L2normalizeFourierCoefficients

Since MTEX version 5.9 we use L2 normalized Wigner-D functions as basis functions for the harmonic series expansion of ODFs/SO3Funs.

Up to MTEX version 5.8 the ODFs has been definded by $$F({\bf R}) = \sum \hat{f}_n^{k,l} \, D_n^{k,l}({\bf R})$$ with $D_n^{k,l}({\bf R}(\alpha,\beta,\gamma)) = \mathrm e^{-\mathrm i k\gamma} \mathrm d_n^{k,l}(\cos\beta) \,e^{-\mathrm i l\alpha}$. Hence the $L_2$ norm of the Wigner-D function $D_n^{k,l}$ was $\sqrt{2n+1}$.

Now since MTEX version 5.9 the Wigner-D functions have $L_2$ norm 1. Hence they are defined by $D_n^{k,l}({\bf R}(\alpha,\beta,\gamma)) = \sqrt{2n+1} \, \mathrm e^{-\mathrm i k\gamma} \mathrm d_n^{k,l}(\cos\beta) \, e^{-\mathrm i l\alpha}$.

Take a look at Wigner-D functions.

Syntax

SO3F = L2normalizeFourierCoefficients(SO3F)