Spectral and Time-Frequency Analysis

  • Zhiguo ZhangEmail author


EEG signals are typically characterized by oscillatory patterns at certain frequency bands. Normally, the EEG data, especially spontaneous EEG data, are analyzed in the frequency domain. The spectral analysis can transform EEG signals from time domain to the frequency domain, which can reveal how the power of EEG signals is distributed along frequencies. Furthermore, as EEG spectrum could substantially vary over time, joint time-frequency analysis is often used to reveal time-varying spectral activities of EEG. Particularly, time-frequency analysis is a powerful method to estimate the event-related EEG spectral patterns, i.e., event-related synchronization/desynchronization (ERS/ERD). In this chapter, I introduce some commonly used spectral estimation methods (e.g., the periodogram, the Welch’s method, and the multitaper method) and time-frequency analysis methods (e.g., short-time Fourier transform and continuous wavelet transform). We also raise some practical issues and cautionary notes when using these methods on EEG data analysis, such as parameter tuning, visualization, and results reporting.


EEG ERS/ERD Fourier transform Periodogram Short-time Fourier transform Wavelet transform 

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  1. Aboy M, Marquez OW, Mcnames J, Hornero R. Adaptive modeling and spectral estimation of nonstationary biomedical signals based on Kalman filtering. IEEE Trans Biomed Eng. 2005;52(8):1485–9. Scholar
  2. Adeli H, Zhou Z, Dadmehr N. Analysis of EEG records in an epileptic patient using wavelet transform. J Neurosci Methods. 2003;123(1):69–87. Scholar
  3. Arnold M, Miltner WH, Witte H, Bauer R, Braun C. Adaptive AR modeling of nonstationary time series by means of Kalman filtering. IEEE Trans Biomed Eng. 1998;45(5):553–62. Scholar
  4. Babadi B, Brown EN. A review of multitaper spectral analysis. IEEE Trans Biomed Eng. 2014;61(5):1555–64. Scholar
  5. Barry RJ, Clarke AR, Johnstone SJ, Brown CR. EEG differences in children between eyes-closed and eyes-open resting conditions. Clin Neurophysiol. 2009;118(12):2765–73.CrossRefGoogle Scholar
  6. Boashash B. Time-frequency signal analysis and processing: a comprehensive reference. Boston: Academic; 2015.Google Scholar
  7. Buzsaki G. Rhythms of the brain. Oxford: Oxford University Press; 2011.Google Scholar
  8. Cahn BR, Polich J. Meditation states and traits: EEG, ERP, and neuroimaging studies. Psychol Bull. 2006;132(2):180–211. Scholar
  9. Cohen MX. Analyzing neural time series data: theory and practice. Cambridge, MA: MIT Press; 2014.CrossRefGoogle Scholar
  10. Cohen MX. Where does EEG come from and what does it mean? Trends Neurosci. 2017;40(4):208–18. Scholar
  11. Cohen MX. A better way to define and describe Morlet wavelets for time-frequency analysis. bioRxiv. 2018;
  12. Delorme A, Makeig S. EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J Neurosci Methods. 2004;134(1):9–21. Scholar
  13. Durka P. Matching pursuit and unification in EEG analysis. Norwood: Artech House; 2007.Google Scholar
  14. Fell J, Röschke J, Mann K, Schäffner C. Discrimination of sleep stages: a comparison between spectral and nonlinear EEG measures. Electroencephalogr Clin Neurophysiol. 1996;98(5):401–10.CrossRefGoogle Scholar
  15. Hu L, Xiao P, Zhang ZG, Mouraux A, Iannetti GD. Single-trial time-frequency analysis of electrocortical signals: baseline correction and beyond. NeuroImage. 2014;84(1):876–87. Scholar
  16. Kaipio JP, Karjalainen PA. Estimation of event-related synchronization changes by a new TVAR method. IEEE Trans Biomed Eng. 2002;44(8):649–56. Scholar
  17. Kay SM. Modern spectral estimation: theory and application. Englewood Cliffs: Prentice Hall; 1988.Google Scholar
  18. Khan ME, Dutt DN. An expectation-maximization algorithm based Kalman smoother approach for event-related desynchronization (ERD) estimation from EEG. IEEE Trans Biomed Eng. 2007;54(7):1191–8. Scholar
  19. Kim SE, Behr MK, Ba D, Brown EN. State-space multitaper time-frequency analysis. Proc Natl Acad Sci U S A. 2018;115(1):E5–E14. Scholar
  20. Luck SJ. An introduction to the event-related potential technique. Cambridge, MA: MIT Press; 2014.Google Scholar
  21. Mallat S. A wavelet tour of signal processing: the sparse way. Burlington: Academic; 2008.Google Scholar
  22. Mitra SK. Digital signal processing: a computer-based approach. New York: McGraw-Hill Inc; 2000.Google Scholar
  23. Mouraux A, Iannetti GD. Across-trial averaging of event-related EEG responses and beyond. Magn Reson Imaging. 2008;26(7):1041–54. Scholar
  24. Niedermeyer E, Lopes da Silva FH. Electroencephalography: basic principles, clinical applications, and related fields. Philadelphia: Lippincott Williams & Wilkins; 2005.Google Scholar
  25. Oppenheim AV, Willsky AS, Nawab SH. Signals and systems. London: Pearson; 1996.Google Scholar
  26. Pernet C, Garrido M, Gramfort, MN, Michel C, Pang E, Salmelin R, Schoffelen JM, Valdes-Sosa PA, Puce A. Best practices in data analysis and sharing in neuroimaging using MEEG. 2018.
  27. Pfurtscheller G, Lopez da Silva FH. Event-related EEG/MEG synchronization and desynchronization: basic principles. Clin Neurophysiol. 1999;110(11):1842–57.CrossRefGoogle Scholar
  28. Proakis JG, Manolakis DK. Digital signal processing: principles, algorithms and applications. Upper Saddle River: Pearson; 2006.Google Scholar
  29. Roach BJ, Mathalon DH. Event-related EEG time-frequency analysis: an overview of measures and an analysis of early gamma band phase locking in schizophrenia. Schizophr Bull. 2008;34(5):907–26. Scholar
  30. Sanei S, Chambers JA. EEG signal processing. New York: Wiley; 2013.Google Scholar
  31. Schlogl A. The electroencephalogram and the adaptive autoregressive model: theory and applications. Aachen: Shaker Verlag GmbH; 2000.Google Scholar
  32. Stoica P, Moses RL. Spectral analysis of signals. Upper Saddle River: Prentice Hall; 2005.Google Scholar
  33. Sweeneyreed CM, Nasuto SJ. A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition. J Comput Neurosci. 2007;23(1):79–111. Scholar
  34. Tarvainen MP, Hiltunen JK, Ranta-Aho PO, Karjalainen PA. Estimation of nonstationary EEG with Kalman smoother approach: an application to event-related synchronization (ERS). IEEE Trans Biomed Eng. 2004;51(3):516–24. Scholar
  35. Zhang ZG, Hung YS, Chan SC. Local polynomial modeling of time-varying autoregressive models with application to time–frequency analysis of event-related EEG. IEEE Trans Biomed Eng. 2011;58(3):557–66. Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Biomedical Engineering, Health Science CenterShenzhen UniversityShenzhenChina

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