Robust Fourier descriptors for characterizing amplitude-modulated waveform shapes.

Fourier descriptors (FD's) have traditionally been used to characterize the boundary shape of closed curves in computer-based images. This study examines the usefulness of FD's for characterizing the shape of amplitude-modulated waveform boundaries. Twenty-eight bioacoustic waveforms representing 7 species-specific sound groups were examined. Nearest-neighbor classification using 32-point waveform envelopes yielded 85.7% recognition rates when Euclidean distances with 8 or 12 FD's were employed. With 4 or 16 FD's, recognition was 82.1% but dropped to 71.4% when the number of FD's was reduced to 3. Evidently only the low-order 4 or 5 FD's are required to characterize most signals examined. Four FD's were adequate representation for linear discriminant analysis, wherein 27 (96.1%) of the samples were classified correctly, and for hierarchical cluster analysis, wherein 26 (92.9%) of the samples clustered into dendrogram subtrees corresponding to the known sound groups. Two sounds accounted for many errors in the classification experiments, and these differed from typical sounds for their respective species groups. In such cases, more than a single FD reference pattern may be required to adequately represent the sounds of a given species.