  Despite the indisputable merits of the Wigner phase-space formulation, it has
not been widely explored for systems with SU(1,1) symmetry, as a simple
operational definition of the Wigner function has proved elusive in this case.
We capitalize on the unique properties of the parity operator, to derive in a
consistent way a \emph{bona fide} SU(1,1) Wigner function that faithfully
parallels the structure of its continuous-variable counterpart. We propose an
optical scheme, involving a squeezer and photon-number-resolving detectors,
that allows for direct point-by-point sampling of that Wigner function. This
provides an adequate framework to represent SU(1,1) states satisfactorily.
