  The ability to detect and scrutinize gravitational waves from the merger and
coalescence of compact binaries opens up the possibility to perform tests of
fundamental physics. One such test concerns the dark, nature of compact
objects: are they really black holes? It was recently pointed out that the
absence of horizons -- while keeping the external geometry very close to that
of General Relativity -- would manifest itself in a series of echoes in
gravitational wave signals. The observation of echoes by LIGO/Virgo or upcoming
facilities would likely inform us on quantum gravity effects or unseen types of
matter. Detection of such signals is in principle feasible with relatively
simple tools, but would benefit enormously from accurate templates. Here we
analytically individualize each echo waveform and show that it can be written
as a Dyson series, for arbitrary effective potential and boundary conditions.
We further apply the formalism to explicitly determine the echoes of a simple
toy model: the Dirac delta potential. Our results allow to read off a few known
features of echoes and may find application in the modelling for data analysis.
