Microphone and speaker array designs have increasingly diverged from simple topologies due to diversity of physical host geometries and use cases. Effective beamformer design must now account for variation in the array’s acoustic radiation pattern, spatial distribution of target and noise sources, and intended beampattern directivity. Relevant tasks such as representing complex pressure fields, specifying spatial priors, and composing beampatterns can be efficiently synthesized using spherical harmonic (SH) basis functions. This paper extends the expansion of common stationary covariance functions onto the SHs and proposes models for encoding magnitude functions on a sphere. Conventional beamformer designs are reformulated in terms of magnitude density functions and beampatterns along SH bases. Applications to speaker far-field response fitting, cross-talk cancelation design, and microphone beampattern fitting are presented.

中文翻译：

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用于波束成形器设计的球面谐波协方差和幅度函数编码

由于物理主机几何形状和用例的多样性，麦克风和扬声器阵列设计越来越偏离简单的拓扑结构。有效的波束形成器设计现在必须考虑阵列声辐射图、目标和噪声源的空间分布以及预期波束图方向性的变化。使用球谐函数 (SH) 基函数可以有效地合成相关任务，例如表示复杂压力场、指定空间先验和组合波束模式。本文将常见的平稳协方差函数扩展到 SH 上，并提出了在球体上编码幅度函数的模型。传统的波束形成器设计根据幅度密度函数和沿 SH 基的波束方向图重新表述。扬声器远场响应拟合的应用，