## 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 f < 700 Hz) 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 f → 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.

Original language | English (US) |
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State | Published - 2020 |

Event | 149th Audio Engineering Society Convention 2020, AES 2020 - Virtual, Online Duration: Oct 27 2020 → Oct 30 2020 |

### Conference

Conference | 149th Audio Engineering Society Convention 2020, AES 2020 |
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City | Virtual, Online |

Period | 10/27/20 → 10/30/20 |

## All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Acoustics and Ultrasonics