State-Space Architectures for Binaural Environment Modeling

Binaural displays for immersive listening must model reverberant environments, multiple sound sources, and accommodate source and head motion. Many displays model such phenomena as a collection of spatially distributed point sources; source signals are filtered with multiple head-related transfer functions (HRTFs) and then combined into a single binaural signal for display. The computational load of such systems scales linearly with the number of HRTFs modeled by the display. ‘Realistic’ auditory scenes often require a large number of HRTFs, hence this framework is computationally untenable. 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; MIMO, SIMO and MISO. The relative merits of each are found to depend on the specific application. If only a single source signal is displayed, a SIMO architecture yields the lowest computational cost for a fixed approximation quality. However, if multiple signals are displayed a pair of MISO systems yield the lowest cost. For the MIMO architecture, the interaural time delay degrades performance substantially and a hybrid technique is described to mitigate this problem. Hankel methods are found to be a good choice for model reduction, and yield displays with superior approximation quality relative to conventional FIR filter arrays of equal computational complexity.