Discrete time-frequency characterizations of dispersive linear time-varying systems

A class of linear time-varying systems can be characterized by dispersive signal transformations, such as nonlinear shifts in the phase of the propagating signal, causing different frequencies to be shifted in time by different amounts. In this paper, we propose a discrete time-frequency model to decompose the dispersive system output into discrete dispersive frequency shifts and generalized time shifts, weighted by a smoothed and sampled version of the dispersive spreading function. The discretization formulation is obtained from the discrete narrowband system model through a unitary warping relation between the narrowband and dispersive spreading functions. This warping relation depends on the nonlinear phase transformations induced by the dispersive system. In order to demonstrate the effectiveness of the proposed discrete characterization, we investigate acoustic transmission over shallow water environments that suffers from severe degradations as a result of modal frequency dispersions and multipath fading. Using numerical results, we demonstrate that the discrete dispersive model can lead to a joint multipath-dispersion diversity that we achieve by properly designing the transmitted waveform and the reception scheme to match the dispersive environment characteristics.