Despite the rapid progress of medical technology and measuring instruments, electroencephalograph (EEG) signal is still too complicated to be interpreted and correlated to various physiological, mental, psychological and conscious states. Hence, a number of researches are devoted to the development of different algorithms for exploring the spatio-temporal-spectral features embedded in EEG. Up to now, the phase property is seldom studied. Nevertheless, the spatial phase relation among EEG recording sites may reflect the source focalization of brain activity. This thesis presents our results of analyzing the phase structure of multi-channel electroencephalogram. This study analyzed the phase structures of 30-channel Zen-meditation EEG (experimental group) and resting EEG (control group) and compared the results. Firstly, instantaneous phase of each EEG channel was estimated by discrete Hilbert transform (DHT). For any given time instant, thirty phases were computed for 30 EEG channels. Since the bilateral symmetry and frontal-posterior relation are important features in EEG study, we then calculated the gradient phase differences between EEG channels located along the transversal (trans electrode array) and longitudinal (chain electrode array) directions. As a consequence, we obtained a bunch of curves named as trans phase-difference (PD) curves and chain PD curves. We observed the linear behavior of PD curves. To further quantify the linear feature, line fitting based on linear regression was applied to PD curves. The slope and resulted R value are compared. Finally, the phase structure property of alpha component was studied. Alpha rhythm was extracted by CWT- (Continuous wavelet transform) based bandpass filter. The same scheme as described above was adopted to obtain the trans and chain PD curves. Histograms of the slopes of alpha PD curves were compared between Zen-meditation EEG and resting EEG. The results reveal that most alpha PD curves of Zen-meditation curves have the slope close to 0
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ABSTRACT ii 目錄 v 表目錄 vii 圖目錄 viii Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Scope of this Thesis 4 Chapter 2 Theories and Methods 5 2-1 Introduction of EEG 5 2-2 Continuous Wavelet Transform 8 2.3 Instantaneous phase analysis 10 2.3.1 Introduction to HHT 10 2.3.2 Discrete Hilbert transform (DHT) 12 2.4 Line fitting 14 2.4.1 Least square method 14 2.4.2 R-squared(R2) 15 2.4.3 Standard error of the estimate (S) 16 Chapter 3 Experiment and Signal Analysis 18 3.1 Experimental Setup and Procedure 18 3.1.1 Protocol 18 3.1.2 Signal Acquisition 18 3.2 Signal analysis 20 3.2.1 Phase difference 20 3.3 Line fitting and R-squared (R2) 24 Chapter 4 Result 27 4.1 Running phase differences of Zen-meditation EEG 27 4.2 Running phase differences of resting EEG (0827) 33 4.3 Linear regression analysis 36 4.4 Alpha wave 39 4.5 Comparison of PD slope histograms in alpha band between Zen-meditation and resting EEG 42 Chapter 5 Conclusion 50 5.1 Conclusion 50 5.2 Future study 51 參考文獻 53 Appendix A 55 Continuous Hilbert transform 55
