Discrete-time, discrete-frequency time-frequency representations

A discrete-time, discrete-frequency Wigner distribution is derived using a group-theoretic approach. It is based upon a study of the Heisenberg group generated by the integers mod N, which represents the group of discrete-time and discrete-frequency shifts. The resulting Wigner distribution satisfies several desired properties. An example demonstrates that it is a full-band time-frequency representation, and, as such, does not require special sampling techniques to suppress aliasing. It also exhibits some interesting and unexpected interference properties. The new distribution is compared with other discrete-time, discrete-frequency Wigner distributions proposed in the literature.