A system and method for rendering a virtual sound source using a plurality of speakers in an arbitrary arrangement includes expanding a wave field of the virtual sound source and a composite wave field generated by the plurality of speakers into multi-pole expansions, and equating the multi-pole expansions to each other to form a continuous equation. A set of constraints is applied to the continuous equation that minimize an error in a sweet spot region resulting in a linear system of equations. The linear system of equations is solved using singular-value decomposition to arrive at a pseudo-inverse representing a multi-dimensional transfer function between the virtual sound source and the plurality of speakers. The multi-dimensional transfer function is then applied to a signal of the virtual sound source to render the virtual sound source in the sweet spot region using the plurality of speakers in the arbitrary arrangement.