Abstract
Panning techniques, such as vector base amplitude panning (VBAP), are a widely used practical approach for spatial sound reproduction using multiple loudspeakers. Although limited to a relatively small listening area, they are very efficient and offer good localization accuracy, timbral quality, as well as a graceful degradation of quality outside the sweet spot. The aim of this paper is to investigate optimal sound reproduction techniques that adopt some of the advantageous properties of VBAP, such as the sparsity and the locality of the active loudspeakers for the reproduction of a single audio object. To this end, we state the task of multiloudspeaker panning as an ${\ell _{1}}$ optimization problem. We demonstrate and prove that the resulting solutions are exactly sparse. Moreover, we show the effect of adding a nonnegativity constraint on the loudspeaker gains in order to preserve the locality of the panning solution. Adding this constraint, ${\ell _{1}}$ -optimal panning can be formulated as a linear program. Using this representation, we prove that unique ${\ell _{1}}$ -optimal panning solutions incorporating a nonnegativity constraint are identical to VBAP using a Delaunay triangulation for the loudspeaker setup. Using results from linear programming and duality theory, we describe properties and special cases, such as solution ambiguity, of the VBAP solution.
Highlights
Sound reproduction over multiple loudspeakers aims at recreating plausible spatial sound scenes, often consisting of multiple audio objects, for either a single listener or over extended listening areas
In this paper we have considered sparse, globally optimal solutions for multi-loudspeaker sound reproduction based on amplitude panning
We have proposed to formulate amplitude panning as an 1 optimization problem in order to retain the advantageous sparsity of amplitude panning methods as vector base amplitude panning (VBAP)
Summary
Sound reproduction over multiple loudspeakers aims at recreating plausible spatial sound scenes, often consisting of multiple audio objects, for either a single listener or over extended listening areas. In [38], authors of the present paper consider the application of convex optimization techniques to listener-centric sound field control, and demonstrate the similarity between 1-optimal and amplitude panning methods by means of numerical examples These approaches generally involve a numerical optimization step to calculate the sparse loudspeaker driving functions, they are significantly more complex than established techniques such as VBAP.
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