Abstract
Phased microphone array beamforming has become a standard technique to localize sound sources. For localization of rotating sound sources at free-space conditions in the frequency domain, a number of algorithms have been investigated. Two most famous algorithms were proposed by Pannert and Maier (J. Sound Vib., 333, 2014) and Herold and Sarradj (Noise Control Eng. J., 63, 2015). The relationship between the cross-spectral matrixes used in these two algorithms is still unclear. This paper investigated their relationship by proposing a new approach to calculate the cross-spectral matrix. Their relationship can then be interpreted from different interpolations used to calculate the sound pressures at virtual rotating array microphones from pressures at real stationary microphones. The former uses Fourier interpolation, while the latter uses linear interpolation. Compared with the latter algorithm, the cross-spectral matrix in the former algorithm has lower computational efficiency, nearly equal sound source location precision, and better sound source strength precision at high frequencies due to its better spectrum reconstruction capability. Additionally, the steering vector based on numerically solving the transcendental equation is proposed as an alternative with higher computational efficiency to the steering vector in the former algorithm.
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