Sparse time-frequency representations.

Auditory neurons preserve exquisite temporal information about sound features, but we do not know how the brain uses this information to process the rapidly changing sounds of the natural world. Simple arguments for effective use of temporal information led us to consider the reassignment class of time-frequency representations as a model of auditory processing. Reassigned time-frequency representations can track isolated simple signals with accuracy unlimited by the time-frequency uncertainty principle, but lack of a general theory has hampered their application to complex sounds. We describe the reassigned representations for white noise and show that even spectrally dense signals produce sparse reassignments: the representation collapses onto a thin set of lines arranged in a froth-like pattern. Preserving phase information allows reconstruction of the original signal. We define a notion of "consensus," based on stability of reassignment to time-scale changes, which produces sharp spectral estimates for a wide class of complex mixed signals. As the only currently known class of time-frequency representations that is always "in focus" this methodology has general utility in signal analysis. It may also help explain the remarkable acuity of auditory perception. Many details of complex sounds that are virtually undetectable in standard sonograms are readily perceptible and visible in reassignment.