A practical formulation of 3 dimensional sound reproduction using Wave Field Synthesis

Sound field reproduction using Wave Field Synthesis has been so far limited to the positioning of virtual sources and listeners in the horizontal plane only although the underlying formulation (Kirchhoff-Helmholtz) describes the reproduction of 3 dimensional sound fields in a 3 dimensional subspace. However, a strict use of this formulation would require a surface loudspeaker array with an impractical number of loudspeakers. The authors propose here an optimized formulation of Wave Field Synthesis in 3 dimensions that account both for the limitation of localization accuracy of elevated sources and the target listening area size. In contrast to other 3 dimensional sound reproduction techniques such as Higher Order Ambisonics, the proposed approach allows for irregular and incomplete loudspeaker layouts for targeting specific areas for virtual positioning and accounting for practical limitations in loudspeaker positioning. The paper also proposes a subjective evaluation of the proposed approach in an extended listening area. The experiment relies on elevated physical sources (loudspeakers) to be matched in localization with virtual sources reproduced with the proposed approach with a 24 channels loudspeaker array that covers the frontal quarter of the upper half of a rectangular room.