Abstract
Though coherence, a classical method to describe the linear correlation between two time series, has wide-ranging applications, from economics to neuroscience, it fails to illustrate the inherently multi-time scales-based correlations. In this paper, we proposed a multiscale-like coherence model, defined as composite multiscale coherence (CMSC) by combining the kth coarse-grain processing with the coherence. We made a comparison with the multiscale coherence (MSC) with coarse-grain process in numerical data to compare the sensitivity profiles to the coupling strength, data length and white Gaussian noise. After that, we applied the proposed model to explore the functional corticomuscular coupling (FCMC) by analyzing the correlation between the EEG and EMG signals. Simulation results reflected that the CMSC method were sensitive to the coupling strength, data length and the white Gaussian noise, and presented more stability along the time scale compared to the MSC method. Our application of CMSC methods on the EEG and EMG signals indicated that the FCMC was of multi-time scale characteristics and higher coherence mainly consisted in the alpha and beta bands at about scale 10, though significant area showed a gradual decline with the scale increasing. Further comparison indicated that both models are equally effective to describe the multiscale characteristics of the FCMC at lower time scales, while some differences emerge at the high time scales. Both simulation and experimental data demonstrate the effectiveness of the proposed multiscale-like model to describe the multiscale correlation between two time series. This study extends the relative researches on the FCMC to the multi-time scale.
Published Version
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