Time-Frequency Implementation of HRTFs

In the context of binaural virtual reality, a sound source is positioned in a 3D space around the listener by filtering it using head-related transfer functions (HRTFs). In a real-time application, a large number of HRTFs needs to be processed. Due to their long impulse responses, this requires a high computational power, which for more than a few simultaneous sources, cannot be implemented directly on current processors. 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 in 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 given by a family of segmented-FFT methods, which permits a trade-off between latency and computational complexity. As an alternative, the subband method can be applied as a technique to represent linear systems in the time-frequency domain. The project applicant showed in a recent work, that the subband method offers an even better tradeoff between latency and computational complexity than segmented-FFT methods. The subband analysis is still mathematically challenging and its optimum configuration is dependant on the application under consideration. The project proposal involves developing and investigation of new techniques for configuring the subband method by using advanced optimization methods in a functional analysis context. As a result, an optimization technique will be obtained which minimizes the computational complexity of the subband method especially useful in real- time virtual acoustic applications. 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. This will permit an efficient implementation of interpolation techniques in the spatialization of moving sources in real-time. The results will be applied to several localization models and evaluated in subjective localization experiments.

Head-related transfer functions (HRTFs) describe the acoustic filtering of incoming sounds by the human morphology, and are essential for listeners to localize sound sources in virtual auditory displays. A bottleneck in many applications is the high computational demans required for rendering complex virtual scenes. To address this issue, we studied efficient HRTF implementations using subband processing, i.e., as an analysis filterbank (FB) converting the signal to be filtered into the time-frequency domain, followed by a transfer matrix representing the filtering operation in that domain, and a synthesis FB converting the result back to time domain. We proposed two approaches. In the first one, the choice of FBs is fixed, and the complexity of the transfer matrix is minimized. This yielded computational savings of about one order of magnitude, in comparison with the most efficient available methods. The second approach jointly optimizes the FBs and transfer matrices. While it yielded further computational savings, they were not major in comparison with the first approach. In view of this, we decided not to pursue this research line any further.Subband processing is a particular case of a more general paradigm called generalized sampling. In view of the above results, we opened the scope of the research by considering other generalized sampling problems, namely spatial sampling and non-regular temporal sampling. We summarize below our research achievements in these two fields.A sensor network is a web of a large number of sensing and computing devices (nodes) connected via a communication network. The whole network can be considered as a multi-channel sampling device, where different channels correspond to different spatial locations. Here, the research challenge consists in achieving distributed algorithms, in the sense of not requiring a central coordinating agent. We studied three problems. The first one consists in estimating an unknown parameter vector based on the available spatial samples. The second problem concerns tracking the evolution of an unknown random vector (typically the position of a target). The third problem consists in determining the node locations based on inter-node distance measurements.New communications technologies today permit remote control and monitoring in a broad range of applications. When signal samples are sent through a communication channel, they become intermittently available due to communication constraints (e.g., failures, congestion, etc.). Hence, the samples at the receiver are only available over a non-regular grid. We studied two problems in which this grid is random with a known statistical model. The first problem consists in estimating the parameters of a system's model, based on the knowledge of its input and output samples obtained in the aforementioned manner. The second one estimates the evolution of a random vector based on the intermittent availability of its partial measurements. In particular, we derived a necessary and sufficient condition to guarantee the stability of the resulting estimator. In doing so, we gave an answer to a problem that was open for about a decade.