This paper addresses the problem of automated detection of Z-calls emitted by Antarctic blue whales (B. m. intermedia). The proposed solution is based on a subspace detector of sigmoidal-frequency signals with unknown time-varying amplitude. This detection strategy takes into account frequency variations of blue whale calls as well as the presence of other transient sounds that can interfere with Z-calls (such as airguns or other whale calls). The proposed method has been tested on more than 105 h of acoustic data containing about 2200 Z-calls (as found by an experienced human operator). This method is shown to have a correct-detection rate of up to more than 15% better than the extensible bioacoustic tool package, a spectrogram-based correlation detector commonly used to study blue whales. Because the proposed method relies on subspace detection, it does not suffer from some drawbacks of correlation-based detectors. In particular, it does not require the choice of an a priori fixed and subjective template. The analytic expression of the detection performance is also derived, which provides crucial information for higher level analyses such as animal density estimation from acoustic data. Finally, the detection threshold automatically adapts to the soundscape in order not to violate a user-specified false alarm rate.
Baseband conversion is a classical signal processing method allowing reduction of the sampling frequency of signals whose spectrum is limited to a narrow frequency band. In our case, the spectrum of the signal of interest occupies a 15 Hz bandwidth, centered around 22.5 Hz. The complex baseband signal is obtained by low-pass filtering the received signal downshifted to baseband (i.e., multiplied by , where n denotes the sample index). Its useful spectrum occupies the band [−7.5 7.5] Hz, so that the baseband signal can theoretically be downsampled at a sampling frequency as low as 15 Hz.
To test the noise's stationarity, the methodology described in Ref. 45 that compares the time-frequency structure between the original dataset and an artificially stationarized version of the data was used. With a significance level set to 5%, the test was successful for 88% of the data. The Gaussianity was tested with Lilliefors' test (Ref. 46) with a 5% significance level. 91% of our background noise dataset successfully passed this test.
Note that this relation is rather pessimistic as it assumes statistical independence between overlapping windows. In practice, the actual false alarm will be slightly lower than what is specified.