Efficient computation of modal transfer function in mode composition beamforming for rotating broadband source localization

For rotating sound source localization, there are mainly two types of frequency-domain beamforming methods, the virtual rotating array (VRA) method and mode composition beamforming (MCB). Compared with the VRA method, MCB overcomes the constraint of microphone array configuration and avoids error introduced by interpolation. In order to obtain the MCB result, modal transfer functions, which are the modal coefficients in the analytical solution of the sound field of rotating source, should be pre-calculated. However, the computation of modal transfer functions takes a long time, especially under a large number of considered frequencies. Therefore, the computational efficiency of MCB is limited by the computation of modal transfer functions. In this paper, an expression of modal transfer functions at multiple considered frequencies is derived first. According to this expression, intermediate variables independent of frequency are computed in a fast way, then modal transfer functions at each considered frequency are calculated through these intermediate variables. This expression is successfully applied to improve the computational efficiency of MCB for rotating broadband source localization.