This work proposes and validates two computational tools for synthesizing distance-dependent head-related transfer function (HRTF), which is vital in spatial sound reproduction. HRTF is an anthropometric feature-dependent function that yields the direction-dependent gain of the auditory system. Even though it is subject to the distance of the auditory source, distance-dependent HRTF measurement is rare due to its high experimental cost. Numerical simulation tools can provide viable alternatives. The required computational resources and time increase exponentially with the frequencies and degree of freedom (DoF) of the simulations; still, it is faster than experimental procedures. This work proposes finite element computational solutions to measure distance-dependent HRTFs using domain truncation methods in association with frequency-dependent adaptive meshing. Two hybrid techniques to find HRTF in the entire region, employing infinite elements (IEs) and non-reflective boundary conditions (NRBCs) with near-field to far-field transformation techniques, have been implemented and analyzed. The proposed methods calculate distance-dependent HRTF in 0.2–20 kHz frequency band, with reduced computational cost and time. Additionally, the spatial resolution of the HRTF measurement has increased a 100-fold. Since locally connected finite elements are used, the near-field effects of HRTF are well incorporated, and the obtained HRTF matches well with the experimental results. The proposed tools can also calculate sufficiently accurate HRTFs even when the surface meshes are of reduced quality. The tools also possess the versatility in effortlessly integrating appropriate bioacoustic attributes (e.g., internal reflection of the middle ear walls) into HRTF numerical models, which is noteworthy.

这项工作提出并验证了两种计算工具，用于合成距离相关的头部相关传递函数 (HRTF)，这在空间声音再现中至关重要。HRTF 是一种人体测量特征依赖函数，它产生听觉系统的方向依赖增益。尽管它受制于听觉源的距离，但距离相关的 HRTF 测量由于其高昂的实验成本而很少见。数值模拟工具可以提供可行的替代方案。所需的计算资源和时间随着模拟的频率和自由度 (DoF) 呈指数增长；尽管如此，它还是比实验程序快。这项工作提出了有限元计算解决方案，以使用与频率相关的自适应网格划分相关的域截断方法来测量距离相关的 HRTF。已经实施和分析了两种在整个区域中寻找 HRTF 的混合技术，采用无限元 (IE) 和具有近场到远场转换技术的非反射边界条件 (NRBC)。所提出的方法在 0.2-20 kHz 频带中计算距离相关的 HRTF，减少了计算成本和时间。此外，HRTF 测量的空间分辨率提高了 100 倍。由于采用了局部连通的有限元，很好地融合了HRTF的近场效应，得到的HRTF与实验结果吻合较好。即使表面网格质量降低，所提出的工具也可以计算足够准确的 HRTF。这些工具还具有将适当的生物声学属性（例如，中耳壁的内反射）轻松集成到 HRTF 数值模型中的多功能性，这一点值得注意。