A method for converting between cylindrical and spherical harmonic representations of sound fields
A method for converting between cylindrical and spherical harmonic representations of sound fields
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声场的柱调和球调和表示之间的转换方法
DOI：
10.1109/icassp.2014.6854498
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
I. Tashev
中科院分区：
文献类型：
--
作者：
Mark R. P. Thomas;J. Ahrens;I. Tashev
球形麦克风和圆形麦克风阵列对于采样可以与扬声器阵列重新合成的声场是有用的。球形麦克风阵列是期望的，因为它们能够捕获三维声场，然而，通常更实际的是以位于水平面中的闭合圆的形式构造扬声器阵列。这导致空间欠采样，因为这种圆形采样只能产生高度不变声场的完美表示。本文研究的后果，这种空间欠采样之间的转换圆柱和球谐分解的波动方程的解决方案。我们通过分析和数值模拟表明：1）空间欠采样的结果是一个纯粹的水平传播声场，以及2）欠采样声场中的行进分量和驻场分量的比率根据入射余纬度而变化。该转换也用于波束形成场景中，并且示出了随着源远离水平面移动，波束形成器响应变得越来越全向。
Spherical microphone and circular microphone arrays are useful for sampling sound fields that may be resynthesized with loudspeaker arrays. Spherical microphone arrays are desirable because of their ability to capture three-dimensional sound fields, however it is often more practical to construct loudspeaker arrays in the form of a closed circle located in the horizontal plane. This leads to a spatial undersampling as such a circular sampling can only yield a perfect representation of a height-invariant sound field. This paper investigates the consequences of such spatial undersampling by converting between cylindrical and spherical harmonic decompositions of solutions to the wave equation. We show analytically and via numerical simulations that 1) the result of the spatial undersampling is a purely horizontally propagating sound field, and 2) the ratio of travelling and standing components in the undersampled sound field varies depending on the incidence colatitude. The conversion is also used in a beamforming scenario and shows that the beamformer response becomes increasingly omnidirectional as the source moves away from the horizontal plane.