Time-frequency approach to radar, sonar and seismic wave propagation with dispersion and attenuation

In many physical situations that involve wave propagation there is dispersion and attenuation. Examples include sonar in shallow water, underground radar, seismic wave propagation, fibre optics, among many others. The author shows that phase-space methods are particularly suited to study propagation with dispersion since in such situations the velocity of propagation is frequency dependent. Depending on the situation the phase space may be time-frequency or position-wavenumber. The author derive explicit expressions for the Wigner distribution for both cases and how it evolves with time are derived. The application to the propagation of noise fields is also discussed.