The Spatial Equivalence Between Wavelet Decomposition and Phase Space Embedding of EEG

Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of EEG is essentially a projection of EEG chaotic attractor onto the wavelet space opened by wavelet filter vectors, which is in correspondence with the phase space embedding of the same EEG. In other words, wavelet decomposition and phase space embedding are equivalent in methodology. Our experimental results show that in both the wavelet space and the embedded space the structure of phase trajectory of EEG is similar to each other. These results demonstrate that wavelet decomposition is effective on characterizing EEG time series.

The Spatial Equivalence Between Wavelet Decomposition and Phase Space Embedding of EEG

Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of EEG is essentially a projection of EEG chaotic attractor onto the wavelet space opened by wavelet filter vectors, which is in correspondence with the phase space embedding of the same EEG. In other words, wavelet decomposition and phase space embedding are equivalent in methodology. Our experimental results show that in both the wavelet space and the embedded space the structure of phase trajectory of EEG is similar to each other. These results demonstrate that wavelet decomposition is effective on characterizing EEG time series.