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Applying the Ambisonics Approach to Planar and Linear Distributions of Secondary Sources and Combinations Thereof

Near-field Compensated Higher Order Ambisonics (NFC-HOA) is an approach to the physical synthesis of sound fields. The typical interpretation of the modern NFC-HOA approach is that the sound field to be synthesized and the spatial transfer function of the employed loudspeakers are expanded into series of spherical harmonics in order to determine the loudspeaker driving signals for spherical arrays. Going one level higher in abstraction, NFCHOA can be interpreted as the single-layer potential solution to the problem, which is solved via a formulation of the synthesis equation in a given spatial frequency domain. The specific spatial frequency domain is selected according to the geometry of the loudspeaker array. For spherical arrays, this spatial frequency domain is the spherical harmonics domain. The presented paper provides an overview over a recent extension of this approach to the employment of planar and linear loudspeaker arrays. In this latter situation, the solution is obtained via a formulation of the synthesis equation in wavenumber domain. The solution is then extended to the employment of combinations of planar or linear arrays of loudspeakers via the Kirchhoff approximation. Along with the solution, a discussion and interpretation of the general procedure and cross-references to other approaches are outlined.