After reviewing the well-stablished notion of black-hole perturbation theory and the concept of quasinormal modes, we present a spectral representation of solutions to relativistic wave equations based on a geometrical approach in which the constant-time surfaces extend until future null infinity. Here, we restrict ourselves to an asymptotically flat, spherically symmetric spacetime (with focus on the Reisnner-Nordstrom solution). With the help of a Laplace transformation on the wave equation in question, we provide a geometrical interpretation to known algorithms (i.e. Leaver’s approach) in addition to deriving an algorithm for obtaining all ingredients of the desired spectral decomposition, including quasi-normal modes, quasi-normal mode amplitudes, and the jump of the Laplace transform along the branch cut. The work explains the procedure extensively and includes detailed discussions of the contribution of infinite frequency modes to the early time response of the black hole and its relation to the QNM-amplitude growth rates.