Study of the relationship between pilot whale (Globicephala melas) behaviour and the ambiguity function of its sounds

Pilot whales produce clicks, whistles and pulsed calls, which form a key component of their social lives. The three types of sound driven by their behavioural states are not directly observable. The mathematical tools which compute properties of sound are natural candidates for analysing the possible relationship between pilot whale sound and behaviour. In this paper, the wideband ambiguity function is used to compute the range resolution, speed resolution, Doppler tolerance, sidelobe-to-mainlobe suppression ratio of the range ambiguity function and sidelobe-to-mainlobe suppression ratio of the speed ambiguity function for pilot whale sound, which can be used to evaluate the abilities of pilot whale sound in detecting targets and resisting the influence of relative speed. Statistical results show that clicks have the best range resolution and its range ambiguity functions have the lowest sidelobe-to-mainlobe suppression ratio. Pulsed calls and part of the whistles have the best speed resolution and its speed ambiguity functions have the lowest sidelobe-to-mainlobe suppression ratio. The other part of whistles has a large Doppler tolerance. Analyzing the five parameters of different types of sound and the corresponding behaviour, we then reach a better understanding of the relationship between pilot whale sound and pilot whale behaviour.