In the context of binaural virtual acoustics, a sound source is positioned in a free-field 3-D space a
round the listener by filtering it via head-related transfer functions (HRTFs). In a real-time application, numerous HRTFs need to be processed. The long impulse responses of the HRTFs require a high computational power, which is difficult to directly implement on current processors in situations involving more than a few simultaneous sources.
Technically speaking, an HRTF is a linear time-invariant (LTI) system. An LTI system can be implemented in the time domain by direct convolution or recursive filtering. This approach is computationally inefficient. A computationally efficient approach consists of implementing the system in the frequency domain; however, this approach is not suitable for real-time applications since a very large delay is introduced. A compromise solution of both approaches is provided by a family of segmented-FFT methods, which permits a trade-off between latency and computational complexity. As an alternative, the sub-band method can be applied as a technique to represent linear systems in the time-frequency domain. Recent work has showed that the sub-band method offers an even better tradeoff between latency and computational complexity than segmented-FFT methods. However, the sub-band analysis is still mathematically challenging and its optimum configuration is dependant on the application under consideration.
TF-VA involves developing and investigating new techniques for configuring the sub-band method by using advanced optimization methods in a functional analysis context. As a result, an optimization technique that minimizes the computational complexity of the sub-band method will be obtained.
Two approaches will be considered: The first approach designs the time-frequency transform for minimizing the complexity of each HRTF. In the second approach, we will design a unique time-frequency transform, which will be used for a joint implementation of all HRTFs of a listener. This will permit an efficient implementation of interpolation techniques while moving sources spatially in real-time. The results will be evaluated in subjective localization experiments and in terms of localization models.