Discrete Time-Frequency Characterizations of Dispersive Linear Time-Varying Systems

Abstract

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.

Source localization on solids utilizing time-frequency analysis of parameterized warped signals

“…These non-linear functions are specific to the nature of the channel through which the signal propagates. Such transformations can be modeled using warping-based time-frequency resampling of the original signals [19].…”

Time-Frequency Characterization and Receiver Waveform Design for Shallow Water Environments

“…1 Note that here, and for the remainder of the manuscript, we assume that the frequencies f are normalized using a reference frequency fr > 0.…”

“…Dispersive linear time-varying (LTV) systems can cause different frequencies to be shifted in time by different amounts [1], [2]. Such dispersive signal transformations are specific to the nature of the system or environment that the signal propagates through.…”

“…In [16], time-reversal was applied to multiple-input multiple-output (MIMO) shallow water communications. On the other hand, in [1], a characterization of the shallow water system was considered using a time-frequency approach. In particular, this characterization matched the dispersive signal transformation caused on the transmitted waveforms.…”

Time-frequency-phase tracking approach : Application to underwater signals in a passive context

“…Therefore, analyzing underwater mammal's vocalizations provides rich information concerning the impact of military activities on the behaviour of marine species. In addition, when the coastal activities are considered, the swallow water propagation must be considered, implying, at very low frequencies, the study of dispersion phenomena [3]. These two types of applications, analysis of underwater mammal vocalizations and operation in dispersive environments, require efficient signal analysis methodologies.…”