There are an increasing number of binaural systems embedded with head-related transfer functions (HRTFs), so listeners can experience virtual environments via conventional stereo loudspeakers or head- phones. As HRTFs vary from person to person, it is difficult to select appropriated HRTFs from already existing databases for users. Once the HRTFs in a binaural audio device hardly match the real ones of the users, poor localization happens especially on the cone of confusion. The most accurate way to obtain personalized HRTFs might be doing practical measurements. It is, however, expensive and time consuming. Modifying non-individualized HRTFs may be an effort-saving way, though the modifications are always accompanied by undesired audio distortion. This paper proposes a flexible HRTF adjustment system for users to define their own HRTFs. Also, the system can keep sounds from suffering intolerable distortion based on an objective measurement tool for evaluating the quality of processed audio.

Principal components analysis (PCA) is frequently used for modelling the magnitude of the head-related transfer functions (HRTFs). Assuming that the HRTFs are minimum phase systems, the phase is obtained from the Hilbert transform of the log-magnitude. In recent years, the PCA applied to HRTFs is also used to model individual HRTFs relating the PCA weights with anthropometric measurements of the head, torso and pinnae. The HRTF log-magnitude is the most used format of input data to the PCA, but it has been shown that if the input data is HRTF linear magnitude, the cumulative variance converges faster, and the mean square error (MSE) is smaller. This study demonstrates that PCA applied directly on HRTF complex values is even better than the two formats mentioned above, that is, the MSE is the smallest and the cumulative variance converges faster after the 8th principal component. Different objective experiments around all the median plane put in evidence the differences which, although small, seem to be perceptually detectable. To elucidate this point, psychoacoustic discrimination tests are done between measured and reconstructed HRTFs from the three types of input data mentioned, in the median plane between -45°. and +9°.

Expressing head-related transfer functions (HRTFs) in the spherical harmonic (SH) domain has been thoroughly studied as a method of obtaining continuity over space. However, HRTFs are functions not only of direction but also of frequency. This paper presents an extension of the SH-based method, utilizing hyperspherical harmonics (HSHs) to obtain an HRTF representation that is continuous over both space and frequency. The application of the HSH approximation results in a relatively small set of coefficients which can be decoded into HRTF values at any direction and frequency. The paper discusses results obtained by applying the method to magnitude spectra extracted from exemplary HRTF measurements. The HRTF representations based on SHs and HSHs exhibit similar reproduction accuracy, with the latter one featuring continuity over both space and frequency and requiring much lower number of coefficients. The developed HSH-based continuous functional model can serve multiple purposes, such as interpolation, compression or parametrization for machine-learning applications.

The use of individualised Head Related Transfer Functions (HRTF) is a fundamental prerequisite for obtaining an accurate rendering of 3D spatialised sounds in virtual auditory environments. The HRTFs are transfer functions that define the acoustical basis of auditory perception of a sound source in space and are frequently used in virtual auditory displays to simulate free-field listening conditions. However, they depend on the anatomical characteristics of the human body and significantly vary among individuals, so that the use of the same dataset of HRTFs for all the users of a designed system will not offer the same level of auditory performance. This paper presents an alternative approach to the use on non-individualised HRTFs that is based on a procedural learning, training, and adaptation to altered auditory cues.We tested the sound localisation performance of nine sighted and visually impaired people, before and after a series of perceptual (auditory, visual, and haptic) feedback based training sessions. The results demonstrated that our subjects significantly improved their spatial hearing under altered listening conditions (such as the presentation of 3D binaural sounds synthesised from non-individualized HRTFs), the improvement being reflected into a higher localisation accuracy and a lower rate of front-back confusion errors.