A set of equations for numerically calculating the interaural level difference in the horizontal plane.

Michael A Akeroyd,Samuel Smith,Jennifer Firth,Simone Graetzer

doi:10.1121/10.0004261

Michael A Akeroyd, Samuel Smith + Show 2 more

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https://doi.org/10.1121/10.0004261

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Abstract

The variation of interaural level difference (ILD) with direction and frequency is particularly complex and convoluted. The purpose of this work was to determine a set of parametric equations that can be used to calculate ILDs continuously at any value of frequency and azimuth in the horizontal plane. They were derived by fitting equations to ILDs derived from the azimuthal-dependence data tabulated by Shaw and Vaillancourt [(1985). J. Acoust. Soc Am. 78, 1120-1123] and assuming left-right symmetry. The equations are shown to fit those data to an overall RMS error less than 0.5 dB.

Highlights

To complement some current projects on spatial hearing, it was necessary to have a set of closed-form equations from which interaural time and level differences (ITDs and interaural level difference (ILD), respectively) could be calculated continuously for any value of azimuth or frequency in the horizontal plane
We report here a set of equations that enable ILDs to be calculated for any angle of azimuth up to 10 kHz
The equations are derived from tabulated data reported by Shaw and Vaillancourt (1985) and assume left-right symmetry

Summary

Introduction

To complement some current projects on spatial hearing, it was necessary to have a set of closed-form equations from which interaural time and level differences (ITDs and ILDs, respectively) could be calculated continuously for any value of azimuth or frequency in the horizontal plane. For ITDs, it is typical to use the expression (rh þ r sin h)/c, where r is the radius of the head, h is the azimuth of the sound source, in radians, and c is the speed of sound (Woodworth, 1938; Blauert, 1997) This expression is derived from a simple geometrical model in which it is assumed that the head is spherical in shape (Duda and Martens, 1998), the two ears are diametrically opposite each other, and the source of sound is sufficiently far away for the wavefronts to be planes. This equation captures two overall phenomena pertaining to the shape of the function of ILD across azimuth and frequency: the dependence on azimuth essentially follows the first half (0-p) of a sinusoid, and the overall magnitude of the ILDs increases with frequency

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