Reconstruction of nonstationary sound fields based on time domain plane wave superposition method
Résumé
A new time-domain plane wave superposition method (TD-PWSM) is proposed to reconstruct nonstationary sound fields. At each time step of this method, the time-wavenumber spectrum of the sound pressure on the virtual source plane is firstly estimated by using the measured sound pressure and the right pseudo-inverse of the time-domain propagation kernel matrix, and then the reconstruction is performed through a superposition of all the time convolutions between the estimated time-wavenumber spectrum of the sound pressure on the virtual source plane and the time-domain propagation kernel at each wavenumber. Since the inverse process at each time step is ill-conditioned, the Tikhonov regularization is introduced to obtain an appropriate solution. The method proposed provides the ability of continuously reconstructing time-dependent pressure signals and overcomes some errors due to the use of the two-dimensional spatial Fourier transforms, which is avoided. Numerical simulations and an experiment demonstrate that it is feasible to reconstruct the nonstationary sound fields via TD-PWSM.
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