Rendering of virtual sound sources with arbitrary directivity in higher order Ambisonics

Higher order Ambisonics (HOA) is a spatial audio reproduction technique aiming at physically synthesizing a desired sound field. It is based on the expansion of sound fields into orthogonal basis functions (spatial harmonics). In this paper we present an approach to the two-dimensional reproduction of virtual sound sources at arbitrary positions having arbitrary radiation directivities. The approach is based on the description of the directional properties of a source by a set of circular harmonics. Consequences of truncation of the circular harmonics expansion and spatial sampling as occurring in typical installations of HOA systems due to the employment of a finite number of loudspeakers are discussed. We illustrate our findings with simulated reproduction results.