  The deviations of non-linear perturbations of black holes from the linear
case are important in the context of ringdown signals with large
signal-to-noise ratio. To facilitate a comparison between the two we derive
several results of linear perturbation theory in coordinates which may be
adopted in numerical work. Specifically, our results are derived in Kerr-Schild
coordinates adjusted by a general height function. In the first part of the
paper we address the questions: for an initial configuration of a massless
scalar field, what is the amplitude of the excited quasinormal mode (QNM) for
any observer outside outside the event horizon, and furthermore what is the
resulting tail contribution? This is done by constructing the full Green's
function for the problem with exact solutions of the confluent Heun equation
satisfying appropriate boundary conditions. In the second part of the paper, we
detail new developments to our pseudospectral numerical relativity code bamps
to handle scalar fields. In the linear regime we employ precisely the
Kerr-Schild coordinates treated by our previous analysis. In particular, we
evolve pure QNM type initial data along with several other types of initial
data and report on the presence of overtone modes in the signal.
