Objectivity in the Study of Marine Mammal Vocalisations: a Wavelet Approach

INTRODUCTION Sounds produced by marine mammals generally have a non-stationary behaviour, ranging from short transients to long tonals, with a huge variety of chirp-like intermediates. Analysis of these sounds needs adapted tools in order to characterise the signals efficiently in both time and frequency dimensions In numerous studies and for well-known reasons, the spectrogram has been used as the interface between sound and feature extraction. The spectrogram popularity in our type of study stems from at least three reasons: firstly, a spectrogram is a two-dimensional picture displaying sounds along two physical dimensions (time and frequency) which are familiar to our auditory system. Little training is needed to recreate an approximate sound image out of a spectrogram and vice-versa. Secondly, real-time implementation can now be performed on off-the-shelf platforms thanks to software availability and the Fast-Fourier-Transform (FFT), which greatly reduces the computational load. Thirdly, as a spectrogram is the squared modulus of a Short-Time-Fourier-Transform (STFT), the underlying parameters, say the window size, the amount of overlapping and window shape are the only parameters affecting the result. The user interface is therefore very simple and little mathematical background is necessary to handle it. For example, Figs.1 & 2 show significant differences when parameters are changed. If more frequency resolution is needed, the window must be longer. As time resolution is lower when long windows are used, a higher overlap is needed in order to attenuate the blocking effect in time-domain. Choosing the window type is more subtle: a higher contrast is obtained with a simple rectangular window but spectral high energy peaks tend to spread over the whole bandwidth (side lobes). The use of smoother windows gives lower contrast but attenuates these side-lobe artefacts. Nevertheless, in many applications, such as in behavioural and communication studies, the spectrogram does not provide enough freedom to the user. When the interest is to obtain a " brain picture " of the sound a marine mammal actually hears, it is indispensable to be able to implement and account for a maximum number of parameters, which describe its auditory perception. Hearing sensitivity and frequency discrimination capabilities are two additional parameters we decided to consider in order to create a new representation. Though hearing sensitivity is straightforwardly computed, frequency discrimination is not. When a system has more resolution in frequency, it has less in time, and vice-versa, this principle is known as the Heisenberg uncertainty principle. Here we …