Averaging of strongly varying signals

Forces acting at the hip joint during a given activity often vary much betw een trials and subjects. Large variations are also encountered in many othe r biomechanical signals. Arithmetic mean curves then lead to falsified resu lts, especially if extreme values occur at very different times. A method w as developed for calculating a typical curve from such varying, time depend ent signals. All cycle times are first averaged and the signals are then mo re and more smoothed using Fourier series with decreasing numbers of harmon ics. 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 Equ al number of extrema remains in all curves. These extrema are then shifted to average positions in time, i.e. the times between consecutive extrema ar e compressed or expanded, and the standard deviation of all curves is calcu lated. The combination of cut off extrema which results in the smallest sta ndard deviation is then used further on. The same time distortions are appl ied to the original curves and their arithmetic mean finally results in the typical signal. This procedure is well suited for averaging hip contact fo rces and other varying signals as long as their complexity and variation is not extremely large.