Contour representations of sound

Abstract

Abstract-Many signals are naturally described by continuous contours in the time-frequency plane, but standard time-frequency methods disassociate continuous structures into isolated "atoms" of energy. Here we propose a method that represents any discrete time-series as a set of time-frequency contours. The edges of the contours are defined by fixed points of a generalized reassignment algorithm. These edges are linked together by continuity such that each contour represents a single phase-coherent region of the timefrequency plane. By analyzing the signal across many time-scales, an over-complete set of contours is generated, and from this redundant set of shapes the simplest, most parsimonious forms may be selected. The result is an adaptive time-frequency analysis that can emphasize the continuity of long-range structure. The proposed method is demonstrated with a few examples.

The Song Must Go On: Resilience of the Songbird Vocal Motor Pathway

“…First, a template vocalization of a selected syllable was manually chosen. Then, features from the template and the rest of the data were computed from a ratio of two quantities: the standard sonogram ( ) of the sound pressure time series , computed with a Gaussian window of time scale , and a sonogram computed with the derivative of the Gaussian window ( ) [29] . …”

“…Using the ratio defined in (1), a group of sounds were aligned using their peak cross-correlation over the features mentioned above. A specified number of renditions were randomly chosen from the cluster of possible template matches to create an aggregate spectral density image, and a sparse time-frequency representation was calculated for each selected sound [29] . We denote the sparse time-frequency representation, , for sound i , and then apply the following transformation, …”