A Sparse Modal Representation for Dolphin Echolocation Transients

Abstract

Characterising echolocation provides a non-invasive means of monitoring cetacean populations, health, and behaviour, offering critical data to inform conservation policy and mitigate the impacts of anthropogenic ocean noise. Echolocation clicks are short broadband transients whose internal oscillatory structure is difficult to compare in a sequence using conventional time- or frequency-domain representations. We introduce a Sparse Modal Representation (SMR) in which each click is described as a sparse superposition of delayed damped resonant modes. The representation separates resonant behaviour from temporal localisation, allowing both narrowband and broadband click components to emerge from the same set of resonant building blocks. The methodology combines Burg autoregressive pole estimation, sparse approximation in an over-complete dictionary, and nonlinear parameter refinement to obtain compact and interpretable modal descriptions of individual transients. The method is evaluated using recordings of free-ranging common dolphins (Delphinus delphis) from the DOLPHINFREE project in the Northern Bay of Biscay. The results demonstrate accurate reconstruction using a limited set of parameters that are repeatable across successive clicks and robust under realistic recording conditions. These conditions include wave, vessel, and sonar interference. Repeatability and robustness are essential for using this parameter set to detect changes in animal behaviour.