State-Space Synthesis of Virtual Auditory Space

Binaural displays for immersive listening must model realistic acoustic environments, multiple sound sources, and accommodate source and head motion. Many displays accomplish this by convolving collections of spatially distributed point sources with head-related transfer functions (HRTFs). The computational load of such a system scales linearly with the number of HRTFs modeled by the display. Realistic scenes often require a large number of HRTFs, and this framework is computationally burdensome. We propose a method that significantly eases this load by formulating the HRTF filter array as a state-space system. Three state-space architectures are explored. The performance of the most general architecture is found to suffer due to the interaural time delay (ITD). This problem may be circumvented with two alternative architectures, although the ideal choice depends on the specific display application. For each architecture, two order-reduction techniques are explored. Both techniques are based on the Hankel operator; one is ad hoc and simple to implement whereas the other is optimal in the Hankel norm. The two methods yield similar auditory performance, although the optimal method may be desirable for HRTF approximation.