Method of designing inverse system for binaural reproduction over loudspeakers by using diagonalization method

This paper proposes a method of controller design for binaural reproduction over loudspeakers, which is one approach to three-dimensional spatial sound reproduction. The required signals in binaural reproduction over loudspeakers are reconstructed at control points in the reproduced sound field, e.g. listening positions, by suppressing the acoustic crosstalk occurring in the propagation of sounds using a decoupling controller. The decoupling control of the reproducing signals makes it possible for the listeners to perceive sound images that are localized in arbitrary directions. An inverse system as the decoupling controller is derived in our study by using state space representation. The proposed method consists of two steps: identification of head-related transfer functions (HRTFs) that are the transfer functions from the loudspeakers to the control points by using the subspace method, and the construction of its inverse system by using the diagonalization method. To test and verify the effectiveness of our proposal, we measured input and output signals using a dummy head and constructed the inverse system with the proposed method. Decoupling simulation indicated that the inverse system we obtained could suppress acoustic crosstalk.