  The sound field separation methods can separate the target field from the
interfering noises, facilitating the study of the acoustic characteristics of
the target source, which is placed in a noisy environment. However, most of the
existing sound field separation methods are derived in the frequency-domain,
thus are best suited for separating stationary sound fields. In this paper, a
time-domain sound field separation method is developed that can separate the
non-stationary sound field generated by the target source over a sphere in
real-time. A spherical array sets up a boundary between the target source and
the interfering sources, such that the outgoing field on the array is only
generated by the target source. The proposed method decomposes the pressure and
the radial particle velocity measured by the array into spherical harmonics
coefficients, and recoveries the target outgoing field based on the time-domain
relationship between the decomposition coefficients and the theoretically
derived spatial filter responses. Simulations show the proposed method can
separate non-stationary sound fields both in free field and room environments,
and over a longer duration with small errors. The proposed method could serve
as a foundation for developing future time-domain spatial sound field
manipulation algorithms.
