Ambisonics rendering has become an integral part of 3D audio for headphones. It works well with existing recording hardware, the processing cost is mostly independent of the number of sound sources, and it elegantly allows for rotating the scene and listener. One challenge in Ambisonics headphone rendering is to find a perceptually well behaved low-order representation of the Head-Related Transfer Functions (HRTFs) that are contained in the rendering pipe-line. Low-order rendering is of interest, when working with microphone arrays containing only a few sensors, or for reducing the bandwidth for signal transmission. Magnitude Least Squares rendering became the de facto standard for this, which discards high-frequency interaural phase information in favor of reducing magnitude errors. Building upon this idea, we suggest Masked Magnitude Least Squares, which optimized the Ambisonics coefficients with a neural network and employs a spatio-spectral weighting mask to control the accuracy of the magnitude reconstruction. In the tested case, the weighting mask helped to maintain high-frequency notches in the low-order HRTFs and improved the modeled median plane localization performance in comparison to MagLS, while only marginally affecting the overall accuracy of the magnitude reconstruction.

Differentiable rendering has become a key ingredient in solving challenging inverse problems in computer graphics and vision. Existing systems can simulate and differentiate the spatial propagation of light. We exploit the duality of light transport simulations and geometric acoustics to apply differential rendering techniques to established acoustic simulation methods. The resulting system is capable of simulating sound according to the geometrical acoustics model and computing derivatives of the output energy spectrograms with respect to arbitrary parameters of the scene, including materials, emitters, microphones, and scene geometry. Contrary to current differentiable transient rendering, we can handle arbitrary simulation depths and achieve constant memory and linear execution times by presenting a temporal extension of Path Replay Backpropagation [Vicini et al. 2021]. We verify our model against established simulation software, and demonstrate the capabilities of optimization with gradients at examples of inverse acoustics and optimizing room parameters. This opens up a new field of research for acoustic optimization that could be as impactful for the acoustic community as differentiable rendering was for the graphics community.

Head-related transfer functions (HRTFs) are essential for virtual acoustic realities because they contain all cues for localizing sound sources in three-dimensional space. Acoustic measurements are one way to obtain high-quality HRTFs. To reduce measurement time, cost, and complexity of measurement systems, a promising approach is to capture only a few HRTFs on a sparse sampling grid and then upsample them to a dense HRTF set by interpolation. However, HRTF interpolation is challenging because small changes in source position can result in significant changes in the HRTF phase and magnitude response. Previous studies have greatly improved the interpolation by time-aligning the HRTFs in pre-processing, but magnitude interpolation errors remain a problem, especially in contralateral regions. Building on time-aligned interpolation, we propose a post-interpolation magnitude correction derived from a frequency-smoothed HRTF representation. Our technical evaluation based on 96 individual simulated HRTF sets shows that the magnitude correction reduces subject-averaged magnitude errors in the higher frequency range by up to 1.5 dB when averaged over all directions and by up to 4 dB in the contralateral region. As a result, interaural level differences in the upsampled HRTFs are also improved. The accompanying perceptual evaluation shows that the magnitude correction significantly reduces perceived coloration and results in a more stable and accurate perceived source position. Additional technical evaluations show that the proposed method outperforms current machine learning based algorithms, can be used with measured HRTFs, and is superior to using a dummy head HRTF set even when only six source positions are used for upsampling.

In the paper “Directional Equalization of Sparse Head-Related Transfer Function Sets for Spatial Upsampling”, published in IEEE/ACM Transactions on Audio, Speech, andLanguage Processing (Volume: 27, Issue: 6, June 2019) [1],Eq. (2) and Eq. (6) are incorrect. In this Comment Correspondence we provide a correction of these Errors.

Acquiring decent full-spherical sets of head-related transfer functions (HRTFs) based on a small number of measurements is highly desirable. For spatial upsampling, HRTF interpolation in the spatially continuous spherical harmonics (SH) domain is a common approach. However, the number of measured HRTFs limits the assessable SH order, resulting in order-limited HRTFs when transformed to the SH domain. Thus, the SH representation of sparse HRTF sets shows restricted spatial resolution and suffers from order-limitation errors. We present a method that reduces these errors by a directional equalization prior to the SH transform. This is done by a spectral division of each HRTF with a corresponding directional rigid sphere transfer function. The processing removes direction-dependent temporal and spectral components and, therefore, significantly reduces the spatial complexity of the HRTF set, allowing for an enhanced interpolation of HRTFs at reduced SH orders. Spatial upsampling is achieved by an inverse SH transform on an arbitrary dense sampling grid. A subsequent de-equalization by a spectral multiplication with the rigid sphere transfer function recovers the energy in higher spatial orders that was not inherent in the sparse HRTF set. For evaluation, HRTFs were calculated for various limited orders from sparse datasets and compared to a reference. The results show that the proposed method clearly outperforms common SH interpolation of HRTF spectra regarding the overall spectral and temporal structure as well as modeled localization performance.

Numerical simulations offer a feasible alternative to the direct acoustic measurement of individual head-related transfer functions (HRTFs). For the acquisition of high quality 3D surface scans, as required for these simulations, several approaches exist. In this paper, we systematically analyze the variations between different approaches and evaluate the influence of the accuracy of 3D scans on the resulting simulated HRTFs. To assess this effect, HRTFs were numerically simulated based on 3D scans of the head and pinna of the FABIAN dummy head generated with 6 different methods. These HRTFs were analyzed in terms of interaural time difference, interaural level difference, energetic error in auditory filters and by their modeled localization performance. From the results, it is found that a geometric precision of about 1 mm is needed to maintain accurate localization cues, while a precision of about 4 mm is sufficient to maintain the overall spectral shape.