  Acoustical signal processing of directional representations of sound fields,
including source, receiver, and scatterer transfer functions, are often
expressed and modeled in the spherical harmonic domain (SHD). Certain such
modeling operations, or applications of those models, involve multiplications
of those directional quantities, which can also be expressed conveniently in
the SHD through coupling coefficients known as Gaunt coefficients. Since the
definition and notation of Gaunt coefficients varies across acoustical
publications, this work defines them based on established conventions of
complex and real spherical harmonics (SHs) along with a convenient matrix form
for spherical multiplication of directionally band-limited spherical functions.
Additionally, the report provides a derivation of the Gaunt coefficients for
real SHs, which has been missing from the literature and can be used directly
in spatial audio frameworks such as Ambisonics. Matlab code is provided that
can compute all coefficients up to user specified SH orders. Finally, a number
of relevant acoustical processing examples from the literature are presented,
following the matrix formalism of coefficients introduced in the report.
