Abstract
A common approach when employing discrete mathematical models is to assess the reliability and credibility of the computation of interest through a process known as solution verification. Present-day computed head-related transfer functions (HRTFs) seem to lack robust and reliable assessments of the numerical errors embedded in the results which makes validation of wave-based models difficult. This process requires a good understanding of the involved sources of error which are systematically reviewed here. The current work aims to quantify the pinna-related high-frequency computational errors in the context of HRTFs and wave-based simulations with finite-difference models. As a prerequisite for solution verification, code verification assesses the reliability of the proposed implementation. In this paper, known and manufactured formal solutions are used and tailored for the wave equation and frequency-independent boundary conditions inside a rectangular room of uniform acoustic wall-impedance. Asymptotic estimates for pinna acoustics are predicted in the frequency domain based on regression models and a convergence study on sub-millimeter grids. Results show an increasing uncertainty with frequency and a significant frequency-dependent change among computations on different grids.
Highlights
The head-related transfer functions (HRTFs) represent the acoustical paths from a stationary sound source to the ears of the listener under free field conditions, encoding the anatomical filtering effects which embed the auditory cues used for localizing sound sources.Unless cue remapping occurs,1 HRTFs are usually not perceptually transferable.2 This is mainly due to the high degree of personalization of the human pinna.3 Currently, the main two methods for obtaining an estimate of individualized HRTFs are measurements and simulations
The present study aims to quantify the quality of computed wave-based pinnarelated transfer function (PRTF)/ HRTF solutions with focus on finite difference time domain (FDTD) methods
The present work showed that the current state in HRTF/PRTF simulation literature which involve a single computation could yield erroneous results: for each input parameter such as b, single-grid computed solutions could be biased relative to the formal solution
Summary
The head-related transfer functions (HRTFs) represent the acoustical paths from a stationary sound source to the ears of the listener under free field conditions, encoding the anatomical filtering effects which embed the auditory cues used for localizing sound sources.Unless cue remapping occurs, HRTFs are usually not perceptually transferable. This is mainly due to the high degree of personalization of the human pinna. Currently, the main two methods for obtaining an estimate of individualized HRTFs are measurements and simulations. This is mainly due to the high degree of personalization of the human pinna.. Depending on the formulation and properties of the continuous solution, any computational implementation and execution will involve model-specific deviations from the formal behavior. Such computational errors could interact in a complex manner requiring empirical reliability assessment of the final computations. Such methods can be transferred from other fields and advantageously employed to empirically estimate the quality of the computations, given the complex PRTF problem at hand
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