Editing Ambisonics (section)

=== Decoding ===
[[Image:Naive Ambisonic Square Decoder Example.png|thumb|200px|right|Naive single-band in-phase decoder for a square loudspeaker layout]]
A basic Ambisonic ''decoder'' is very similar to a set of virtual microphones. For perfectly regular layouts, a simplified decoder can be generated by pointing a virtual cardioid microphone in the direction of each speaker. Here is a square:
:<math>LF = (\sqrt{2}W + X + Y)\sqrt{8}</math>
:<math>LB = (\sqrt{2}W - X + Y)\sqrt{8}</math>
:<math>RB = (\sqrt{2}W - X - Y)\sqrt{8}</math>
:<math>RF = (\sqrt{2}W + X - Y)\sqrt{8}</math>
The signs of the <math>X</math> and <math>Y</math> components are the important part, the rest are gain factors. The <math>Z</math> component is discarded, because it is not possible to reproduce height cues with just four loudspeakers in one plane.

In practice, a real Ambisonic decoder requires a number of psycho-acoustic optimisations to work properly.<ref>Eric Benjamin, Richard Lee, and Aaron Heller, [http://www.ai.sri.com/ajh/ambisonics/BLaH3.pdf ''Is My Decoder Ambisonic?''], 125th AES Convention, San Francisco 2008</ref>

Currently, the All-Round Ambisonic Decoder (AllRAD) can be regarded as the standard solution for loudspeaker-based playback,<ref>Franz Zotter and Matthias Frank, [https://aes2.org/publications/elibrary-page/?id=16554 ''All-Round Ambisonic Panning and Decoding'']. Journal of the Audio Engineering Society, 2012, 60(10): 807-820.</ref> and Magnitude Least Squares (MagLS)<ref>Christian Schörkhuber and Markus Zaunschirm, [https://pub.dega-akustik.de/DAGA_2018/data/articles/000301.pdf ''Binaural Rendering of Ambisonic Signals via Magnitude Least Squares'']. Fortschritte der Akustik, DAGA, Munich, 2018.</ref> or binaural decoding, as implemented for instance in the IEM and SPARTA Ambisonic production tools.<ref name="IEMPI">Daniel Rudrich et al, [https://plugins.iem.at ''IEM Plug-in Suite'']. 2018 (accessed 2024)</ref><ref name="SPARTA">Leo McCormack, [https://leomccormack.github.io/sparta-site/ ''Spatial Audio Real-Time Applications'']. 2019 (accessed 2024)</ref>

Frequency-dependent decoding can also be used to produce binaural stereo; this is particularly relevant in Virtual Reality applications.