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The computed excitation vectors of each basis function $m$ at level $\ell$ are just the samples on the sphere represented as $\zeta_m^\ell(\phi_i,\theta_j)$.

These samples are interpolated to get samples $\zeta_m^{\ell-1}(\phi_\tilde{i},\theta_\tilde{j})$ at level $\ell-1$

Fast Spherical Filter is one of the algorithm that starts the interpolation process by taking Fourier transform of samples $\zeta_m^\ell(\phi_i,\theta_j)$ in $\phi$ direction at first and continues$\dots$

Right now I perform this interpolation for each basis which is very slow.

Instead, I was thinking whether

  1. Is it possible to take the Fourier Transform of samples of all the basis at once like?

$$\mathrm{FT}\left[\zeta_{m=0}^\ell(\phi_i,\theta_j),\,\zeta_{m=1}^\ell(\phi_i,\theta_j),\dots,\,\zeta_{m=\mathrm{M-1}}^\ell(\phi_i,\theta_j)\right]$$

  1. How do I setup the input/output strides, number of transforms, input/output distance etc?

I am using Intel oneAPI MKL libraries to compute the forward and backward Fourier transform.

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  • $\begingroup$ Further, what are number of transforms and in the current context $\mathrm{M}$ be number of transforms and the distance is $\mathrm{M}*i*j$? $\endgroup$
    – jomegaA
    May 14 at 12:23

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