  We present a method to determine the shot noise in quantum systems from
knowledge of their time evolution - the latter being obtained using numerical
simulation techniques. While our ultimate goal is the study of interacting
systems, the main issues for the numerical determination of the noise do not
depend on the interactions. To discuss them, we concentrate on the single
resonant level model, which consists in a single impurity attached to
non-interacting leads, with spinless fermions. We use exact diagonalisations
(ED) to obtain time evolution, and are able to use known analytic results as
benchmarks. We obtain a complete characterization of finite size effects at
zero frequency, where we find that the finite size corrections scale $\propto
G^2$, $G$ the differential conductance. We also discuss finite frequency noise,
as well as the effects of damping in the leads.
