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Define p closer to equations, remove periods after equations
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felicialim authored and tdaede committed Aug 22, 2023
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Expand Up @@ -2390,9 +2390,9 @@ This specification RECOMMENDs dynamic down-mixing matrices generated by the down

This section provides RECOMMENDED static down-mix matrices to render to 3.1.2ch from 5.1.2ch, 5.1.4ch, 7.1.2ch, and 7.1.4ch.

In all the matrices below, \(p = 0.707\). Implementations MAY use a limiter defined in [[#processing-post-limiter]] to preserve the energy of audio signals instead of using normalization factors.
Implementations MAY use a limiter defined in [[#processing-post-limiter]] to preserve the energy of audio signals instead of using normalization factors.

The 3.1.2ch down-mix matrix for 5.1.2ch is:
The 3.1.2ch down-mix matrix for 5.1.2ch is given below, where \(p = 0.707\).

\[
\begin{bmatrix}
Expand Down Expand Up @@ -2422,10 +2422,10 @@ The 3.1.2ch down-mix matrix for 5.1.2ch is:
\text{Ltf2} \\
\text{Rtf2} \\
\text{LFE}
\end{bmatrix}.
\end{bmatrix}
\]

The 3.1.2ch down-mix matrix for 5.1.4ch is:
The 3.1.2ch down-mix matrix for 5.1.4ch is given below, where \(p = 0.707\).

\[
\begin{bmatrix}
Expand Down Expand Up @@ -2457,10 +2457,10 @@ The 3.1.2ch down-mix matrix for 5.1.4ch is:
\text{Ltb} \\
\text{Rtb} \\
\text{LFE}
\end{bmatrix}.
\end{bmatrix}
\]

The 3.1.2ch down-mix matrix for 7.1.2ch is:
The 3.1.2ch down-mix matrix for 7.1.2ch is given below, where \(p = 0.707\).

\[
\begin{bmatrix}
Expand Down Expand Up @@ -2494,10 +2494,10 @@ The 3.1.2ch down-mix matrix for 7.1.2ch is:
\text{Ltf2} \\
\text{Rtf2} \\
\text{LFE}
\end{bmatrix}.
\end{bmatrix}
\]

The 3.1.2ch down-mix matrix for 7.1.4ch is:
The 3.1.2ch down-mix matrix for 7.1.4ch is given below, where \(p = 0.707\).

\[
\begin{bmatrix}
Expand Down Expand Up @@ -2531,7 +2531,7 @@ The 3.1.2ch down-mix matrix for 7.1.4ch is:
\text{Ltf2} \\
\text{Rtf2} \\
\text{LFE}
\end{bmatrix}.
\end{bmatrix}
\]


Expand Down Expand Up @@ -2971,7 +2971,7 @@ For a given channel-based input audio and the list of CLs ({CL #i: i = 1, 2, ...
- If Ti-1 = 0, the top channels of the [=down-mixed audio=] for CL #i are contained in this [=Channel Group=] #i.
- If Ti-1 = 2, the Ltf and Rtf channels of the [=down-mixed audio=] for CL #i are contained in this [=Channel Group=] #i.

An example of a transformation matrix with 4 CGs (2ch/3.1.2ch/5.1.2ch/7.1.4ch) is given below:
An example of a transformation matrix with 4 CGs (2ch/3.1.2ch/5.1.2ch/7.1.4ch) is given below, where \(p = 0.707\).

\[
\begin{array}{c}
Expand Down Expand Up @@ -3032,8 +3032,8 @@ An example of a transformation matrix with 4 CGs (2ch/3.1.2ch/5.1.2ch/7.1.4ch) i
\end{bmatrix}
=
\begin{bmatrix}
1 & p_2 & 0 & \delta(k) \ast \alpha(k) & 0 & \delta(k) \ast \beta(k) & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & p_2 & 1 & 0 & \delta(k) \ast \alpha(k) & 0 & \delta(k) \ast \beta(k) & 0 & 0 & 0 & 0 & 0 \\
1 & p & 0 & \delta(k) \ast \alpha(k) & 0 & \delta(k) \ast \beta(k) & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & p & 1 & 0 & \delta(k) \ast \alpha(k) & 0 & \delta(k) \ast \beta(k) & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & w(k) \ast \delta(k) \ast \alpha(k) & 0 & w(k) \ast \delta(k) \ast \beta(k) & 0 & 1 & 0 & \gamma(k) & 0 & 0 \\
0 & 0 & 0 & 0 & w(k) \ast \delta(k) \ast \alpha(k) & 0 & w(k) \ast \delta(k) \ast \beta(k) & 0 & 1 & 0 & \gamma(k) & 0 \\
Expand All @@ -3059,5 +3059,5 @@ An example of a transformation matrix with 4 CGs (2ch/3.1.2ch/5.1.2ch/7.1.4ch) i
\text{Ltb} \\
\text{Rtb} \\
\text{LFE}
\end{bmatrix}.
\end{bmatrix}
\]

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