Abstract
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.
Highlights
Acoustic waves emitted by a transient sound source interact with the surrounding environment, undergoing a variety of transformations due to interference, scattering, and absorption.1 In practice, these transformations change the spectrum of the original wave, often resulting in a bandpass filtering effect in terms of incidence angles that are attenuated
We propose a different partitioning of the wavenumber-frequency domain, shown in Fig. 2(h), into band limited regions described by hyperbolic dispersion curves and lines of constant phase velocity
An experimental analysis is performed using dictionary learning of reverberant sound fields measured with a microphone array
Summary
Acoustic waves emitted by a transient sound source interact with the surrounding environment, undergoing a variety of transformations due to interference, scattering, and absorption. In practice, these transformations change the spectrum of the original wave, often resulting in a bandpass filtering effect in terms of incidence angles that are attenuated. The edge has a frequency-dependent impedance, even some wavelengths can be attenuated In this context, we are interested in all such phenomena that result in transient acoustic waves that have a band limited spectrum: we shall refer to them as waves localized in space-time and wavenumber-frequency domains. One of the simplest examples is the case of harmonic plane waves—localized in the wavenumber-frequency domain, which are well suited to represent steady-state responses but ineffective to represent waves localized in space-time. Another example of space-wavenumber localization is the effect due to finite aperture and sensor density introduced by microphone array techniques such as near-field acoustic holography.. The hypothesis is tested with a theoretical analysis of the pressure spectra of a transient monopole source, as well as with an experimental analysis applying dictionary learning on reverberant sound fields
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