  Sound field decomposition predicts waveforms in arbitrary directions using
signals from a limited number of microphones as inputs. Sound field
decomposition is fundamental to downstream tasks, including source
localization, source separation, and spatial audio reproduction. Conventional
sound field decomposition methods such as Ambisonics have limited spatial
decomposition resolution. This paper proposes a learning-based Neural Sound
field Decomposition (NeSD) framework to allow sound field decomposition with
fine spatial direction resolution, using recordings from microphone capsules of
a few microphones at arbitrary positions. The inputs of a NeSD system include
microphone signals, microphone positions, and queried directions. The outputs
of a NeSD include the waveform and the presence probability of a queried
position. We model the NeSD systems respectively with different neural
networks, including fully connected, time delay, and recurrent neural networks.
We show that the NeSD systems outperform conventional Ambisonics and DOANet
methods in sound field decomposition and source localization on speech, music,
and sound events datasets. Demos are available at
https://www.youtube.com/watch?v=0GIr6doj3BQ.
