Spectral analysis of the call of the male killer whale

Abstract
Poulter previously presented sonagram analyses of underwater sound recordings of various sea mammals, calling attention to the apparent harmonic progression of components of these signals. Other workers have questioned the presence of these harmonics in the original data and have suggested that they may instead be introduced during the analysis. In this paper we use underwater sound recordings of the male killer whale Namu, taken with equipment flat within ±2 dB to beyond 18 342 Hz, the upper limit of the analysis, to show by means of digital spectral analysis methods that a harmonic progression exists. In the signals analyzed, peaks in the estimated spectrum were observed at each integer multiple of the fundamental frequency. In view of the broad frequency response of the recording equipment and the precision of the subsequent digital analysis, we can say with confidence that these harmonics were actually present in the whaler's call. For the analysis, portions of an audio recording were converted to digital form. In the conversion, a bandpass filter was used to attenuate power below 40 Hz and above 10 kHz. Digital analysis techniques similar to those proposed by Bingham, Godfrey, and Tukey were then used. For each time span of data to be analyzed, a windowed Fourier transform was first computed, using a fast Fourier transform program. The power spectrum was next computed, as the squared modulus of the windowed transform, and a correction was made for the attenuation of high frequencies during A-to-D conversion. The autocorrelation function was estimated by computing the inverse transform of the power spectrum. A moderate amount of digital smoothing was then applied to the spectrum to reduce irregularities due to noise. The resulting smoothed spectrum is used as an estimate of the power spectral density function.

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