  We propose a reliable scheme for engineering a general cavity-field state.
This is different from recently presented strategies,where the cavity is
supposed to be initially empty and the field is built up photon by photon
through resonant atom-field interactions. Here, a coherent state is previously
injected into the cavity. So, the Wigner distribution function of the desired
state is constructed from that of the initially coherent state. Such an
engineering process is achieved through an adaptation of the recently proposed
technique of projection synthesis to cavity QED phenomena.
