Firtha, G.; Fiala, P.; Schultz, F.; Spors, S. (2018): “On the General Relation of Wave Field Synthesis and Spectral Division Method for Linear Arrays.” In: IEEE/ACM Trans. Audio Speech Language Process., 26(12):2393-2403
was recently published. The topic is also covered in Gergely Firtha’s dissertation in chapter 4, please see his open access project https://github.com/gfirtha/gfirtha_phd_thesis
Sound field synthesis aims at the reproduction of an arbitrary target sound field over an extended listening area applying a densely spaced loudspeaker ensemble. Two basic analytic methodologies—the explicit and the implicit—exist in order to derive the required loudspeaker driving functions. The explicit solution aims at the direct solution of the involved integral equation describing the general sound field synthesis problem, resulting in driving functions in the form of a spectral integral. The implicit solution extracts the driving function from an appropriate boundary integral representation of the target sound field. So far the relationship between two approaches was investigated for target field specific synthesis scenarios. For linear arrays this paper introduces a high-frequency approximation for the explicit solution resulting in a novel, purely spatial domain formulation of the direct approach. The presented driving functions allow the synthesis of an arbitrary virtual sound field, optimizing the reproduction on an arbitrary reference line. It is furthermore shown that for an arbitrary virtual sound field, the implicit solution constitutes a high-frequency approximation of the explicit method.