Features of a Discrete Wigner

We discuss important attributes of a discrete Wigner distribution derived using a group-theoretic approach. The nature of this approach enables this distribution to satisfy numerous mathematical properties, including marginals and the Weyl correspondence. A few issues concerning the relationship of this distribution with group theory are explored in detail. In particular , the discrete distribution depends on the parity of the signal length i.e. odd distributions are computed diierently than even ones. This dependence is explained and a surprising consequence is demonstrated. We also describe how this distribution satisses covariance properties. The three fundamental types of sym-plectic transformations (dilation/compression, shearing, and rotation) are are given and interpreted for this discrete case.