Shift covariant time-frequency distributions of discrete signals

Many commonly used time-frequency distributions are members of the Cohen cl ass, This class is defined for continuous signals, and since time-frequency distributions in the Cohen class are quadratic, the formulation for discre te signals is not straightforward. The Cohen class can be derived as the cl ass of all quadratic time-frequency distributions that are covariant to tim e shifts and frequency shifts. In this paper, we extend this method to thre e types of discrete signals to derive what we will call the discrete Cohen classes. The properties of the discrete Cohen classes differ from those of the original Cohen class. To illustrate these properties, we also provide e xplicit relationships between the classical Wigner distribution and the dis crete Cohen classes.