The following audio examples accompany the publication
J. Ahrens, H. Helmholz, D. Alon, S. Amengual Garí, “The Far-Field Equatorial Array for Binaural Rendering,” IEEE ICASSP, 2021 (DOI: 10.1109/ICASSP39728.2021.9414368).
The DOI of the audio examples is 10.5281/zenodo.4807499.
We provide binaural renderings for both the proposed equatorial array as well as for a conventional spherical microphone of the same orders (5 and 8). All audio examples are based on simulated microphone responses in a free field. They tend not to sound very spatial because of the lack of reverberation. All examples assume a head orientation of the listener into 45° azimuth whereby the captured sound field impinges always from 0° azimuth.
The audio examples were created with sound_field_analysis-py.
8th-Order Arrays
The 8th-order equatorial array has 17 equi-angularly spaced microphones, the 8th-order conventional array uses a 110 microphones on a Lebedev grid. Both arrays have a radius of 8.75 cm.
A single plane wave with different elevations of the propagation direction
These examples correspond to Fig. 5 in the paper.
Elevation | Spherical array (8th order) | Equatorial array (8th order) |
0° | ||
30° | ||
60° | ||
90° |
The spherical array and the equatorial array sound very much alike for 0° elevation of the propagation direction of the plane wave. Note also that the equatorial array produces the correct interaural time difference even for non-horizontal sound incidence.
Even with the conventional array, you will most likely hear that the perceived elevation does not correspond to the actual one. This may be a consequence of the fact that we’re using non-individual HRTFs. The artifacts of the array may also play a role. You will also hear that the lateraliztion of the perceived incidence direction reduces with increasing elevation of the propagation direction of the impinging plane wave. This is to be expected as the increase of elevation reduces the interaural differences in the binaural signal.
A single point source in the horizontal plane at different distances
The presented approach assumes distant sources in the stage where it removes the scattering off the sphere from the captured source field. The following examples illustrate what the limitations of this are. Note that all of the following audio examples are normalized, which means that they all sound mostly equally loud. It is typically not possible to hear the distance of a sound source without any reverberation being present.
Note that with this normalization, all renderings from the conventional spherical array sound virtually identical to the 0° plane wave example from above. We therefore skip presenting such audio examples here.
Source distance | Equatorial array (8th order) |
5 m | |
4 m | |
3 m |
It becomes evident that the scattering removal introduces a strong low-frequency boost for source distances of 3 m and less for this particular setup. It was unfortunately not possible to include an analysis of this in the paper. It is subject to on-going work. Note that the 3-m-example sounds a little quieter because of the normalization.
5th-Order Arrays
The 5th-order equatorial array has 11 equi-angularly spaced microphones, the 5th-order conventional array uses a 50 microphones on a Lebedev grid. Both arrays have a radius of 4.2 cm, which is similar to the Eigenmike.
A single plane wave with different elevations of the propagation direction
Elevation | Spherical array (5th order) | Equatorial array (5th order) |
0° | ||
30° | ||
60° | ||
90° |
A single point source in the horizontal plane at different distances
Source distance | Equatorial array (5th order) |
3 m | |
2 m | |
1 m |
The observations are very much the same as with the 8th-order arrays whereby the minimal required source distance for avoiding the low-frequency boost is shorter for the 5th-order array.