In response to renewed interest in virtual and augmented reality, the need for high-quality spatial audio systems has emerged. The reproduction of immersive and realistic virtual sound requires high resolution individualized head-related transfer function (HRTF) sets. In order to acquire an individualized HRTF, a large number of spatial measurements are needed. However, such a measurement process requires expensive and specialized equipment, which motivates the use of sparsely measured HRTFs. Previous studies have demonstrated that spherical harmonics (SH) can be used to reconstruct the HRTFs from a relatively small number of spatial samples, but reducing the number of samples may produce spatial aliasing error. Furthermore, by measuring the HRTF on a sparse grid the SH representation will be order-limited, leading to constrained spatial resolution. In this paper, the effect of sparse measurement grids on the reproduced binaural signal is studied by analyzing both aliasing and truncation errors. The expected effect of these errors on the perceived loudness stability of the virtual sound source is studied theoretically, as well as perceptually by an experimental investigation. Results indicate a substantial effect of truncation error on the loudness stability, while the added aliasing seems to significantly reduce this effect.

中文翻译：

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具有稀疏头部相关传递函数的球谐表示的双耳声响度稳定性

为了响应人们对虚拟现实和增强现实的新兴趣，出现了对高质量空间音频系统的需求。身临其境的逼真虚拟声音的再现需要高分辨率的个性化头部相关传递函数 (HRTF) 集。为了获得个性化的 HRTF，需要进行大量的空间测量。然而，这样的测量过程需要昂贵且专业的设备，这促使使用稀疏测量的 HRTF。先前的研究表明，球谐函数 (SH) 可用于从相对较少的空间样本中重建 HRTF，但减少样本数量可能会产生空间混叠误差。此外，通过在稀疏网格上测量 HRTF，SH 表示将受到顺序限制，导致空间分辨率受限。在本文中，通过分析混叠和截断误差来研究稀疏测量网格对再现的双耳信号的影响。这些误差对虚拟声源的感知响度稳定性的预期影响在理论上进行了研究，并通过实验研究在感知上进行了研究。结果表明截断误差对响度稳定性有很大影响，而添加的混叠似乎显着降低了这种影响。以及通过实验研究在感知上。结果表明截断误差对响度稳定性有很大影响，而添加的混叠似乎显着降低了这种影响。以及通过实验研究在感知上。结果表明截断误差对响度稳定性有很大影响，而添加的混叠似乎显着降低了这种影响。