  We report development of a code to calculate the scalar self-force on a
scalar-charged particle moving on generic bound orbits in the Kerr spacetime.
The scalar self-force model allows rapid development of computational
techniques relevant to generic gravitational extreme-mass-ratio inspirals
(EMRIs). Our frequency-domain calculations are made with arbitrary numerical
precision code written in \textsc{Mathematica}. We extend spectral source
integration techniques to the Kerr spacetime, increasing computational
efficiency. We model orbits with nearly arbitrary inclinations
$0\leq\iota<\pi/2$ and eccentricities up to $e \lesssim 0.8$. This effort
extends earlier work by Warburton and Barack where motion was restricted to the
equatorial plane or to inclined spherical orbits. Consistent with a recent
discovery by Thornburg and Wardell \cite{ThorWard17} in time-domain
calculations, we observe self-force oscillations during the radially-outbound
portion of highly eccentric orbits around a rapidly rotating black hole. As
noted previously, these oscillations reflect coupling into the self-force by
quasinormal modes excited during pericenter passage. Our results confirm the
effect with a frequency-domain code. \emph{More importantly, we find that
quasinormal bursts (QNBs) appear directly in the waveform following each
periastron passage.} These faint bursts are shown to be a superposition of the
least-damped overtone (i.e., fundamental) of at least four ($l=m \le 4$)
quasinormal modes. Our results suggest that QNBs should appear in gravitational
waveforms, and thus provide a gauge-invariant signal. Potentially observable in
high signal-to-noise ratio EMRIs, QNBs would provide high-frequency components
to the parameter estimation problem that would complement low-frequency
elements of the waveform.
