Speaker
Description
Any linear time-invariant system admits a state-space realization. In contrast to classical transfer-function models, state-space formulations remain numerically robust at high orders. They can also be more computationally efficient than block-wise convolution-based rendering, especially for MIMO systems. Another advantage is access to model order reduction methods that produce compact models with a priori error bounds.We argue that state-space models deserve renewed attention in acoustics. While more common in earlier work, they have partly fallen out of focus. They are beneficial in many areas, but head-related transfer functions (HRTFs) are especially well suited to highlight their advantages.Despite this potential, state-space HRTF models are still rare in virtual acoustics. Such models can be constructed from simulations or measured data; here, we focus on head-related impulse response measurements. The few approaches reported in the literature indicate clear advantages, but they have struggled to achieve very high fidelity because of computational bottlenecks in the reduction algorithms rather than in the state-space models themselves.In previous work, we have already demonstrated the feasibility of modern numerical linear algebra methods such as the randomized or tangential Eigensystem Realization Algorithm for acoustical applications. Building on this foundation, we show that these advances remove the relevant bottlenecks for HRTF modelling. High-fidelity state-space HRTF models can thus be constructed reliably and with negligible error. We further provide user-friendly open-source Python implementations of the reduction algorithms and efficient solvers for rendering. Overall, the talk aims to show that state-space models are again a practical framework for acoustical modelling, with HRTFs providing an instructive example.