Eigenbeam analysis of the diversity in bat biosonar beampatterns

A quantitative analysis of the interspecific variability in bat biosonar beampatterns has been carried out on 267 numerical predictions of emission and reception beampatterns from 98 different species. Since these beampatterns did not share a common orientation, an alignment was necessary to analyze the variability in the shape of the patterns. To achieve this, beampatterns were aligned using a pairwise optimization framework based on a rotation-dependent cost function. The sum of the p-norms between beam-gain functions across frequency served as a figure of merit. For a representative subset of the data, it was found that all pairwise beampattern alignments resulted in a unique global minimum. This minimum was found to be contained in a subset of all possible beampattern rotations that could be predicted by the overall beam orientation. Following alignment, the beampatterns were decomposed into principal components. The average beampattern consisted of a symmetric, positionally static single lobe that narrows and became progressively asymmetric with increasing frequency. The first three "eigenbeams" controlled the beam width of the beampattern across frequency while higher rank eigenbeams account for symmetry and lobe motion. Reception and emission beampatterns could be distinguished (85% correct classification) based on the first 14 eigenbeams.