Discrete Bai distribution function and its sampling requirements

In recent years, many phase space distributions have been proposed, and one of the more independently interesting is the Bai distribution function (BDF). The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function, and be applied in linear frequency modulated signal parameter estimation and optical partial coherence areas. Currently, the BDF is only defined for continuous signals. However, for both simulation and experimental purposes, the signals must be discrete. This necessitates the development of a BDF analysis workflow for discrete signals. In this work, we analyze the sampling requirements imposed by the BDF and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts. Our results permit more accurate simulations using BDFs, which will be useful in applying them to problems such as partial coherence.