Add option to use weights in the forward spherical Fourier transforms
It would be extremely beneficial to be able to add weights to the forward discrete spherical Fourier transforms (both “normal” and least-squares). The implementation is supposedly quite simple as shown below.
- Normal DSFT:
fnm = Yn’ * W * f
- Least-Squares DSFT:
(Yn’ * W * Yn)\(Yn’ * W * f)
where Yn
are the spherical harmonics, W
is a diagonal matrix of appropriate dimensions with the weights on the main diagonal and f
is the spherical function to be transformed (the sampled sound field in most - if not all - cases).