A joint distribution approach to wave propagation and array processing

We discuss dispersive wave propagation and show that the Wigner distribution is a powerful approach because it simplifies the issues immensely. We show that the spatial time-frequency array processing formulation of Amin et al., can be viewed as a projection of a Wigner distribution in space, wavenumber, time and frequency. We also show that there is a very simple yet illuminating and accurate approximation between the Wigner distribution of a wave at two different spatial points. In particular, the Wigner distributions of the wave at two different locations are related by a frequency-dependent time-shift that depends explicitly on the dispersion relation, in a very straightforward way.