  Signal averaging is the process that consists in computing a mean shape from
a set of noisy signals. In the presence of geometric variability in time in the
data, the usual Euclidean mean of the raw data yields a mean pattern that does
not reflect the typical shape of the observed signals. In this setting, it is
necessary to use alignment techniques for a precise synchronization of the
signals, and then to average the aligned data to obtain a consistent mean
shape. In this paper, we study the numerical performances of Fr\'echet means of
curves which are extensions of the usual Euclidean mean to spaces endowed with
non-Euclidean metrics. This yields a new algorithm for signal averaging without
a reference template. We apply this approach to the estimation of a mean heart
cycle from ECG records.
