We consider the analytically solvable model of a Gaussian pulse tunneling through a transmission resonance with a Breit-Wigner characteristic. The solution allows for the identification of two opposite pulse propagation regimes: if the resonance is broad compared to the energetic width of the incident Gaussian pulse a weakly deformed and slightly delayed transmitted Gaussian pulse is found. In the opposite limit of a narrow resonance the dying out of the transmitted pulse is dominated by the slow exponential decay characteristic of a quasi-bound state with a long life time (decaying state). We discuss the limitation of the achievable pulse transfer rate resulting from the slow decay. Finally, it is demonstrated that for narrow resonances a small second component is superimposed to the exponential decay which leads to characteristic interference oscillations.

6 pages, 4 figures