  We formulate continuous time quantum walks (CTQW) in a discrete quantum
mechanical phase space. We define and calculate the Wigner function (WF) and
its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF
of the CTQW shows characteristic features in phase space. Revivals of the
probability distributions found for continuous and for discrete quantum carpets
do manifest themselves as characteristic patterns in phase space.
