Characterization of shape diversity in bat biosonar beampatterns

Abstract

Numerical beampattern estimates for a large digital shape data set with 361 three-dimensional models of the pinna and noseleaf shapes from 106 different bat species are currently in preparation. Shape samples in this data set have been selected to represent taxonomic diversity and balance noseleaves versus pinnae. The data set will be used to analyze the biodiversity in bat beampatterns. In order to facilitate the extraction of interspecific patterns, spherical harmonics are being evaluated as an analysis tool to describe the spatial frequency content of the beampatterns. Spherical harmonics are the angular portion of a set of solutions to Laplace's equation represented in a system of spherical coordinates. The higher the harmonic, the more solutions are in the respective set. Regardless of the number of solutions, each set forms an orthogonal system. For a compressed characterization of the beampatterns, the representation of the beampattern shape at a given frequency is expressed as a power spectrum; the norm of the vector of the weighting coefficients for all basis functions in the set of a harmonic is taken to represent the portion of the total power explained by a particular harmonic. This power spectrum was found to reflect several beampattern properties well.