In recent years, spatial audio reproduction has been widely researched with many studies focusing on headphone-based spatial reproduction. A popular format for spatial audio is higher order Ambisonics (HOA), where a spherical microphone array is typically used to obtain the HOA signals. When a spherical array is not available, beamforming-based binaural reproduction (BFBR) can be used, where signals are captured with arrays of a general configuration. While shown to be useful, no comprehensive studies of BFBR have been presented and so its limitations and other design aspects are not well understood. This paper takes an initial step towards developing a theory for BFBR and develops guidelines for selecting the number of beamformers. In particular, the average directivity factor of the microphone array is proposed as a measure for supporting this selection. The effect of head-related transfer function (HRTF) order truncation that occurs when using too many beamformer directions is presented and studied. In addition, the relation between HOA-based binaural reproduction and BFBR is discussed through analysis based on a spherical array. A simulation study is then presented, based on both a spherical and a planar array, demonstrating the proposed guidelines. A listening test verifies the perceptual attributes of the methods presented in this study. These results can be used for more informed beamformer design for BFBR.

中文翻译：

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基于波束成形的双耳再现中波束成形器数量的选择


近年来，空间音频再现得到了广泛的研究，许多研究集中在基于耳机的空间再现。空间音频的流行格式是高阶高保真度立体声响复制 (HOA)，其中通常使用球形麦克风阵列来获取 HOA 信号。当球形阵列不可用时，可以使用基于波束成形的双耳再现 (BFBR)，其中使用通用配置的阵列捕获信号。虽然 BFBR 被证明是有用的，但尚未进行全面的研究，因此其局限性和其他设计方面尚不清楚。本文朝着发展 BFBR 理论迈出了第一步，并制定了选择波束形成器数量的指南。特别地，提出了麦克风阵列的平均方向性因子作为支持这种选择的度量。提出并研究了使用过多波束形成器方向时发生的头部相关传递函数 (HRTF) 阶次截断的影响。此外，通过基于球形阵列的分析讨论了基于HOA的双耳再现与BFBR之间的关系。然后提出了基于球形和平面阵列的模拟研究，展示了所提出的指导方针。听力测试验证了本研究中提出的方法的感知属性。这些结果可用于 BFBR 的更明智的波束形成器设计。