Wigner distributions and ambiguity functions of 2-D quaternionic and Monogenic Signals
Signal Processing, IEEE Transactions on, 53 (8):
3111--3128 (August 2005)DOI: 10.1109/TSP.2005.851134
Abstract
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.