  We present a procedure that allows the construction of the metric
perturbations and electromagnetic four-potential, for gravitational and
electromagnetic perturbations produced by sources in Kerr spacetime. This may
include, for example, the perturbations produced by a point particle or an
extended object moving in orbit around a Kerr black hole. The construction is
carried out in the frequency domain. Previously, Chrzanowski derived the vacuum
metric perturbations and electromagnetic four-potential by applying a
differential operator to a certain potential $\Psi $. Here we construct $\Psi $
for inhomogeneous perturbations, thereby allowing the application of
Chrzanowski's method. We address this problem in two stages: First, for vacuum
perturbations (i.e. pure gravitational or electromagnetic waves), we construct
the potential from the modes of the Weyl scalars $\psi_{0}$ or $\phi_{0}$.
Second, for perturbations produced by sources, we express $\Psi $ in terms of
the mode functions of the source, i.e. the energy-momentum tensor $T_{\alpha
\beta}$ or the electromagnetic current vector $J_{\alpha}$.
