  Following a general method proposed earlier, we construct here Wigner
functions defined on coadjoint orbits of a class of semidirect product groups.
The groups in question are such that their unitary duals consist purely of
representations from the discrete series and each unitary irreducible
representation is associated with a coadjoint orbit. The set of all coadjoint
orbits (hence UIRs) is finite and their union is dense in the dual of the Lie
algebra. The simple structure of the groups and the orbits enables us to
compute the various quantities appearing in the definition of the Wigner
function explicitly. Possible use of the Wigner functions so constructed, in
image analysis and quantum optical measurements, is suggested.
