A Model of Head-Related Transfer Functions based on a State-Space Analysis

Abstract

This dissertation develops and validates a novel state-space method for binaural auditory display. Binaural displays seek to immerse a listener in a 3D virtual auditory scene with a pair of headphones. The challenge for any binaural display is to compute the two signals to supply to the headphones. The present work considers a general framework capable of synthesizing a wide variety of auditory scenes. The framework models collections of head-related transfer functions (HRTFs) simultaneously. This framework improves the flexibility of contemporary displays, but it also compounds the steep computational cost of the display. The cost is reduced dramatically by formulating the collection of HRTFs in the state-space and employing order-reduction techniques to design efficient approximants. Order-reduction techniques based on the Hankel-operator are found to yield accurate low-cost approximants. However, the inter-aural time difference (ITD) of the HRTFs degrades the time-domain response of the approximants. Fortunately, this problem can be circumvented by employing a state-space architecture that allows the ITD to be modeled outside of the state-space. Accordingly, three state-space architectures are considered. Overall, a multiple-input, single-output (MISO) architecture yields the best compromise between performance and flexibility. The state-space approximants are evaluated both empirically and psychoacoustically. An array of truncated FIR filters is used as a pragmatic reference system for comparison. For a fixed cost bound, the state-space systems yield lower approximation error than FIR arrays for D >10, where D is the number of directions in the HRTF collection. A series of headphone listening tests are also performed to validate the state-space approach, and to estimate the minimum order N of indiscriminable approximants. For D = 50, the state-space systems yield order thresholds less than half those of the FIR arrays. Depending upon the stimulus uncertainty, a minimum state-space order of 7 ≤ N ≤ 23 appears to be adequate. In conclusion, the proposed state-space method enables a more flexible and immersive binaural display with low computational cost.