Coherent states in finite-dimensional Hilbert space and their Wigner representation

We consider two definitions of coherent states in a finite-dimensional Hilbert space based on (i) truncation of the usual coherent state expansion and (ii) generalization of the displacement operator acting on vacuum. The number-phase Wigner function is computed for such states. Analytical results and numerically computed graphs are presented. Special attention is paid to two-level slates and to their Stokes parameter representations.