# 12 Decoding

Ambisonics is a non-speaker dependent reproduction format and needs to be decoded for a given speaker array. The more speakers in the array the more accurate the soundfield will be reproduced. For virtual reality applications, a binaural conversion is necessary for headphone use. For the home, a square speaker array or 5.1 configurations are possible. To decode for a square speaker array, a basic decoding method considers the spatial coordinates of the loudspeakers. The loudspeaker located in the direction $(φ_{l},θ_{l})$ is thus fed by the signal:

 $L_{l}=\frac{1}{N_{L}}(\frac{W}{\sqrt{2}}+Xcosφ_{l}cosθ_{l}+Ysinφ_{l}cosθ_{l}+% Zsinθ_{l})$

For a square setup, the four loudspeaker signals are obtained as:

$L_{RF}=\frac{1}{\sqrt{2}}(W+X-Y)$

$L_{LF}=\frac{1}{\sqrt{2}}(W+X+Y)$

$L_{LB}=\frac{1}{\sqrt{2}}(W-X+Y)$

$L_{RB}=\frac{1}{\sqrt{2}}(W-X-Y)$

The directivity factor of 0.707 in the equations above results in a cardioid source directional response for each loudspeaker. This is optimum for listening positions close to the loudspeakers or outside the loudspeaker array. Where the intended listening area is significantly smaller than the speaker array, a more hypercardioid shape can be employed by increasing the directivity factor, which results in improved imaging for centrally located listeners. 1818Malham, David G, and Anthony Myatt. 1995. "3-D Sound Spatialization using Ambisonic Techniques". Computer Music Journal. 19 (4): 58.