Shift covariant time-frequency distributions of discrete signals

Many commonly used time-frequency distributions are members of the Cohen class, This class is defined for continuous signals, and since time-frequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic time-frequency distributions that are covariant to time shifts and frequency shifts. In this paper, we extend this method to three 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 explicit relationships between the classical Wigner distribution and the discrete Cohen classes.