  We study theoretically the dipole radiation of a hydrogen atom driven by an
intense sub-cycle pulse. The time-dependent Schr\"odinger equation for the
system is solved by ab initio calculation to obtain the dipole response.
Remarkably, a narrowband emission lasting longer than the driving pulse appears
at a frequency just above the ionization threshold. An additional calculation
using the strong field approximation also recovers this emission, which
suggests that it corresponds to the oscillation of nearly-bound electrons that
behave similarly to Rydberg electrons. The predicted phenomenon is unique to
ultrashort driving pulses but not specific to any particular atomic structure.
