  A novel approach for analysing cardiac rhythm data is presented in this
paper. Heartbeats are decomposed into the five fundamental $P$, $Q$, $R$, $S$
and $T$ waves plus an error term to account for artefacts in the data which
provides a meaningful, physical interpretation of the heart's electric system.
The morphology of each wave is concisely described using four parameters that
allow to all the different patterns in heartbeats be characterized and thus
differentiated
  This multi-purpose approach solves such questions as the extraction of
interpretable features, the detection of the fiducial marks of the fundamental
waves, or the generation of synthetic data and the denoising of signals. Yet,
the greatest benefit from this new discovery will be the automatic diagnosis of
heart anomalies as well as other clinical uses with great advantages compared
to the rigid, vulnerable and black box machine learning procedures, widely used
in medical devices.
  The paper shows the enormous potential of the method in practice;
specifically, the capability to discriminate subjects, characterize
morphologies and detect the fiducial marks (reference points) are validated
numerically using simulated and real data, thus proving that it outperforms its
competitors.
