gaunt.lib

Library of real Gaunt coefficients up to spherical harmonics degree $L = 5$.

The real Gaunt coefficient is defined as the integral over three real spherical harmonics¹:

\[\begin{equation} C(i,j,k) = \int_\limits{\theta = 0}^{2 \pi} \int_\limits{\phi = -\pi/2}^{\pi/2} Y_i(\theta, \phi) Y_j(\theta, \phi) Y_k(\theta,\phi) \cos(\phi) \text{d}\theta \text{d}\phi, \label{eq:cijk} \end{equation}\]

where $i, j, k$ are the three spherical harmonics ACN indices. These coefficients are needed for directional filtering of Ambisonic sound scene².

Functions

Cijk(i,j,k)

Return the real Gaunt coefficient $C(i,j,k)$, with $(i,j,k) \in \mathbb{N}^3$, $0 \leq i \leq 35$, $0 \leq j \leq 35$ and $0 \leq k \leq 35$.

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