Directional Mixer

This tools applies $S$ max-$r_E$ beampatterns to the Ambisonic sound scene. It can be used as an Ambisonic “directional mixer”. This means that a directional filtering is operated to enhance and reduce some directions according to the chosen beampatterns¹. The proposed beampatterns are on-axis normalized max-$r_E$ beampatterns of degree $L_1$

as shown in Fig.1. They have an high side-lobe attenuation while maintaining a narrow main lobe². For $L_1 = 0$ the beampattern is omnidirectional. The higher the beampattern degree, the more selective the directionnal filtering. At execution time, the steering angles ($\theta, \phi)$, the degree $L_1$ as well as the gain in dB of the each $S$ beampatterns can be changed. This directional filtering effect requires a higher degree of re-expansion $\tilde{L}$ for the filtered sound scene such that¹:

\[\begin{equation} \tilde{L} = L + L_1, \end{equation}\]

where $L$ is the input Ambisonic sound scene degree and $L_1$ is the beampattern degree. However, it is possible to choose the same degree for the output ($\tilde{L} = L$) with reasonable results.

Compilation parameters

• S: number of beampatterns to apply on the input sound scene,
• L: maximal Spherical Harmonics degree for the input $(L > 0)$,
• L1: maximal max-$r_E$ beampatterns degree ($L1 \geq 0$).

In the current implemtation $L + L1 \leq 10$.

Warning: the compilation can last several hours as $L_1$ and $S$ increase. Don’t forget the flag -t 0 with the faust2... scripts.

Inputs / Outputs

• Inputs: $(L+1)^2$
• Outputs: $(L+L_1+1)^2$ or $(L+1)^2$

User Interface

For the $i$-th beampattern:

Element	OSC	Min value	Max value
Gain (dB)	gain_i	-10	10
Azimuth $\theta$ ($^\circ$)	azimuth_i	-180	180
Elevation $\phi$ ($^\circ$)	elevation_i	-90	90
Degree $L_1$	degree_i	0	L1
On	on_i	0	1

Example of use

Let’s start with a sound scene a degree $L = 7$ composed of several unit-amplitude plane waves with various direction of arrival.

The square normalized amplitude of this scene is shown in Fig.2. Now we apply two max-$r_E$ beampatterns on this scene:

• Beampattern 1: degree $L_{1,1} = 1$, of amplitude $g_1 = 0$ dB, steering angles ($\theta_1 = -135^\circ$, $\phi_1 = 45^\circ$),
• Beampattern 2: degree $L_{1,1} = 2$, of amplitude $g_2 = 10$ dB, steering angles ($\theta_2 = 75^\circ$, $\phi_2 = 0^\circ$).

The square normalized amplitude of the resulting sound scene is shown in Fig.3 at degree $\tilde{L} = 7$ and in Fig.4 at degree $\tilde{L} = 9$.