When patching an HOA or B-Format input to a source, or a HOA room to a channel-based output, a transcoder will be automatically inserted. This transcoder will, by default, be set to the Ring or Sloane speaker arrangement corresponding to the HOA order, and, will select an energy-preserving decoder.

Ring and Sloane are uniform setups which are recommended for optimized transcoding. I will guarantee a precise localization, in particular when transcoding an ambisonic input in order to use it in a room.

Projection decoding is also sometimes called ‘sampling ambisonic decoding’ (SAD). It is the simplest form of ambisonic decoding. It samples the virtual panning function at the loudspeaker directions. SAD is optimal for loudspeakers arranged as t-design layouts, with $t \geqslant (2N+1)$ ($N$ being the Ambisonics order). Typically, the SAD should only be used for 2D loudspeaker layouts, i.e. arranged regularly in a circle. Avoids this decoder for 3D setups.

*What is a t-design layout?*

To keep it really simple, t-design is a mathematical way of constructing sphere perimeters or circle surfaces with an array of point that is homogenous. In 2D the point simply put on a circle and are evenly spaced. In 3D, things get much more complicated many t-design point layout exist. In Spat Revolution, we chose to use the method used by the mathematician Sloane for our speaker layouts.

The pseudo-inverse decoder, or ‘mode-matching decoder’ (MMAD), is suitable for both 2D and 3D. It is based on a pseudo-inverse of the re-encoding matrix. MMAD is well-behaved for regular loudspeaker arrangements. It can also give good results with slightly irregular setups. However, it can become unstable with strongly irregular setups, i.e. it can completely blow up the speaker feeds. So, be careful.

The regularized pseudo-inverse decoder or ‘regularized-mode-matching decoder’ (RMMAD) is somehow similar to MMAD, however it uses a regularization factor for stabilization of the pseudo-inverse. This regularization factor (alpha) varies from 0% to 100%. A value of 0% provides results similar to MMAD. A value of 100% generates even energy distribution, i.e. results similar to EPAD. Intermediate values of alpha allow to ‘blend’ MMAD and EPAD.

EPAD (Energy preserving ambisonic decoding) and AllRAD (All-round Ambisonic decoding) are other HOA decoding methods suitable for 2D and 3D HOA, and they can cope with any kind of loudspeaker arrangement. These decoding methods always work, as soon as there are enough loudspeakers; they are always feasible and by nature numerically stable. EPAD uses a regularized matrix inversion such that the decoded energy is preserved even with non-uniformly arranged arrays (and even for directions with only sparse loudspeaker coverage). EPAD is the default method in spat5 (and the one we usually recommend).

‘All-round Ambisonic decoding’ (AllRAD) is designed in two steps. First, an optimal virtual loudspeaker layout using t-design arrangement is considered (for which the SAD is optimal). Secondly, the signals of these virtual loudspeakers are mapped to the real loudspeakers via VBAP.

‘Improved All-Round Ambisonic Decoding’ (AllRAD+) combines AllRAD and SAD. Constant energy that is achieved for the idealized virtual loudspeaker setup in AllRAD is corrupted by the VBAP stage as, per loudspeaker pair, all virtual sources are super-imposed linearly instead of energetically. The prevailing linear superposition increases the energy wherever the loudspeaker spacing is large. Roughly, at such directions AllRAD doubles the energy, whereas it is halved at directions with dense loudspeaker spacing. Conversely, SAD might lose all energy where the loudspeaker spacing is large and roughly doubles it where the loudspeaker spacing is dense. AllRAD+ tries to solve this issue by combining (i.e. mixing) SAD and AllRAD. The loudness variation of AllRAD+ is competitive with EPAD and its angular mapping resembles AllRAD.