A unified definition for the discrete-time, discrete-frequency, and discrete-time/Frequency Wigner distributions

Various discrete definitions of the Wigner distribution (WD) for discrete-time signals have been proposed in previous works. The formulation developed in this paper leads to natural and unified definitions of discrete versions of the WD. They are directly related to the continuous and preserve most of its properties. The discretization is first considered in the time domain (DTWD), in the frequency domain (DFWD), and then in both domains simultaneously (DTFWD). In each case, the aliasing problem is studied and generalized interpolation formulas allowing the reconstruction of the continuous WD are derived. The DTFWD is particulary relevant for computer implementation of the WD.