Wavelet Frequency-Temporal Relative Phase Pattern of the Surface Electromyogram for Investigation of Intramuscular Synchronization

Abstract

Cross-correlation is often used as the primary technique to compare two biological signals. The cross-correlation technique is an effective means to measure the synchronization of two signals if the relative phases at all frequencies are distributed linearly, that is, there is a group delay. The group delay assumption of cross-correlation analysis imposes an unfavourable restriction on signals with relative phase correlation which varies at different frequencies. Traditional Fourier analysis applied to a short data segments, namely the Short Time Fourier Transform (STFT), provides phase information for each frequency component, but it is not suitable for biological signals with non-stationary statistics for which the ideal segment length is unknown. The application of a wavelet based phase analysis technique is discussed in this study. The frequency decomposition and temporally localized nature of the wavelet transform provides localized phase-frequency information for two signals. A wavelet frequency temporal relative phase pattern (WFT-RPP) technique to extract relative phase information at specific frequencies over the time course of a time-varying signal was developed. The technique was tested on simulated data and surface electromyographic (sEMG) data recorded from upper limb muscles in human subjects as they performed a series of dynamic push and pull tasks. Selected sEMG channel pairs are compared against each other using the WFT-RPP technique to extract the relative phase information and repetitive relative phase patterns for certain muscle pairs were observed. The properties of the WFT-RPP and the merits and weaknesses of using the technique for determining intermuscular sEMG synchronization is discussed.