Human Head-related Transfer Functions Research Articles

Least squares versus non-linear cost functions for a virtual artificial head

In order to take into account spatial information into binaural recordings, it is common practice to use so-called artificial heads. Disadvantageously artificial heads are inherently non-individual and bulky devices. Alternatively, the individual frequency-dependent directivity pattern of human head related transfer functions (HRTFs) can also be approximated by a microphone array with appropriate filters [Rasumow et al. (2011)]. Such a setup may be referred to as a virtual artificial head (vah). The filters for the application of the vah can be derived by minimizing a narrow band cost function including regularization constraints. As a first approach, it is appropriate to apply a least-squares cost function. The major advantage is its closed form solution [cf. Rasumow et al. (2011)], whereas from a psychoacoustically point of view, it seems more reasonable to minimize the dB-error instead. The latter cost function must, however, be minimized iteratively. We propose a minimization procedure for and present first results regarding the subjective appraisal of binaural filters derived using both cost functions. Future work includes the extension of this work to binaural cost functions.

Energy based Markov Chain Monte Carlo algorithms for Bayesian model selection

Markov Chain Monte Carlo (MCMC) algorithms for Bayesian model selection have been increasingly applied to acoustics applications. One of challenging tasks required in Bayesian model selection is the exploration of high-dimensional multi-variate spaces such that a key quantity, termed the Bayesian evidence, can be estimated in order to rank a set of competing models. This work presents a class of energy-based MCMC algorithms specifically designed to estimate the Bayesian evidence. As illustrative examples, the energy-based MCMC algorithms are applied to the problem of filter design as used in human head-related transfer functions and in acoustic impedance boundaries within the finite-difference time-domain framework for room-acoustics simulations.

Spike-Timing-Based Computation in Sound Localization

Spike timing is precise in the auditory system and it has been argued that it conveys information about auditory stimuli, in particular about the location of a sound source. However, beyond simple time differences, the way in which neurons might extract this information is unclear and the potential computational advantages are unknown. The computational difficulty of this task for an animal is to locate the source of an unexpected sound from two monaural signals that are highly dependent on the unknown source signal. In neuron models consisting of spectro-temporal filtering and spiking nonlinearity, we found that the binaural structure induced by spatialized sounds is mapped to synchrony patterns that depend on source location rather than on source signal. Location-specific synchrony patterns would then result in the activation of location-specific assemblies of postsynaptic neurons. We designed a spiking neuron model which exploited this principle to locate a variety of sound sources in a virtual acoustic environment using measured human head-related transfer functions. The model was able to accurately estimate the location of previously unknown sounds in both azimuth and elevation (including front/back discrimination) in a known acoustic environment. We found that multiple representations of different acoustic environments could coexist as sets of overlapping neural assemblies which could be associated with spatial locations by Hebbian learning. The model demonstrates the computational relevance of relative spike timing to extract spatial information about sources independently of the source signal.

The location-dependent nature of perceptually salient features of the human head-related transfer functions

The human head-related transfer function (HRTF) has been recorded binaurally from eight subjects using an "in-ear" recording system, for 343 stimulus locations around the head. There are a number of systematic changes in the HRTF as a function of horizontal location and elevation, on and off the median plane, that could be used as cues to sound location. To identify which components of the HRTF might provide perceptually salient cues to sound location, the HRTFs were transformed using an auditory filter model which accounts for the frequency dependence of auditory sensitivity and the frequency and level-dependent characteristics of the auditory filters. These transformations indicated a systematic variation in the frequency of the peak excitation as a function of the horizontal location of a broad band stimulus. Furthermore, there were differences in the frequency range over which elevation-dependent changes in the excitation patterns varied as a function of the vertical meridian. Interaural level differences were also estimated using the excitation patterns. The across frequency pattern of ILDs were roughly symmetrical about the interaural axis, although there were substantial differences between each ear in the magnitude of the ILDs generated for ipsilateral sounds locations.

Measuring the human head-related transfer functions: A novel method for the construction and calibration of a miniature ‘‘in-ear’’ recording system

A method for the construction of a small "in-ear" system for recording the human-free field-to-eardrum and headphone-to-eardrum transfer functions is described. Customized in-ear inserts were obtained by a simple ear printing and electroplating method, resulting in a thin (< 0.25 mm) outer shell that minimized obstruction of the entrance at the ear canal. The insert can be used to position a microphone probe tube deep within the auditory canal. The effects of this recording system on the sound field in the ear canal were calibrated using a model head equipped with a second internal microphone close to the eardrum. Transfer functions were recorded for 343 different stimulus locations in free space and for a headphone sound source. For the free-field stimuli the presence of the recording system resulted in a small attenuation with maximum effects around 3.5 and 12.5 kHz (-1.5 and -2.0 dB, respectively). Passing the data through an auditory filter model reduced the averaged attenuation to less than -1.4 dB. Phase was undistorted up to 2.5 kHz. These results suggests that the perturbations produced by the insert are unlikely to be perceptually relevant.

A computational theory of spectral cue localization

This paper presents a computational theory of localization based on analysis of the cues contained in the spectrum received at the eardrum. It is well established that monaural localization, and binaural localization onto the cone of confusion, for pure tone stimuli are unrelated to the actual source position. On the other hand, broad spectrum stimuli are localized with some accuracy. This paper outlines the properties that the operations performed on a received spectrum must have in order for the source to be localized accurately. The use of the two simplest nontrivial such operations, the first and second finite differences of the spectrum, respectively, are explored in detail. This analysis shows that so long as the spectrum of the sound source has a locally constant slope, accurate localization using such operators is possible. A simulation of the localization process making use of measured human head-related transfer functions (HRTF’s) and two recorded spectra demonstrates that the second-order finite difference operator produces much more accurate and robust estimates than the first-order operator.