Top: Estimated loudness, which was chosen as a perceptually-motivated representation of the magnitude, of the left-ear HRTF. The top-left plot shows the Reference (original HRTF) and the other plots show HRTFs preprocessed with the nine methods at N = 3 and interpolated over all available directions (11 950). Bottom: violin plots showing the PSD between each method and the reference for the approximate 110-point Lebedev grid (lower is better), where the vertical dashed lines indicate that the groups on the left are significantly different (p < 0.05) than the groups on the right.