[opus] Channel Mapping Family for Ambisonics

[Michael Graczyk]

I've discussed hemispherical ambisonics and mixing matrices with a few
people. The consensus is that there is no set of hemispherical basis
functions common enough to warrant inclusion yet. We should force
channel counts to be values (l + 1)^2 for simplicity and to keep the
possibility open of including hemispherical bases should one ever
become popular.

As for mixing matrices, we are not confident in any choices for setups
beyond stereo. Although there have been papers and studies on
HOA->surround decoding, there are no readily available options for
orders besides  4. (HOA is higher order ambisonics, orders > 1).
Since these are only recommendations, we should be cautious and
provide only a stereo downmixing matrix. It looks like this would go
in 5.1.1.5? The matrix should be

 L = 0.5(W + Y)
 R = 0.5(W - Y)

and can be used for all orders (all channel counts >= 4). W is channel
1, Y is channel 2.

Here's the revised content. What do you guys think?

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Channel Mapping Family 2

Allowed numbers of channels: (1 + l)^2 for l = 1...15.

Explicitly 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196,
225. Ambisonics from first to fifteenth order.


Each channel is assigned to an ambisonic component in Ambisonic
Channel Number (ACN) order. The ambisonic component with degree n and
ambisonic index m corresponds to channel (n * (n + 1) + m).

Channels are normalized with Schmidt Semi-Normalization (SN3D). In
SN3D, the spherical harmonic of degree n and index m is normalized
according to sqrt((2 - delta(m)) * ((l - m)! / (l + m)!)), where
delta(0) = 1 and delta(m) = 0 otherwise.

The interpretation of the ambisonics signal as well as the channel
order and normalization are described in [ambix].
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and in section 5.1.1.5

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Implementations MAY use the matrix in Figures ? to implement
downmixing from multichannel files using Channel Mapping Family 2
(Section 5.1.1.?), which are known to give acceptable results for
stereo.


     /   \   /                  \ /  W  \
     | L |   | 0.5  0.5 0.0 ... | |  Y  |
     | R | = | 0.5 -0.5 0.0 ... | | ... |
     \   /   \                  / \ ... /
                   Figure ?
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