Spherical loudspeaker array modeling and control using different basis function representations
Dima Khaykin and Boaz Rafaely
A potential use of a spherical loudspeaker array for producing arbitrary radiation patterns has recently been studied. Different control strategies were developed and proposed for this goal. This work attempts to make a connection between two popular control strategies: the loudspeaker units input signals and the gains of spherical harmonics directivities. These control strategies make use of two sets of basis functions: caps velocity and spherical harmonics, respectively, that fully span the radiation subspace. A new set of basis functions that spans the same subspace as spherical harmonics and cap velocity is developed using a singular-value decomposition and shown to be of finite order, unlike the spherical harmonics set. These new basis functions provide an indication of the way the spherical loudspeaker array produces the spherical harmonics modes of different orders. Control strategy based on these new basis functions is formulated and its performance compared to already mentioned strategies by producing quiet zones as an application of active sound control. In addition, the ability of this new control strategy to design various radiation patterns analytically, rather than by numerical optimization, is discussed and demonstrated.