Wigner distributions and ambiguity functions of 2-D quaternionic and monogenic signals

The paper presents new notions of Wigner distributions and corresponding ambiguity functions defined by quaternionic Fourier transforms of correlation products of recently defined quaternionic and monogenic two-dimensional (2-D) signals. The properties of new defined Wigner distributions are compared with Wigner distributions of 2-D analytic signals with single-quadrant spectra. It is well known that Wigner distributions of complex signals are real functions. Differently, the Wigner distributions of quaternionic and monogenic signals may be quaternionic-valued functions. However, it may happen that some 2-D slices of 4-D Wigner distributions are real functions.