A Formula for Low-Frequency Interaural Level Difference

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R. Sridhar, and E. Choueiri, "A Formula for Low-Frequency Interaural Level Difference," Paper 10412, (2020 October.). doi:
R. Sridhar, and E. Choueiri, "A Formula for Low-Frequency Interaural Level Difference," Paper 10412, (2020 October.). doi:
Abstract: A formula for low-frequency interaural level difference (LF-ILD) as a function of source distance and direction is derived from rigid-sphere head-related transfer function (RS-HRTF) theory. Since ILD at low frequencies (typically ƒ < 700Hz) is a dominant cue for near-field distance perception in the free-field, a simple formula akin to the Woodworth formula for high-frequency interaural time difference, may be beneficial to easily and efficiently implement distance- and direction-dependent LF-ILDs for real-time spatial audio applications on devices with limited computational resources. By evaluating the limit as ƒ → 0 of the infinite series representation of the RS-HRTF for finite source distances, an exact, closed-form expression for the “DC gain” as a function of source distance and direction is derived. For a given source location, using this expression to compute the DC gain at the left and right “ears,” and then taking the ratio of the two quantities gives the desired LF-ILD. As an example, it is shown that the derived formula may be used to extrapolate far-field ILD spectra of a rigid sphere to the near-field exactly for low frequencies and with sufficiently high accuracy for higher frequencies. Furthermore, the derived formula, like the Woodworth formula, is well-suited to individualization.

@article{sridhar2020a,
author={sridhar, rahulram and choueiri, edgar},
journal={journal of the audio engineering society},
title={a formula for low-frequency interaural level difference},
year={2020},
volume={},
number={},
pages={},
doi={},
month={october},}
@article{sridhar2020a,
author={sridhar, rahulram and choueiri, edgar},
journal={journal of the audio engineering society},
title={a formula for low-frequency interaural level difference},
year={2020},
volume={},
number={},
pages={},
doi={},
month={october},
abstract={a formula for low-frequency interaural level difference (lf-ild) as a function of source distance and direction is derived from rigid-sphere head-related transfer function (rs-hrtf) theory. since ild at low frequencies (typically ƒ < 700hz) is a dominant cue for near-field distance perception in the free-field, a simple formula akin to the woodworth formula for high-frequency interaural time difference, may be beneficial to easily and efficiently implement distance- and direction-dependent lf-ilds for real-time spatial audio applications on devices with limited computational resources. by evaluating the limit as ƒ → 0 of the infinite series representation of the rs-hrtf for finite source distances, an exact, closed-form expression for the “dc gain” as a function of source distance and direction is derived. for a given source location, using this expression to compute the dc gain at the left and right “ears,” and then taking the ratio of the two quantities gives the desired lf-ild. as an example, it is shown that the derived formula may be used to extrapolate far-field ild spectra of a rigid sphere to the near-field exactly for low frequencies and with sufficiently high accuracy for higher frequencies. furthermore, the derived formula, like the woodworth formula, is well-suited to individualization.},}

TY - paper
TI - A Formula for Low-Frequency Interaural Level Difference
SP -
EP -
AU - Sridhar, Rahulram
AU - Choueiri, Edgar
PY - 2020
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - October 2020
TY - paper
TI - A Formula for Low-Frequency Interaural Level Difference
SP -
EP -
AU - Sridhar, Rahulram
AU - Choueiri, Edgar
PY - 2020
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - October 2020
AB - A formula for low-frequency interaural level difference (LF-ILD) as a function of source distance and direction is derived from rigid-sphere head-related transfer function (RS-HRTF) theory. Since ILD at low frequencies (typically ƒ < 700Hz) is a dominant cue for near-field distance perception in the free-field, a simple formula akin to the Woodworth formula for high-frequency interaural time difference, may be beneficial to easily and efficiently implement distance- and direction-dependent LF-ILDs for real-time spatial audio applications on devices with limited computational resources. By evaluating the limit as ƒ → 0 of the infinite series representation of the RS-HRTF for finite source distances, an exact, closed-form expression for the “DC gain” as a function of source distance and direction is derived. For a given source location, using this expression to compute the DC gain at the left and right “ears,” and then taking the ratio of the two quantities gives the desired LF-ILD. As an example, it is shown that the derived formula may be used to extrapolate far-field ILD spectra of a rigid sphere to the near-field exactly for low frequencies and with sufficiently high accuracy for higher frequencies. Furthermore, the derived formula, like the Woodworth formula, is well-suited to individualization.

A formula for low-frequency interaural level difference (LF-ILD) as a function of source distance and direction is derived from rigid-sphere head-related transfer function (RS-HRTF) theory. Since ILD at low frequencies (typically ƒ < 700Hz) is a dominant cue for near-field distance perception in the free-field, a simple formula akin to the Woodworth formula for high-frequency interaural time difference, may be beneficial to easily and efficiently implement distance- and direction-dependent LF-ILDs for real-time spatial audio applications on devices with limited computational resources. By evaluating the limit as ƒ → 0 of the infinite series representation of the RS-HRTF for finite source distances, an exact, closed-form expression for the “DC gain” as a function of source distance and direction is derived. For a given source location, using this expression to compute the DC gain at the left and right “ears,” and then taking the ratio of the two quantities gives the desired LF-ILD. As an example, it is shown that the derived formula may be used to extrapolate far-field ILD spectra of a rigid sphere to the near-field exactly for low frequencies and with sufficiently high accuracy for higher frequencies. Furthermore, the derived formula, like the Woodworth formula, is well-suited to individualization.

Open Access

Authors:
Sridhar, Rahulram; Choueiri, Edgar
Affiliation:
3D Audio and Applied Acoustics Lab, Princeton University, NY, USA
AES Convention:
149 (October 2020)
Paper Number:
10412
Publication Date:
October 22, 2020Import into BibTeX
Subject:
Immersive Audio
Permalink:
http://www.aes.org/e-lib/browse.cfm?elib=20949