Analysis on summing virtual source localization in the sagittal plane

Multicnannel spatial sound with height requires summing virtual source between two adjacent loudspeakers vertically arranged in different sagittal planes. Some previous experiments showed that vertical summing localization in different sagittal planes is possible in certain cases. However, two adjacent loudspeakers arranged with a conventional spatial interval fails to provide correct magnitude spectra of binaural pressures, which are regarded as an important cue for vertical localization. Based on Wallach's hypothesis that the change of interaural time difference (ITD) caused by head turning around the vertical and front-back axes provides low-frequency dynamic cues for front-back and vertical localization, our previous work has analyzed the vertical summing localization by two adjacent loudspeakers in the median plane. The present work extends the analysis to the case of vertical summing localization in arbitrary sagittal plane. By using a simple shadowless head model and head-related transfer functions from KEMAR artificial head, the ITD and its change with head turning are analyzed and compared between a single real source and a summing virtual source. The results indicate that, pair-wise amplitude panning is able to create virtual sources between loudspeakers only for some two-loudspeaker configurations in the sagittal plane. Moreover, a virtual source localization experiment is conducted, yielding results consistent with those of the analysis.