Applications of operator theory and symmetry arguments to sound field recording and reproduction

Abstract

The problem of recording and reproducing sound fields using microphone/loudspeaker arrays is treated by exploiting its symmetries. This approach leads to well-known results, such as high-order Ambisonics corresponding to the requirement of the error field to be invariant under rotations. More importantly, it allows us to treat some difficult problems critical to the application of sound field recording and reproduction to virtual reality, where one or more users can freely move around a realistic environment. In this presentation, we consider three of these problems. First, we present a method to extrapolate extended sound field information from conventional spherical microphone array recordings by imposing symmetry constrains based on a priori knowledge of the sound source positions. Second, we apply the same symmetry constrains to the problem of sound field reproduction, allowing us to formulate a method of presenting spatial sound to moving listeners. Finally, we consider the problem of describing and reproducing the sound field due to a moving sound source.