  This paper reports results from numerical simulations of the gravitational
radiation emitted from non--rotating compact objects(both neutron stars and
Schwarzschild black holes) as a result of the accretion of matter. A hybrid
procedure is adopted: we evolve, in axisymmetry, the linearized equations
describing metric and fluid perturbations, coupled with a nonlinear
hydrodynamics code that calculates the motion of the accreting matter. The
initial matter distribution is shaped in the form of extended quadrupolar
shells of dust or perfect fluid. Self--gravity and radiation reaction effects
of the accreting fluid are neglected. This idealized setup is used to
understand the qualitative features appearing in the energy spectrum of the
gravitational wave emission from compact stars or black holes, subject to
accretion processes involving extended objects. A comparison for the case of
point--like particles falling radially onto black holes is also provided. Our
results show that, when the central object is a black hole, the spectrum is far
from having only one clear, monochromatic peak at the frequency of the
fundamental quasi-normal mode, but it shows a complex pattern, with
interference fringes produced by the interaction between the infalling matter
and the underlying perturbed spacetime: most of the energy is emitted at
frequencies lower than that of the fundamental mode of the black hole. Similar
results are obtained for extended shells accreting onto neutron stars, but in
this case the stellar fundamental mode is clearly excited. Our analysis shows
that the gravitational wave signal driven by accretion is influenced more by
the details and dynamics of the process, than by the quasi--normal mode
structure of the central object.
