Patil, S. T., and Bormane, D. S., Electroencephalograph Signal Analysis During Bramari. 9th Int. Conference on Inf.Technology (ICIT 06). 26–32, 2006.Google Scholar
  63. 63.
    Pincus, S. M., Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA. 88:2297–2301, 1991 doi: 10.1073/pnas.88.6.2297.MATHCrossRefMathSciNetGoogle Scholar
  64. 64.
    Pincus, S. M., and Goldberger, A. L., Physiological time-series analysis: what does regularity quantify? Am. J. Physiol. 266:H1643–H1656, 1994.Google Scholar
  65. 65.
    Pincus, S. M., and Keefe, D. L., Quantification of hormone pulsatility via an approximate entropy algorithm. Am. J. Physiol. 262:E741–E754, 1992.Google Scholar
  66. 66.
    Pradhan, N., and Dutt, D. N., Data compression by linear prediction for storage and transmission of EEG signals. Int. J. Biomed. Comput. 35(3):207–217, 1994 doi: 10.1016/0020-7101(94)90076-0.CrossRefGoogle Scholar
  67. 67.
    Proakis, J., and Manolakis, D.,Digital Signal Processing. Prentice-Hall. 1996, Chapter 12.Google Scholar
  68. 68.
    Rao, R. M., and Bopardikar, A.S.,Wavelet Transforms introduction to theory and applications. Addison Wesley, Longman Inc, Reading, MA, 1998.Google Scholar
  69. 69.
    Renna, M., Handy, J., and Shah, A., Low Baseline Bispectral Index of the Electroencephalogram in Patients with Dementia. Anesth. Analg. 96:1380–1385, 2003 doi: 10.1213/01.ANE.0000059223.78879.0F.CrossRefGoogle Scholar
  70. 70.
    Renyi, A., On measures of entropy and information. Proc. Fourth. Berkeley Symp. Math. Stat. Prob. 1:547–561, 1961.MathSciNetGoogle Scholar
  71. 71.
    Richmann, J. S., and Moorman, J. R., hysiological time series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol. 278:2039–2049, 2000.Google Scholar
  72. 72.
    Robert, L., Ren-Gue, L., Chwan-Lu, T., heng-Kuan, Z., Chih-Feng, C., and Joe-Air, J., A new approach for identifying sleep apnea syndrome using wavelet transform and neural networks. Biomedical engineering-Applications. Basis Commun. 18:138–143, 2006.Google Scholar
  73. 73.
    Roháľová, M., Sykacek, P., Koskaand, M., and Dorffner, G., Detection of the EEG Artifacts by the Means of the (Extended) Kalman Filter. Meas. Sci. Rev. 1(1):59–62, 2001.Google Scholar
  74. 74.
    Sandha, G. S., Singh, P. K., Oberoi, N. D., and Nagchoudhuri, D., Phase Correlations in Human EEG Signal: A Case Study. Second IEEE International Workshop on Electronic Design, Test and Applications. 41 – 43, 2004.Google Scholar
  75. 75.
    Sauer, T., Yorke, J. A., and Casdagli, M., Embedology. J. Stat. Phys. 65:579–616, 1991 doi: 10.1007/BF01053745.MATHCrossRefMathSciNetGoogle Scholar
  76. 76.
    Sheikhani, A., Behnam, H., Mohammadi, M. R., and Noorozian, M., Analysis of EEG background activity in Autism disease patients with bispectrum and STFT measure. Proceedings of the 11th Conference on 11th WSEAS International Conference on Communications. 11:318–322, 2007.Google Scholar
  77. 77.
    In-Ho, S., Doo-Soo, L., and Sun I, K., Recurrence quantification analysis of sleep electroencephalogram in sleep apnea syndrome in humans. Neurosci. Lett. 366(2):148–153 doi: 10.1016/j.neulet.2004.05.025.CrossRefGoogle Scholar
  78. 78.
    Srinivasan, N., Wong, M. T., & Krishnan, S. M. (2003). A new Phase Space Analysis Algorithm for Cardiac Arrhythmia Detection pp. 82–85. Mexico: Proceedings of the 25th Annual International Conference of the IEEE EMBS Cancun.Google Scholar
  79. 79.
    Stam, C. J., Pijn, J. P., Suffczynski, P., and da silva, F. H. L., Dynamics of the human alpha rhythm:evidence for online. Clin. Neurophysiol. 110:1801–1813, 1999 doi: 10.1016/S1388-2457(99)00099-1.CrossRefGoogle Scholar
  80. 80.
    Stanski, D. R., Using Pharmacodynamic Modelling of the Electroencephalogram (EEG) to understand anesthetic drug clinical pharmacology. Drug Metab. Pharmacokinet. 5(4):504–508, 1990.Google Scholar
  81. 81.
    Steyn-Ross, M. L., Steyn Ross, D. A., Sleigh, J. W., and Liley, D. T., Theoretical Electroencephalogram stationary spectrum for a white noise driven cortex:evidence for a general anesthetic-induced phase transition. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics. 60(6):7299–7311, 1999 doi: 10.1103/PhysRevE.60.7299.Google Scholar
  82. 82.
    Stoica, .P, and Moses, R. L., Introduction to Spectral Analysis. Prentice-Hall, 1997.Google Scholar
  83. 83.
    Subasi, A., EEG signal classification using wavelet feature extraction and a mixture of expert model. Expert Syst. Appl. An Int. J. 32(4):1084–1093, 2007 doi: 10.1016/j.eswa.2006.02.005.CrossRefGoogle Scholar
  84. 84.
    Swiderski, B., Osowski, S., and Rysz, A., Lyapunov Exponent of EEG Signal for Epileptic Seizure Characterization. Proceedings of the 2005 European Conference on Circuit Theory and Design. 2(28):153–156, 2005.CrossRefGoogle Scholar
  85. 85.
    Takens, F., Detecting Strange Attractors in Turbulence. In D. Rand, L. S. Young (Eds.), Dynamical Systems and Turbulence. Springer: Berlin, 1981.Google Scholar
  86. 86.
    Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J. D., Testing for nonlinearity in time series: the method of surrogate data. Physica D. 58:77–94, 1992 doi: 10.1016/0167-2789(92)90102-S.CrossRefGoogle Scholar
  87. 87.
    Tzyy-Ping, J., Makeig, S., Mckeown, M. J., Bell, A. J., Te-Won, L., and Sejnowski, T. J., Imaging Brain Dynamics Using Independent Component Analysis. Proc. IEEE. 89(7):1107–1122, 2001 doi: 10.1109/5.939827.CrossRefGoogle Scholar
  88. 88.
    Venkatramanan, S., and Kalpakam, N. V., Aiding the detection of Alzheimer’s disease in clinical electroencephalogram recording by selective de-noising of ocular artifacts. International Conference on Communications, circuits and systems. 2:965–968, 2004.Google Scholar
  89. 89.
    Vetterli, M., Wavelet anf filter banks:theory and design. IEEE Trans. Signal Process. 40(9):2207–2232, 1992 doi: 10.1109/78.157221.MATHCrossRefGoogle Scholar
  90. 90.
    Wei-Chih, L., Hung-Wen, C., and Chien-Yeh, H., Discovering EEG Signals Response to Musical Signal Stimuli by Time-frequency analysis and Independent Component Analysis. Proceedings of the 27th Annual IEEE Engineering in Medicine and Biology Conference Shanghai:China. 2765–2768, 2005Google Scholar
  91. 91.
    Welch, P. D., The use of Fast Fourier Transform for the Estimation of Power Spectra: A Method based on time averaging over short, modified periodograms. IEEE Trans Audio Electroacoust. AU-15:70–73, 1967 doi: 10.1109/TAU.1967.1161901.CrossRefMathSciNetGoogle Scholar
  92. 92.
    Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A., Determining Lyapunov exponents from a time series. Physica. D 16:285–317, 1985 doi: 10.1016/0167-2789(85)90011-9.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • D. Puthankattil Subha
    • 1
  • Paul K. Joseph
    • 1
  • Rajendra Acharya U
    • 2
  • Choo Min Lim
    • 2
  1. 1.Department of Electrical EngineeringNational Institute of TechnologyCalicutIndia
  2. 2.Department of Electronics and Computer engineeringNgee Ann PolytechnicSingaporeSingapore

Personalised recommendations