Features of a discrete Wigner distribution

Abstract

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 (1964) 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 differently than even ones. This dependence is explained and a surprising consequence is demonstrated. We also describe how this distribution satisfies covariance properties. The three fundamental types of symplectic transformations (dilation/compression, shearing, and rotation) are are given and interpreted for this discrete case.