An investigation of surface electromyogram (EMG) of antagonist muscles in patients with Parkinson's disease (PD) and essential tremor (ET) was carried out. A comparison was made between two methods for calculating instantaneous phases of envelopes of EMG signals. The first method is based on calculating the ridges of wavelet spectrograms of envelopes of EMG signals. The second method is based on using the Hilbert transform. Statistically significant difference between the mean values of the phase difference of the EMG signal envelopes was found in the antagonist muscles in PD and ET patients.

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Classical methods for signal analysis are limited to describe either the global features or the local features. This paper proposes a new mathematically founded concept called wave train electrical activity analysis to investigate both local and global features in biomedical signals simultaneously. First, mathematical means for the investigation of the properties of the wave trains observed in the biomedical signals, histograms of wave train parameters and AUC diagrams, are discussed. Second, several examples of the practical application of the method of the wave train electrical activity analysis are considered. Specifically, its application is demonstrated in the investigation of epileptic seizures as well as the differential diagnosis of neurodegenerative diseases, Parkinson’s disease and essential tremor.