where is the normalised spherical harmonics. Also, the inverse transform of is given by

where indicates the complex conjugate.

The integral in Eq. (12) is evaluated numerically in the
manner described in **3.2** as follows:

where is the coefficient of the normalised spherical harmonics. One can use FFT in the computation of the outer sum with respect to in Eq. (13). Using one set on the unit sphere one obtains another set via

Operations in Eqs. (15) and (16) are called `interpolation' (`anterpolation') if . In this paper, we determine the numbers and following Song et al.[8]