Comparison of Power Spectrum Predictors in Computing Coherence Functions for Intracortical EEG Signals

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Aydin S.

ANNALS OF BIOMEDICAL ENGINEERING, vol.37, pp.192-200, 2009 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 37
  • Publication Date: 2009
  • Doi Number: 10.1007/s10439-008-9579-8
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.192-200
  • Keywords: Coherence function, EEG synchronization, AR model, PSD predictors, SYNCHRONIZATION
  • Hacettepe University Affiliated: No


The present study compares two Auto-Regressive (AR) model based (Burg Method (BM) and Yule Walker Method) and two subspace based (Eigen Method and Multiple Signal Classification Method) power spectral density predictors in computing the Coherence Function (CF) to observe EEG synchronization between right and left hemispheres. For this purpose, two channels intracortical EEG series recorded from WAG/Rij rats (a genetic model for human absence epilepsy) are analyzed. In tests, AR model-based predictors result the close performance such that the CF estimations are sensitive to the AR model order. Dealing with the subspace-based predictors; certain peaks in CF estimations can also be detected in case of low noise subspace dimension. Besides, they are more computational complexity. In conclusion, high order BM is proposed in EEG synchronization. The results support that each EEG sequence probably meets a high order AR model where the dimension of the related noise subspace is relatively low in comparison to the model order.


Overall results show that Set A consists of pre-lesion EEG series, whereas the others are related to epileptic lesions: There are more lesions in both Set D and Set E in comparison to Set B and Set C. All data sets show sleep-wave like oscillations.

Parametric PSD predictors (BM, YWM) are based on the AR model. The data is not windowed in performing these methods. Therefore, application of them eliminates the assumption that the autocorrelation sequence is zero outside the window. The BM and YWM are applied to short time EEG series at low SNR. It is stated that these predictors exhibit spectral line splitting in case of high SNR and sensitive to the initial phase in case of sinusoidal noisy signals.10 In the present application, the high order (p ≥ 20) parametric predictors provide us to useful CF estimations in the present EE synchronization where the number of FFT is 128.

Subspace-based PSD predictors (EM, MM) are based on an eigen-decomposition of the correlation matrix of the noisy data. These methods assume that the data consists of some real sinusoids and then the frequencies of sinusoidal components are estimated. For the data at low SNR, it is difficult to determine the number of principal eigenvectors.10 In the present case study, subspace-based predictors can also provide useful estimations when the empirically selected subspace dimension is low (K = 10) such that the EM is less sensitive to this parameter. Therefore, the low dimensional EM can also be proposed in EEG synchronization for short time EEG series at low SNR. However, adequate estimations are obtained when the number of FFT is 256 at least.

In conclusion, it can be said that high order AR model-based predictors are more suitable than the subspace-based predictors. The reasons of this superiority can be summarized as: When the sampling frequency is low, short epochs are advised in EEG analysis as best guarantee for wide sense stationary. Therefore, a stable AR model can be yielded by the parametric estimations. High frequency resolution can be obtained by using both BM and YWM without consuming a large memory.

Note that, the recent results support that the short time intracortical EEG series can be represented by a high order (p ≥ 20) AR model as indicated in past literature.2,6 In the former EEG study, p = 10 was provided for successful AR modeling with high accuracy. It was suggested in the latter study that p = 30 is the best order to verify normality in EEG series collected during anesthesia.