Spatial relationships between interaural differences in a room

Abstract

The interaural ratio, as it occurs for a human head in a room, can be represented by a filter with a complex transfer function of the spatial location of the head. The log of this transfer function has real and imaginary parts, respectively, the interaural level difference (ILD) and the interaural phase difference (IPD). Because the filter is causal, the ILD and IPD spatial functions are Hilbert transforms of each other if the interaural filter is a minimum phase function of the head location. Interaural differences for a spherical “head” with tiny probe microphones, separated by a head diameter of 17.5 cm, were measured by Mr. Zane Crawford in an empty room having a volume of 63 $m∧3$ and a reverberation time of 0.4 s. The head was moved in increments of 2.54 cm over a two dimensional grid 102 cm by 23 cm. Measurements at 250 Hz showed that the ILD and IPD were almost perfectly related by Hilbert transforms. Measurements at 500 and 1000 Hz showed increasing deviations. Because a function is orthogonal to its Hilbert transform, the ideal ILD is orthogonal to the IPD. Therefore, at locations where the ILD is the most stable function of space, the IPD is the most unstable and vice versa.