  Parametric resonance in a single-field inflationary model with a periodic
structure on the potential gives rise to curvature perturbations with large
amplitudes on small scales, which could result in observable primordial black
holes (PBHs) and concomitant gravitational waves (GWs) induced by curvature
perturbations in the radiation-dominated era. In such a model, GWs associated
with the PBH formation were investigated in Ref. [1]. In this paper, we
consider a stochastic GW background sourced by inflaton perturbations
resonantly amplified during inflation. We compute the energy spectra of induced
GWs produced both during inflation and in the radiation-dominated era, and find
that the peak of the energy spectrum of the former is much higher than that of
the latter, but is located at a lower frequency. Moreover, the energy spectrum
of induced GWs produced during inflation exhibits a unique oscillating
character in the ultraviolet region. Both the stochastic GW backgrounds are
expected to be detected by future space-based laser interferometers.
