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

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%.

[1]  M. Leek.  Adaptive procedures in psychophysical research , 2001, Perception & psychophysics.

[2]  M. van Walstijn,et al.  On the numerical solution of the 2d wave equation with compact fdtd schemes , 2008 .

[3]  Marc Aretz.  Specification of Realistic Boundary Conditions for the FE Simulation of Low Frequency Sound Fields in Recording Studios , 2009 .

[4]  A. R. Gourlay,et al.  A Classification of Split Difference Methods for Hyperbolic Equations in Several Space Dimensions , 1969 .

[5]  J. Blauert,et al.  Group delay distortions in electroacoustical systems , 1978 .

[6]  Jonathan W. Peirce,et al.  PsychoPy—Psychophysics software in Python , 2007, Journal of Neuroscience Methods.

[7]  B. Schultz.  Levene's Test for Relative Variation , 1985 .

[8]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[9]  D. M. Green,et al.  Discrimination of transient signals having identical energy spectra. , 1970, The Journal of the Acoustical Society of America.

[10]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[11]  Brian Hamilton,et al.  ROOM ACOUSTICS MODELLING USING GPU-ACCELERATED FINITE DIFFERENCE AND FINITE VOLUME METHODS ON A FACE-CENTERED CUBIC GRID , 2013 .

[12]  Maarten van Walstijn,et al.  Room Acoustics Simulation Using 3-D Compact Explicit FDTD Schemes , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[13]  Lauri Savioja,et al.  REAL-TIME 3D FINITE-DIFFERENCE TIME-DOMAIN SIMULATION OF LOW- AND MID-FREQUENCY ROOM ACOUSTICS , 2010 .

[14]  S. McKee,et al.  Statistical properties of forced-choice psychometric functions: Implications of probit analysis , 1985, Perception & psychophysics.

[15]  B. Treutwein.  Adaptive psychophysical procedures , 1995, Vision Research.

[16]  Henrik Møller,et al.  On the audibility of all-pass phase in electroacoustical transfer functions , 2007 .

[17]  Gilbert A. Soulodre,et al.  Evaluation of Objective Loudness Meters , 2004 .

[18]  A. Watson,et al.  Quest: A Bayesian adaptive psychometric method , 1983, Perception & psychophysics.

[19]  Stefan Bilbao,et al.  ON FINITE DIFFERENCE SCHEMES FOR THE 3-D WAVE EQUATION USING NON-CARTESIAN GRIDS , 2013 .

[20]  Brian C. J. Moore,et al.  Discrimination of Group Delay in Clicklike Signals Presented via Headphones and Loudspeakers , 2005 .

[21]  David Middleton,et al.  Sampling and Reconstruction of Wave-Number-Limited Functions in N-Dimensional Euclidean Spaces , 1962, Inf. Control..

[22]  John B. Schneider,et al.  FDTD dispersion revisited: faster-than-light propagation , 1999 .

[23]  S. Shapiro,et al.  An Analysis of Variance Test for Normality (Complete Samples) , 1965 .

[24]  Vesa Välimäki,et al.  Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques , 2000, IEEE Trans. Speech Audio Process..

[25]  Tapio Lokki,et al.  The perceptual effects of dispersion error on room acoustic model auralization , 2011 .

[26]  Douglas Preis,et al.  Perception of phase distortion in all-pass filters , 1985 .