Multifractional Property Analysis of Human Sleep Electroencephalogram Signals

Part of the Signals and Communication Technology book series (SCT)


In Chap. 13, different human sleep stages are investigated by studying the fractional and multifractional properties of sleep EEG signals. From analyzing the results for the fractional property of short term sleep EEG signals in different sleep stages, we can conclude that the average Hurst parameter H is different during different sleep stages. In comparison, the analysis results of multifractional characteristics for long term sleep EEG signals provided more detailed and more valuable information on various sleep stages. In different sleep stages, the fluctuations of local Hölder exponent H(t) exhibit distinctive properties, which are closely related to the distinct characteristics in a specific sleep stage. The emphasis of this study is to provide a novel and more effective analysis technique for dynamic sleep EEG signals.


Fractional Property Sleep Disorder Sleep Stage Hurst Parameter Multifractional Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 22.
    Beran, J.: Statistics for Long-Memory Processes, 1st edn. CRC Press, Boca Raton (1994) MATHGoogle Scholar
  2. 39.
    Cajueiro, D.O., Tabak, B.M.: Time-varying long-range dependence in US interest rates. Chaos Solitons Fractals 34(2), 360–367 (2007) MATHCrossRefGoogle Scholar
  3. 67.
    Cohen, S., Marty, R.: Invariance principle, multifractional Gaussian processes and long-range dependence. Ann. Inst. Henri Poincaré B, Probab. Stat. 44(3), 475–489 (2008) MathSciNetMATHCrossRefGoogle Scholar
  4. 73.
    Crovella, M.E., Bestavros, A.: Self-similarity in world wide web traffic evidence and possible causes. IEEE/ACM Trans. Netw. 5(6), 835–846 (1997) CrossRefGoogle Scholar
  5. 90.
    Falconer, K.J.: The local structure of random processes. J. Lond. Math. Soc. 67(3), 657–672 (2003) MathSciNetMATHCrossRefGoogle Scholar
  6. 100.
    Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.-K., Stanley, H.E.: PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (2000) Google Scholar
  7. 123.
    Hurst, H.E.: Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. 116(3), 770–799 (1951) Google Scholar
  8. 124.
    Hwa, R.C., Ferree, T.C.: Scaling properties of fluctuations in the human electroencephalogram. Phys. Rev. E 66(2), 02190 (2002), 1–18 CrossRefGoogle Scholar
  9. 125.
    Iber, C., Ancoli-Israel, S., Chesson, A., Quan, S.F.: The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications. American Academy of Sleep Medicine, Darien (2007) Google Scholar
  10. 126.
    Ichimaru, Y., Moody, G.B.: Development of the polysomnographic database on CD-ROM. Psychiatry Clin. Neurosci. 53(2), 175–177 (1999) CrossRefGoogle Scholar
  11. 127.
    Ignaccolo, M., Latka, M., Jernajczyk, W., Grigolini, P., West, B.J.: The dynamics of EEG entropy. J. Biol. Phys. 36(2), 185–196 (2010) CrossRefGoogle Scholar
  12. 138.
    Kettani, H., Gubner, J.A.: A novel approach to the estimation of the long-range dependence parameter. IEEE Trans. Circuits Syst. 53(6), 463–467 (2006) CrossRefGoogle Scholar
  13. 174.
    Linkenkaer-Hansen, K., Nikouline, V.V., Palva, J.M., Ilmoniemi, R.J.: Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neurosci. 21(4), 1370–1377 (2001) Google Scholar
  14. 177.
    Loomis, A.L., Harvey, E.N., Hobart, G.A.: Cerebral states during sleep, as studied by human brain potentials. J. Exp. Psychol. 21(2), 127–144 (1937) CrossRefGoogle Scholar
  15. 178.
    López, T., Martínez-González, C.L., Manjarrez, J., Plascencia, N., Balank, A.S.: Fractal analysis of EEG signals in the brain of epileptic rats, with and without biocompatible implanted neuroreservoirs. Appl. Mech. Mater. 15, 127–136 (2009) CrossRefGoogle Scholar
  16. 214.
    Natarajan, K., Acharya, R.U., Alias, F., Tiboleng, T., Puthusserypady, S.K.: Nonlinear analysis of EEG signals at different mental states. Biomed. Eng. Online 3(1) (2004) Google Scholar
  17. 216.
    Nurujjaman, M., Narayanan, R., Iyengar, A.N.S.: Comparative study of nonlinear properties of EEG signals of normal persons and epileptic patients. Nonlinear Biomed. Phys. 3(1) (2009) Google Scholar
  18. 224.
    Osorio, I., Frei, M.G.: Hurst parameter estimation for epileptic seizure detection. Commun. Inf. Syst. 7(2), 167–176 (2007) MathSciNetGoogle Scholar
  19. 232.
    Peltier, R.F., Vehe, J.L.: Multifractional Brownian motion: definition and preliminary results. Technical report 2645, Institut National de Recherche en Informatique et en Automatique (1995) Google Scholar
  20. 245.
    Rechtschaffen, A., Kales, A. (eds.): A Manual of Standardized Terminology, Techniques and Scoring System for Sleep Stages of Human Subjects, 1st edn. Public Health Service, US Government Printing Office, Washington (1968) Google Scholar
  21. 263.
    Serinaldi, F.: Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series. Phys. A, Stat. Mech. Appl. 389(14), 2770–2781 (2010) CrossRefGoogle Scholar
  22. 267.
    Sheng, H., Chen, Y.Q., Qiu, T.: On the robustness of Hurst estimators. IET Signal Process. (2011). doi: 10.1049/iet-spr.2009.0241 Google Scholar
  23. 268.
    Sheng, H., Chen, Y.Q., Qiu, T.: Tracking performance and robustness analysis of Hurst estimators for multifractional processes. IET Signal Process. (2011) Google Scholar
  24. 305.
    Acharya, R.U., Faust, O., Kannathal, N., Chua, T., Laxminarayan, S.: Non-linear analysis of EEG signals at various sleep stages. Comput. Methods Programs Biomed. 80(1), 37–45 (2005) CrossRefGoogle Scholar
  25. 314.
    Šušmáková, K.: Human sleep and sleep EEG. Meas. Sci. Rev. 4(2), 59–74 (2004) Google Scholar
  26. 318.
    Watters, P.A.: Fractal structure in the electroencephalogram. Complex. Int. 5 (1998).

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.School of Electronic and Information EngineeringDalian Jiaotong UniversityDalianPeople’s Republic of China
  2. 2.Department of Electrical and Computer Engineering, CSOISUtah State UniversityLoganUSA
  3. 3.School of Electronic and Information EngineeringDalian University of TechnologyDalianPeople’s Republic of China

Personalised recommendations