New Two-Dimensional Wigner Distribution and Ambiguity Function Associated with the Two-Dimensional Nonseparable Linear Canonical Transform

Two-dimensional Wigner distribution (2D WD) and ambiguity function (2D AF) are important tools for time–frequency analysis and signal processing, especially in the analysis of 2D chirp signals. In this paper, based on the classical 2D WD and 2D AF, a new kind of 2D WD and 2D AF associated with 2D nonseparable linear canonical transform (2D NSLCT) are proposed, namely NSLCWD and NSLCAF. The definition obtained by this method not only has the advantages of 2D NSLCT, but also has the good characteristics of 2D WD (2D AF). The emergence of the new definition also broadens the development of 2D theory to a certain extent. Then, we derive a series of important properties related to the new definition and present theoretical proof. Moreover, we find that the original 2D WD and 2D AF exist as special cases of two new definitions. In addition, the relationship between the new definition and 2D NSLCT is also the focus of our discussion. Finally, the NSLCWD and NSLCAF are applied to detect different forms of 2D chirp signals. The results confirm that our new definitions, NSLCWD and NSLCAF, are useful and effective.