Spherical Harmonic Components

Images created by the Quantum Chemistry Group, Universidad de Oviedo, Spain

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Things to note

The colour convention is that red lobes are in-phase (positive) and green lobes are out-of-phase (negative).

In Ambisonics, the convention is for the x-axis to be pointing away from the viewer and the y-axis to be pointing left. As depicted here, they are pointing towards the viewer and right; this rotation just toggles the colours of some of the lobes.

Zero- and first-order components

With Ambisonics, a sound field is decomposed into spherical harmonic components, termed W, X, Y and Z. These are collectively called B-Format. The responses look like this:

Higher-order components

The zero- and first-order components can be augmented by second- and third-order spherical harmonic components. To date, because of the need for an impractical number of transmission channels, little work has been carried out on higher-order Ambisonic systems. However, work has started on the development of the necessary microphones and decoders.

Second-order Ambisonics requires five transmission channels for horizontal surround sound and nine for full-sphere. Third-order Ambisonics requires seven channels for horizontal and sixteen for full-sphere. It is also possible to mix a high-order horizontal with a lower-order full-sphere; this would require an intermediate number of transmission channels, as listed in the following table:

of channels
3 h horizontal 1 0 WXY
4 f full-sphere 1 1 WXYZ
5 hh horizontal 2 0 WXYUV
6 fh mixed-order 2 1 WXYZUV
9 ff full-sphere 2 2 WXYZRSTUV
7 hhh horizontal 3 0 WXYUVPQ
8 fhh mixed-order 3 1 WXYZUVPQ
11 ffh mixed-order 3 2 WXYZRSTUVPQ
16 fff full-sphere 3 3 WXYZRSTUVKLMNOPQ

Second-order components

The second-order spherical harmonic responses look like this:

Third-order components

The third-order spherical harmonic responses look like this:

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