AES Europe 2026

We present a spectral-like reformulation of 2D ambisonics,
enabling an alternative representation of the sound field
in terms of amplitudes; phases. We hypothesise that it
simplifies the representation; creative manipulation of
2D ambisonics, beyond encoded directional point sources.

In 2D high-order ambisonics (HOA) of order N, a sound field
can be represented as a 2π-periodic angular function as a
combination of circular harmonics (Y_m) weighted by the
coefficients (a_m) with m ∈ [-N, N]. This representation
can be reformulated in terms of N+1 amplitudes; N
phases, similarly to a Fourier decomposition.

A simple example of this representation is the ambisonic
encoder at an angle theta. Phases are then multiples of a
phase phi = theta/2π, as frequencies are multiples of a
fundamental in harmonic sounds. Therefore, the
amplitude-phase approach can draw on the field of sound
synthesis, between harmonic; inharmonic modelling.
Operations on ambisonic vectors in amplitude-phase also
rely on Fourier representation, namely the spectral
convolution of two vectors (element-wise products of the
amplitudes, element-wise sums of the phases). Spectral
convolution has vast potential in ambisonics, allowing to
represent all the usual spatial operations (geometric;
transformative) in a simple manner.

To test this approach, we are currently developing an
ambisonic synthesiser based on Faust functions running in
Max environment. We are evaluating the scope of this
representation, both theoretical; compositional,;
then attempt to expand this approach to 3D ambisonics.