3D sound is a new trend in various media, such as movies, video games, and musicals. Interpolated head-related transfer functions (HRTFs) are a key factor in its production, due
to real-time system limitations in storing measured HRTFs. In addition, the
interpolation of HRTFs can reduce the need to measure a large amount of HRTFs and
the associated effort. In this research, we used the PKU-IOA HRTF Database and
covered three interpolation techniques, namely bilinear rectangular, bilinear
triangular, and tetrahedral. Bilinear interpolations can be used to compute
weights in interpolating measured HRTFs in a linear fashion, with respect to
azimuth and elevation angles. Such interpolations have been proposed for three
measurement points that form a triangle or for four measurement points that
form a rectangle, surrounding the HRTF at a desired point. These geometrical
approaches compute weights from a distance of the desired point from each
measurement point. Tetrahedral interpolation, meanwhile, is a technique for
HRTF measurements in 3D (i.e. azimuth, elevation, and distance) using barycentric weights. Based on our experiments, 3D tetrahedral
interpolation results in the best average mean square error (MSE) of 3.72% for minimum phase head related impulse responses (HRIRs) and best average spectral distortion (SD) of
2.79 dB for magnitude HRTFs, compared to 2D bilinear interpolations (i.e.
rectangular and triangular interpolation). Regarding the latter, bilinear
rectangular interpolation generally performs better than the triangular
variety. Additionally, the use of minimum phase HRIRs as input data results in
more optimal interpolated data than magnitude HRTFs. We therefore propose an
optimal framework for obtaining estimated HRIRs by interpolating minimum phase
HRIRs using tetrahedral interpolation. Such HRIRs have been simulated to
produce virtual 3D moving sound in a horizontal plane with a difference of 2.5o
of azimuth angle. The simulated moving sound that is heard moves naturally in a
clockwise direction from an azimuth angle of 0o to 360o.
