  We present a method to construct signatures of periodic-like data. Based on
topological considerations, our construction encodes information about the
order and values of local extrema. Its main strength is robustness to
reparametrisation of the observed signal, so that it depends only on the form
of the periodic function. The signature converges as the observation contains
increasingly many periods. We show that it can be estimated from the
observation of a single time series using bootstrap techniques.
