  This paper is based on recent work which provided an exact analytical
description of scattering fidelity experiments with a microwave cavity under
the variation of an antenna coupling [K\"ober et al., Phys. Rev. E 82, 036207
(2010)]. It is shown that this description can also be used to predict the
decay of the fidelity amplitude for arbitrary Hermitian perturbations of a
closed system. Two applications are presented: First, the known result for
global perturbations is re-derived, and second, the exact analytical expression
for the perturbation due to a moving S-wave scatterer is worked out. The latter
is compared to measured data from microwave experiments, which have been
reported some time ago. Finally, we generalize an important relation between
fidelity decay and parametric level correlations to arbitrary perturbations.
