Individual head-related transfer functions (HRTFs) allow for an accurate representation of three-dimensional audio scenes via headphones. Given the high spatial resolution necessary for good localization results, a set of HRTFs usually comprises a large number of impulse responses (FIR filters), one filter pair for every measured source direction. This leads to a very long measurement duration, because every acoustic path has to be measured separately. Furthermore, the resulting large sets of filters require a high memory capacity. A more compact representation using high-quality interpolation of HRTFs is hence desirable. Interpolation of HRTFs is typically performed using a decomposition into onset delays and minimum phase components prior to the interpolation itself. In this thesis, an interpolation of unmodified HRTFs is investigated, using an adapted discrete spherical harmonic transform. In doing so, suitable HRTF features that are to be interpolated, e.g. time-delay and attenuation, deserve some notice as to avoid undesired artifacts. Especially the unwrapped phase, which can be considered as a frequency-dependent temporal delay, is intensely investigated. As a result of this investigation, a spherical phase unwrapping algorithm based on the concept of neighbouring points is presented. The results are verified via psychoacoustical error measures using measured and simulated HRTFs.