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