Cross-correlation between EMG and center of gravity during quiet stance: theory and simulations

Several signal processing tools have been employed in the experimental study of the postural control system in humans. Among them, the cross-correlation function has been used to analyze the time relationship between signals such as the electromyogram and the horizontal projection of the center of gravity. The common finding is that the electromyogram precedes the biomechanical signal, a result that has been interpreted in different ways, for example, the existence of feedforward control or the preponderance of a velocity feedback. It is shown here, analytically and by simulation, that the cross-correlation function is dependent in a complicated way on system parameters and on noise spectra. Results similar to those found experimentally, e.g., electromyogram preceding the biomechanical signal may be obtained in a postural control model without any feedforward control and without any velocity feedback. Therefore, correct interpretations of experimentally obtained cross-correlation functions may require additional information about the system. The results extend to other biomedical applications where two signals from a closed loop system are cross-correlated.