Audibility of dispersion error in room acoustic finite-difference time-domain simulation as a function of simulation distance

Abstract

Finite-difference time-domain (FDTD) simulation has been a popular area of research in room acoustics due to its capability to simulate wave phenomena in a wide bandwidth directly in the time-domain. A downside of the method is that it introduces a direction and frequency dependent error to the simulated sound field due to the non-linear dispersion relation of the discrete system. In this study, the perceptual threshold of the dispersion error is measured in three-dimensional FDTD schemes as a function of simulation distance. Dispersion error is evaluated for three different explicit, non-staggered FDTD schemes using the numerical wavenumber in the direction of the worst-case error of each scheme. It is found that the thresholds for the different schemes do not vary significantly when the phase velocity error level is fixed. The thresholds are found to vary significantly between the different sound samples. The measured threshold for the audibility of dispersion error at the probability level of 82% correct discrimination for three-alternative forced choice is found to be 9.1 m of propagation in a free field, that leads to a maximum group delay error of 1.8 ms at 20 kHz with the chosen phase velocity error level of 2%.

Audibility of dispersion error in room acoustic finite-difference time-domain simulation in the presence of absorption of air

“…There is no significant difference between the distributions of the observations in the different distance groups. The maximum group delay values agree with the findings of the previous threshold study, 2 where the mean value of the measured maximum group delay value was found to be 1.8 ms.…”

“…The selection of a single scheme is justified with the result presented in Ref. 2, that with schemes with a similar phase velocity error contour, the audibility of the error as function of distance is similar. Therefore, in order to reduce the number of trials, only a single scheme condition is used.…”

“…Due to this similarity, it is likely that the air absorption masks the group delay error partially, or completely at a certain distance limit with a low-enough phase velocity error level. Even though several studies have examined the audibility of dispersion error in the context of room acoustic simulation, [1][2][3] the perceptual threshold of the phase velocity error has not been addressed to the present authors' knowledge. Such a threshold is highly useful due to the fact that the phase velocity error can be evaluated directly from the sampling frequency of the simulation.…”

FDTD Methods for 3-D Room Acoustics Simulation With High-Order Accuracy in Space and Time

“…In Fig. 10, we plot (k X ) for various schemes (leaving out some large-star schemes, for clarity); and we focus on (k X ) ≤ 5%-for brevity, and because there is recent evidence that high-fidelity auralizations require phase velocities errors to be as low as 2% to mitigate audible phase artifacts [18]. From Fig.…”

“…Digital Object Identifer 10.1109/TASLP.2017.00000000 audible phase artifacts [18]. Mitigating such effects through grid oversampling incurs significant additional computational costs and therefore is not always practical for large-scale simulations.…”