On the existence of discrete Wigner distributions

Among the myriad of time-frequency distributions, the Wigner distribution stands alone in satisfying many desirable mathematical properties. Attempts to extend definitions of the Wigner distribution to discrete signals have not been completely successful. In this letter, we propose an alternative definition for the Wigner distribution, which has a clear extension to discrete signals. Under this definition, we show that the Wigner distribution does not exist for certain classes of discrete signals.