Separation of nonstationary sound fields on spheres by time-domain deconvolution

This paper proposes three sound field separation (SFS) methods in time domain based on pressure-pressure measurements, radial velocity-radial velocity measurements, and pressure-radial velocity measurements to extract the nonstationary sound field radiated by the target source in a noisy environment. These SFS methods construct time convolution formula that directly relate the sound field radiated by the target source to the measured pressure and particle velocity. Then the sound field radiated by the target source is extracted by a deconvolution procedure where the Tikhonov regularization method is incorporated to suppress the influence of measurement noise. Numerical simulations investigated the performance of the three SFS methods. The results demonstrate that all the three SFS methods could remove the influence of disturbing sources and separate out the target sound fields in time and space domains effectively. Furthermore, the proposed SFS method based on pressure-pressure measurements can accurately separate the pressure radiated by the target source. Additionally, the radial velocity separation using the SFS method based on radial velocity-radial velocity measurements demonstrates slightly higher accuracy compared to that achieved by pressure-radial velocity measurements.