  We use a noncommutative generalization of Fourier analysis to define a broad
class of pseudo-probability representations, which includes the known bosonic
and discrete Wigner functions. We characterize the groups of quantum unitary
operations which correspond to phase-space transformations, generalizing
Gaussian and Clifford operations. As examples, we find Wigner representations
for fermions, hard-core bosons, and angle-number systems.
