The possibility of calculating vibrationally resolved spectra from
very short numerically exact and approximate quantum dynamical
propagations using the new Filter-Diagonalization
method is explored. The benchmark process under study concerns
electron photodetachment in the
I-Ar2 complex. Comparison with results obtained from long time
propagations and with experiment reveals the power of the 
Filter-Diagonalization scheme. Using the new methodology it now becomes
possible to extract positions of spectral 
peaks for large polyatomic systems from 
approximate quantum propagations e.g., by means of the 
recently developed Classical Separable
Potential approach.