Applying extra- and interpolation methods to measured and simulated HRTF data using spherical harmonic decomposition
Head-Related Transfer Functions (HRTFs) describe a persons or a dummy-heads perception of sound for different angles of incidence. These data are usually simulated or measured on discrete points in space on a fixed distance. Anywhere in between these points the HRTF can either be approximated by one of its neighbors or interpolated from the other measurement points. One way to do so is to approximate the HRTFs as a continuous mode-limited function by spherical harmonic decomposition, allowing to get a function value for any desired direction. Using the reciprocity principle the incident sound field of the HRTF can be formulated as an exterior radiation problem. With a given set of HRTF data on a fixed distance from the center of the head, this approach allows to extrapolate the range of the HRTF (distance from head to sound source) to larger or smaller values, making it possible to e.g. calculate near-field HRTFs from far-field measurement data. In this paper, these known inter- and extrapolation methods will be applied to both a simulated and measured set of HRTF data.