State-space models of head-related transfer functions for virtual auditory scene synthesis.

This study investigates the use of reduced-order state-space models of collections of head-related transfer functions (HRTFs). Recent head-phone applications have motivated interest in binaural displays that can render multiple simultaneous virtual sound sources, acoustic reflections, and source and listener motion. In the present study, a multi-direction framework is considered that can render such phenomena by filtering source signals with a collection of HRTFs rather than individual HRTFs. The collection of HRTFs is implemented in the state-space, and approximation techniques are applied to construct low-order approximants that are indiscriminable from full-order HRTFs. Two experiments are described in which five observers are asked to discriminate between state-space and full-order renderings. Depending on the stimulus conditions and discrimination task, order thresholds of 7<or=N<or=24 are sufficient for an array of 50 HRTFs surrounding the listener. For comparison, a reference system of truncated minimum-phase impulse responses is also considered.