Robust analysis of sound field reproduction by ambisonics based on singular-value decomposition

Abstract

Ambisonics is a series of spatial sound systems with flexible loudspeaker configuration, which aims at reconstructing physical sound field in local region. Robustness of Ambisonics reproduction, which reflects the sensitivity of reproduced sound field to small errors, such as loudspeaker gain mismatch, is an important performance of sound reproduction. Condition number is generally used as an index to evaluate the robustness on whole, but this is insufficient because the robustness of reproduced sound field may be related to the target reproduction direction. To gain insights into the detail feature of robustness in Ambisonics reproduction, a method based on singular-value decomposition (SVD) is proposed to analyze reproduced sound field. The results indicate that the small singular values of transfer matrix and the proportion of Ambisonics coded vector projecting to the corresponding singular vectors dominate the robustness of Ambisonics reproduction. The robustness becomes worse only when such proportion of Ambisonics coded vector projection have relatively large energy. The proposed method is validated by simulating the sound pressure errors due to random mismatch of loudspeaker signals gain in some horizontal and spatial loudspeaker configurations. [Work supported by the National Natural Science Foundation of China, Grant No.11174087, and the State Key Lab of Subtropical Building Science, South China University of Technology, Grant No. 2014KB23.]