On the representation of wavefronts localized in space-time and wavenumber-frequency domains

This Letter reports evidence suggesting a representation system for transient waves with band limited spectra, referred to here as localized waves in the space-time and wavenumber-frequency domains. A theoretical analysis with a transient monopole shows that the wavenumber-frequency pressure spectrum is distributed over hyperbolic regions of propagating waves and evanescent waves. An experimental analysis is performed, applying dictionary learning to reverberant sound fields measured with a microphone array in three rooms. The learned components appear to be related by analytical transformations in the spectra, suggesting a partitioning characterized by hyperbolic dispersion curves and multiple directions and times of arrival.