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High-resolution time–frequency representation of EEG data using multi-scale wavelets

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  • Yang Li
  • Wei-Gang Cui
  • Mei-Lin Luo
  • Ke Li
  • Lina Wang

Abstract

An efficient time-varying autoregressive (TVAR) modelling scheme that expands the time-varying parameters onto the multi-scale wavelet basis functions is presented for modelling nonstationary signals and with applications to time–frequency analysis (TFA) of electroencephalogram (EEG) signals. In the new parametric modelling framework, the time-dependent parameters of the TVAR model are locally represented by using a novel multi-scale wavelet decomposition scheme, which can allow the capability to capture the smooth trends as well as track the abrupt changes of time-varying parameters simultaneously. A forward orthogonal least square (FOLS) algorithm aided by mutual information criteria are then applied for sparse model term selection and parameter estimation. Two simulation examples illustrate that the performance of the proposed multi-scale wavelet basis functions outperforms the only single-scale wavelet basis functions or Kalman filter algorithm for many nonstationary processes. Furthermore, an application of the proposed method to a real EEG signal demonstrates the new approach can provide highly time-dependent spectral resolution capability.

Suggested Citation

  • Yang Li & Wei-Gang Cui & Mei-Lin Luo & Ke Li & Lina Wang, 2017. "High-resolution time–frequency representation of EEG data using multi-scale wavelets," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(12), pages 2658-2668, September.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:12:p:2658-2668
    DOI: 10.1080/00207721.2017.1340986
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    1. Dahlhaus, R. & Neumann, M. & Von Sachs, R., 1997. "Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes," SFB 373 Discussion Papers 1997,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Shu Wang & Hua-Liang Wei & Daniel Coca & Stephen Billings, 2013. "Model term selection for spatio-temporal system identification using mutual information," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(2), pages 223-231.
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