Compression of Cuvier’s beaked whale (Ziphius cavirostris) vocalizations using fast orthogonal search

Abstract Remote sensing of beaked whale vocalizations poses significant problems due to limited communications bandwidths. Many beaked whales vocalize (click) at frequencies up to 50 kHz Hence high bandwidth sampling (typically 100+ kHz) and processing is required in order to detect the clicks, but transmitting the data from a remote sensor using a low-bandwidth (4800 baud) satellite link results in a real-time bottleneck. Even if auto-detection algorithms were used on the remote sensor, some data would need to be relayed to a human operator to verify the classification. Hence, the ability to compress the data in a manner that does not impede the ability to detect and classify the transient signal is required. Typical audio compression techniques have a maximum sampling rate of 48 kHz which is too low to collect beaked whale clicks and still obey the Nyquist criterion. In addition, audio compression algorithms also have a psycho-acoustic model that aids in the compression of the signal but distorts the audio signal. This paper presents a compression algorithm that uses a non-linear modelling technique called fast orthogonal search (FOS) to create a functional expansion of the acoustic data. The candidate functions used in the functional expansion are transient signals that model Cuvier’s beaked whale ( Ziphius cavirostris ) clicks as well as sinusoidal functions for modelling whale songs. A compression ratio of 93 is achieved by transmitting candidate identification numbers and weights for only the candidate functions that are chosen by the FOS algorithm. The acoustic signal is recreated using the weights and candidate numbers transmitted. The reconstructed time series is used as an input to a band-limited energy detector for whale vocalizations. The raw data and the reconstructed data have comparable probability of detection and missed detections, with fewer false alarms for the reconstructed signal.