Coefficient of Cross Correlation and the Time Domain Correspondence

Time histories of neuromuscular and mechanical variables of human motion are often compared by using discrete timing events (onset, offset, time to peak, zero crossing, etc). The determination of these discrete timing points is often subjective and their interpretation can cause confusion when attempting to compare patterns. In this technical note, cross correlation and the 95% confidence interval of its maximum value are proposed as an objective means of pattern recognition and comparison. EMG patterns of cycling at different cadences were used as an example to demonstrate the effectiveness of this cross correlation method in identification of changes between conditions. Using a standard method of threshold identification, different onset and offset values can be found by using different thresholds, and the sequence of the offset timings between conditions can change. This is a clear indication of the inherent subjectivity with these discrete timing methods. In contrast, calculation of cross correlation for incremental phase shifts permits the identification of a maximal value that is an objective measure of the actual phase shifting between the two time series. Further, calculation of the 95% confidence interval allows one to determine whether the phase shifting is statistically significant. The application of this method is not limited to EMG pattern comparison, and can also be applied to other time histories such as kinematic and kinetic parameters of human motion.