  Sudden turn-on of a matter-wave source leads to characteristic oscillations
of the probability density which are the hallmark feature of diffraction in
time. The apodization of matter waves relies on the use of smooth aperture
functions which suppress such oscillations. The analytical dynamics arising
with different aperture functions are discussed systematically for switching-on
processes, and for single and many-pulse formation procedures. The possibility
and time scale of a revival of the diffraction-in-time pattern is also
analysed. Similar modulations in time of the pulsed output coupling in
atom-lasers are responsible for the dynamical evolution and characteristics of
the beam profile. For multiple pulses, different phase schemes and regimes are
described and compared. Strongly overlapping pulses lead to a saturated,
constant beam profile in time and space, up to the revival phenomenon.
