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Analysis of the sphericalwave truncation error for spherical harmonic soundfield expansions

机译:球面谐波声域扩展的球形波截断误差分析

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Three dimensional soundfield recording and reproduction is an area of ongoing investigation and its implementation is increasingly achieved through use of the infinite Spherical Harmonic soundfield expansion. Perfect recording or reconstruction requires infinite microphones or loudspeakers, respectively. Thus, real-world approximations to both require spatial discretisation, which truncates the soundfield expansion and loses some of the soundfield information. The resulting truncation error is the focus of this paper, specifically for soundfields comprising of spherical waves. We define two norms of the truncation error to signal ratio, L2 and L∞, for comparison and use in different situations. Finally we observe how some of these errors converge to the plane wave case under certain circumstances.
机译:三维声场录音和再现是正在进行的调查领域,通过使用无限球形谐波声场扩展越来越多地实现其实施。完美的录音或重建分别需要无限的麦克风或扬声器。因此,对两者的实际近似都需要空间离散化,其截断声场扩展并丢失一些声场信息。由此产生的截断误差是本文的焦点,专门用于包括球形波的声场。我们将截断误差的两个规范定义为信号比,L2和L∞,以便在不同情况下使用和使用。最后,我们在某些情况下观察一些这些错误如何收敛到平面波形。

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