Pulse propagation and classification in time/frequency and position/wave number phase space.

Abstract

In dispersive pulse propagation, different frequencies travel at different velocities, and, hence, the pulse is nonstationary in that it changes over time and distance. Joint phase space representations, such as the Wigner distribution and the spectrogram, are often employed to study nonstationary signals, and, hence, it is natural to consider their application to dispersive propagation. We consider position/wave number and time/frequency representations of a pulse propagating with dispersion and damping. We give the Wigner distribution of the pulse at a particular time/position in terms of the Wigner distribution of the initial pulse. Approximations of this result are derived, which are accurate and remarkably simple to apply, as compared to the stationary phase approximation. The approximations provide insights as well, in that they show how each point in phase space propagates at the group velocity, and lead to new features for classification, based on local phase space moments, that are invariant to t...