  We consider various filtered time discretizations of the periodic
Korteweg--de Vries equation: a filtered exponential integrator, a filtered Lie
splitting scheme as well as a filtered resonance based discretisation and
establish convergence error estimates at low regularity. Our analysis is based
on discrete Bourgain spaces and allows to prove convergence in $L^2$ for rough
data $u_{0} \in H^s,$ $s>0$ with an explicit convergence rate.
