Sparse Contour Representations of Sound

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 time-frequency 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.