Averaging of strongly varying signals

Forces acting at the hip joint during a given activity often vary much between trials and subjects. Large variations are also encountered in many other biomechanical signals. Arithmetic mean curves then lead to falsified results, especially if extreme values occur at very different times. A method was developed for calculating a typical curve from such varying, time dependent signals. All cycle times are first averaged and the signals are then more and more smoothed using Fourier series with decreasing numbers of harmonics. The remaining extrema are analysed to decide whether they are typical for all curves or not. This is done by systematically cutting off a varying number of extrema at the beginning or end of all curves. After this an equal number of extrema remains in all curves. These extrema are then shifted to average positions in time, i.e. the times between consecutive extrema are compressed or expanded, and the standard deviation of all curves is calculated. The combination of cut off extrema which results in the smallest standard deviation is then used further on. The same time distortions are applied to the original curves and their arithmetic mean finally results in the typical signal. This procedure is well suited for averaging hip contact forces and other varying signals as long as their complexity and variation is not extremely large.