On the existence of discrete Wigner distributions

Among the myriad of time-frequency distributions, the Wigner distribution s tands alone in satisfying many desirable mathematical propel ties. Attempts to extend definitions of the Wigner distribution to discrete signals have not been completely successful. In this letter, we propose an alternative d efinition for the Wigner distribution, which has a clear extension to discr ete signals. Under this definition, we show that the Wigner distribution do es not exist for certain classes of discrete signals.