Sampling Ambisonic Decoder

This tool decodes a $L$-th degree Ambisonic sound scene on a $N$-node loudspeaker layout using the Sampling Ambisonic Decoder (SAD) technique: For each loudspeaker, the driving signal is calculated from a continuous distribution of loudspeaker¹, sampled at the loudspeaker position (hence the term “sampling decorder”).

For the $n$-th loudspeaker at position $(r_n, \theta_n, \phi_n)$, with $n \in \{1, \cdots, N\}$, the driving signal $s_n(z)$ is given by:

\[\begin{equation} s_n(z) = \sum_{l=0}^L \frac{w_{\text{max-}r_E, l}(L)}{F_l(r_n, z)} \sum_{m=-l}^l Y_{l,m}(\theta_n, \phi_n) b_{l, m}(z) \label{eq:spk} \end{equation},\]

where $w_{\text{max-}r_E}$ are the max-$r_E$ weights, $\frac{1}{F_l(r_n, z)}$ are the The Near Field Compensation (NFC) filters), $Y_{l,m}(\theta_n, \phi_n)$ are the Spherical Harmonics evaluated at loudspeaker direction and $b_{l,m}(z)$ are the Ambisonic components.

The NFC filters can be activated or not at compilation time with parameter nfcon. If activated (nfcon=1), the gain attenuation and propagation delay between loudspeakers are as well equalized. If not activated (nfcon=0), $\frac{1}{F_l(r_n, z)} = 1$ in Eq. \eqref{eq:spk}.

Compilation parameters

• L: maximal Spherical Harmonics degree (i.e., Ambisonics order), $L > 0$,
• N: number of loudspeakers, $N > 0$,
• nfcon: activate or not NFC: 0 for no NFC, 1 for NFC.
• speaker(n) = (x, y, z) $n$-th loudspeaker Cartesian coordinates in meters. One loudspeaker per line.

Inputs / Outputs

• Inputs: $(L+1)^2$
• Outputs: $N$

User Interface

Element	OSC	Min value	Max value
Outputs level (dB)	levelout	-70	6