Reconstruction of nonstationary sound fields based on the time domain plane wave superposition method

Abstract

A time-domain plane wave superposition method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of time convolutions between the estimated time-wavenumber spectrum of the sound pressure on a virtual source plane and the time-domain propagation kernel at each wavenumber. By discretizing the time convolutions directly, the reconstruction can be carried out iteratively in the time domain, thus providing the advantage of continuously reconstructing time-dependent pressure signals. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time-wavenumber spectrum on the virtual source plane. Because the double infinite integral of the two-dimensional spatial Fourier transform is discretized directly in the wavenumber domain in the proposed method, it does not need to perform the two-dimensional spatial fast Fourier transform that is generally used in time domain holography and real-time near-field acoustic holography, and therefore it avoids some errors associated with the two-dimensional spatial fast Fourier transform in theory and makes possible to use an irregular microphone array. The feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers.