Particle Velocity Assisted Three Dimensional Sound Field Reproduction Using a Modal-Domain Approach

In literature, particle velocity has been introduced to improve performance of spatial sound field reproduction systems. However, all existing work requires to have accurate particle velocity measurements at all of the discrete control points, which is difficult to obtain in real-world applications. In this work, we formulate continuous particle velocity expressions over space as a function of pressure coefficients in the modal domain that can be easily extracted by using a higher order microphone. The sound field within a target region is controlled by a weighted cost function we built to optimize the continuous particle velocity, as well as sound pressure, on the boundary of the region. In contrast to the conventional spatial sound field reproduction methods in the modal domain, the proposed method allows for non-uniform loudspeaker geometry with a limited number of loudspeakers, thus providing a flexible array arrangement. The performance of the proposed method is evaluated through numerical simulations in both a free field and a reverberant room. Finally, we prove the proposed method in an objective experiment with real-world measurements of room impulse response.