  We advocate for an alternative description of gravitational radiation from
black holes based on complex angular momentum techniques (analytic continuation
of partial wave expansions, duality of the ${\cal S}$-matrix and effective
resummations involving its Regge poles and the associated residues, Regge
trajectories, semiclassical interpretations, etc.). Such techniques, which
proved to be very helpful in various areas of physics to describe and analyze
resonant scattering, were only marginally used in the context of black hole
physics. Here, by considering the multipolar waveform generated by a massive
particle falling radially from infinity into a Schwarzschild black hole, we
show that they could play a fundamental role in gravitational-wave physics.
More precisely, from the multipole expansion defining the Weyl scalar $\Psi_4$,
we extract the Fourier transform of a sum over Regge poles and their residues
which can be evaluated numerically from the associated Regge trajectories. This
Regge pole approximation permits us to reconstruct, for an arbitrary direction
of observation, a large part of the multipolar waveform $\Psi_4$. In
particular, it can reproduce with very good agreement the quasinormal ringdown
as well as with rather good agreement the tail of the signal. This is achieved
even if we take into account only one Regge pole and, if a large number of
modes are excited, the result can be improved by considering additional poles.
Moreover, while quasinormal-mode contributions do not provide physically
relevant results at "early times" due to their exponentially divergent behavior
as time decreases, it is not necessary to determine from physical
considerations a starting time for the Regge ringdown.
