Non-Stationary Sound Field Reconstruction Within the Bayesian Framework

To realize the non-stationary sound field reconstruction, this paper proposes a time-domain plane wave superposition method based on Bayesian inference. The method first represents sound fields as a superposition of the wave number spectrum of the sound pressures of the virtual sound source with the time convolution between the propagation kernel of each wave number. Then, the sound pressure signal can be reconstruced directly in the time domain. Benefiting from direct sampling in the time-domain wave number domain, the method does not suffer from wrapping errors induced by the Fourier transform. During the reconstruction process, Bayesian estimation is used to obtain regularization parameters at each time step; further exploiting the sparse nature of the sound source in the wave number domain, sparse Bayesian learning is used to achieve sparse estimation of the wave number spectrum. The superiority of Bayesian inference for solving the time-domain plane wave number spectrum is verified by numerical simulations of a circular piston sound source.