Multifractal analysis of birdsong and its correlation structure

Abstract

The time series recordings of typical songs of songbirds exhibit highly complex and structured behavior, whichis characteristic of their species and stage of development, and need to be analyzed by methods that can uncovertheir correlation structure. Here we analyze a typical song of a canary using Hurst exponents and multifractalanalysis, which uncovers the correlation structure of typical song segments. These are then compared with thecorresponding quantities from shuffled data, which destroys the temporal correlations and iterative amplitude-adjusted Fourier transform (IAAFT) data. It is seen that temporal correlations are responsible for the multifractalbehavior seen in the data and that two-point correlations, which are preserved by the transform, are importantin the high-fluctuation regime. Higher-order correlations and intersyllabic gaps dominate the behavior of thelow-fluctuation regime. These observations are supported by the simplicial characterization of the correspondingtime series networks. Complexity measures are also used to analyze the amplitude envelope time series. Theseindicate that intersyllabic gaps contribute a significant fraction to the complexity of the birdsong. Our methodprovides a detailed characterization of the data, which can enable the comparison of real and synthetic birdsongand comparisons across stages of development and species. A brief comparison with the song of the zebra finchsupports this.