Sperm whale click analysis using a recursive time-variant lattice filter

Abstract

Sperm whale clicks, which are nonstationary broadband transients, are analyzed using the normalized recursive exact least-square time-variant lattice filter. The results are compared with those obtained using the classical techniques of energy detection and correlation. The algorithm presented in the paper, derived from an exact least-square formalism is well adapted to the nonstationary signal processing. At each time-step, the adaptive Schur filter calculates an optimal orthogonal signal representation using second-order statistics of the signal, resulting in a set of time-varying Schur coefficients. These coefficients are used to detect clicks and to estimate the click interpulse interval. The latter is commonly used to estimate individual body length and can thus be used for assessments of features of sperm whale populations. The results obtained using simulated and real-world signals demonstrate that a second-order signal description based on the time-varying Schur coefficients is efficient and robust i.e. resistant to the background noise. The adaptive Schur filter detects sperm whale clicks and estimates the interpulse intervals better than both classical waveform energy and correlation methods.