Magnitude-Corrected and Time-Aligned Interpolation of Head-Related Transfer Functions

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.