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Signal averaging is the process that consists in computing a mean shape froma set of noisy signals. In the presence of geometric variability in time in thedata, the usual Euclidean mean of the raw data yields a mean pattern that doesnot reflect the typical shape of the observed signals. In this setting, it isnecessary to use alignment techniques for a precise synchronization of thesignals, and then to average the aligned data to obtain a consistent meanshape. In this paper, we study the numerical performances of Fr\'echet means ofcurves which are extensions of the usual Euclidean mean to spaces endowed withnon-Euclidean metrics. This yields a new algorithm for signal averaging withouta reference template. We apply this approach to the estimation of a mean heartcycle from ECG records.

Fr\'echet means of curves for signal averaging and application to ECG data analysis