Panner

This tool allows to pan $S$ sources on $N$ loudspeakers using Ambisonic equivalent panning laws¹. The $i$-th source, with $i \in \{1, \cdots, S\}$ carries a signal denoted $s_i(z)$ in the discrete domain. Encoded as a point source, its position is $(r_i,\theta_i,\phi_i)$ from origin and it emits a spherical wave. For the $n$-th loudspeaker with $n \in \{1, \cdots, N\}$ and coordinates $(r_n, \theta_n, \varphi_n)$, the driving signal $s_n$ is given by:

\[\begin{equation} s_n = \sum\limits_{i=0}^{S} \sum_{l=0}^{L} s_i(z) z^{- \lfloor \frac{r_i}{c} \rfloor} w_{\text{max-}r_E, l}(L) \frac{F_l(r_i, z)}{F_l(r_n, z)} (2 l + 1) P_l(\cos(\gamma_i(n))), \label{eq:panning_law} \end{equation}\]

where $P_l$ is the $l$-th Legendre polynomial, $w_{\text{max-}r_E}$ are the max-$r_E$ weights, $\frac{F_l(r_i, z)}{F_l(r_n, z)}$ are the The Near Field (NF) filters), and $\gamma_i(n) = \cos(\phi_i) \cos(\phi_n) \cos(\theta_i - \theta_n) + \sin(\phi_i) \sin(\phi_n)$ is the angle between the $i$-th source and the $n$-th loudspeaker.

The NF filters can be activated or not at compilation time with parameter nfon. If activated (nfon=1), the gain attenuation and propagation delay between loudspeakers are as well equalized. If not activated (nfon=0), $\frac{F_l(r_i, z)}{F_l(r_n, z)} = 1$ in Eq. \eqref{eq:panning_law}, that is to say that no near field effect is included in the process.

In addition, a delay $\frac{r_i}{c}$ due to the propagation time can be included. When the source moves, this produces a Doppler effect, which can be activated or not at runtime.

Compilation parameters

• S: number of source, $S > 0$
• L: maximal Spherical Harmonics degree, $L > 0$,
• N: number of loudspeaker, $N > 0$,
• nfon: activate or not NF filters: nfon=0 for no NF, nfon=1 for NF.
• speaker(n) = (x, y, z) $n$-th loudspeaker Cartesian coordinates in meters. One loudspeaker per line.
• coord : Choice of coordinate system : 0 => Spherical, 1 => Cartesian,
• doppler : Possibility of Doppler effect : 0 => No, 1 => Yes.

Inputs / Outputs

• Inputs: $S$
• Outputs: $N$

User Interface

Element	OSC	Min value	Max value
Gain (dB)	gain_i	-20	20
Doppler (doppler = 1)	doppler_i	0	1
Radius $r$) (m) (coord = 0)	radius_i	0.75	50
Azimuth $\theta$ ($^\circ$) (coord = 0)	azimuth_i	-180	180
Elevation $\phi$ ($^\circ$) (coord = 0)	elevation_i	-90	90
$x$ (m) (coord = 1)	x_i	-50	50
$y$ (m) (coord = 1)	y_i	-50	50
$z$ (m) (coord = 1)	z_i	-50	50