The Short-Time-Duration Narrow-Bandwidth Character of Odontocete Echolocation Signals

Abstract

Descriptions are presented of echolocation signals as observed in a number of Odontocete species. It is illustrated that all of these signals have a remarkably small bandwidth considering their time duration. In fact, these signals achieve the maximum concentration in the time/frequency space that is physically possible. This is demonstrated by comparing the signal waveforms with the result of a computation of the waveform that has the absolute minimum possible time duration and bandwidth for a given mean frequency and time delay. There appears to be a striking resemblance between the actual echolocation waveforms and the waveform computed with the same mean frequency and time delay. This holds not for one, but for all the species considered here and, in the case of bifrequent sonar, not only for the high-frequncy component, but equally well for the low-frequency one. Moreover, it can also be shown that all these waveforms are approximately their own Fourier sine transforms. Waveform characterisation could, therefore, be very adequately based on one ‘quantum’ number only. Such waveforms yield the best possible signal-to-noise ratios when they have to be detected in broad background noise. In addition, for these signals of short duration and small bandwidth, a simple square-law detector closely approximates the performance of a matched-filter detector.