  Stroboscopic wavepacket basis sets [P. Bokes, F. Corsetti, R. W. Godby, Phys.
Rev. Lett. 101, 046402 (2008)] are specifically tailored for a description of
time-dependent processes in extended systems like non-periodic geometries of
various contacts consisting of solids and molecules. The explanation of the
construction of such a basis for two simple finite systems is followed by a
review of the general theory for extended systems with continuous spectrum. The
latter is further elaborated with the introduction of the interaction
representation which takes the full advantage of the time-dynamics built into
the basis. The formalism is applied to a semi-analytical example of electronic
transport through resonant tunnelling barrier in 1D. Through the time-dependent
generalisation of the Landauer formula given in terms of the Fourier expansion
of the transmission amplitude we analyze the temporal character of the onset of
the steady-state. Various time-scales in this process are shown to be directly
related to the energetic structure of the resonant barrier.
