  Ambisonics is an established framework to capture, process, and reproduce
spatial sound fields based on its spherical harmonics representation. We
propose a generalization of conventional spherical ambisonics to the spheroidal
coordinate system and spheroidal microphone arrays, which represent sound
fields by means of spheroidal wave functions. This framework is referred to as
spheroidal ambisonics and a formulation for the case of prolate spheroidal
coordinates is presented. Spheroidal ambisonics allows analytical encoding of
sound fields using spheroidal microphone arrays. In addition, an analytical
conversion formula from spheroidal ambisonics to spherical ambisonics is
derived in order to ensure compatibility with the existing ecosystem of
spherical ambisonics. Numerical experiments are performed to verify spheroidal
ambisonic encoding and transcoding when used for spatial sound field recording.
It is found that the sound field reconstructed from the transcoded coefficients
has a zone of accurate reconstruction which is prolonged towards the long axis
of a prolate spheroidal microphone array.
