Phase Space Approach and Approximations for Wave Propagation

We consider wave propagation in a dispersive medium with damping. We have previously shown that a significant simplification occurs if one formulates the wave propagation problem in phase space. In our previous work, we used the Wigner distribution as the phase space representation. In this paper, we extend this approach to other phase space distributions, including the well-known spectrogram (or lofargram), and also to the ambiguity function.