Dynamical correlation of non-stationary signals in time domain-A comparative study

In a thorough study, the multitaper (MTM) and the extended continuous wavelet-transform (CWT) coherence-analysis methods were compared in terms of there application in determining the dynamics from the electroencephalogram (EEG) and electromyogram (EMG) signals of patients with Parkinsonian tremor. The main aim of the study in a biological point of view is to analyze whether the basic tremor frequency and its first harmonic frequency of Parkinsonian tremor are really harmonically related or are in fact distinct processes. The extension of the CWT is achieved by using a Morlet wavelet as the analysis window with an adjustable relative bandwidth which gives the flexibility in setting a desired frequency resolution. In order to obtain a perspective view of the two methods, they were applied to two different model signals to determine their actual threshold in detecting short-lived changes in the analysis of non-stationary signals and to determine their noise thresholds by adding external noise to the signals to test the reduction in coherence to be not merely due to the random fluctuations in stochastic signals. Beyond applying an autoregressive 2nd-order and a coupled van der Pol model system, however, also true EEG and EMG data from five Parkinson patients were used. The results were compared in terms of the time and frequency resolutions of these two methods, and it was determined that the multitaper method was able to detect reduction in power and coherence as short as 1 s. The extended CWT analysis only revealed gaps that were longer than 3 s. The time gaps in the coherence indicate the loss of connection between the cortex and muscle during the respective time intervals. This more accurate analysis of the MTM was also seen in the dynamical EEG EMG coherence at the tremor frequency and its first harmonic of Parkinsonian patients. In terms of our biological aim, this shows distinct prevalence of the corticomuscular coupling at those frequencies over time. Applying this method to biological data reveals important aspects about their dynamics, e.g., the distinct dynamics between basic frequency and first harmonic frequency over time in Parkinsonian tremor. (C) 2010 Elsevier Ltd. All rights reserved.