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Fix the syntax in docs

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TheM14
2026-09-07 11:20:54 +08:00
parent b619dee523
commit c8676d7aa3
5 changed files with 21 additions and 21 deletions
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THIRD_PARTY_NOTICES.md
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@@ -10,7 +10,7 @@
第 5.2.2 节（Table 1 的 $Q=8$/ 第 5.2.2 节（Table 1 的 $Q=8$/
$Q=4$ 系数，delay 6）： $Q=4$ 系数，delay 6）：
$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr)$$ $$G_q^p[n] = g^p[n]\cdot\exp\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr)$$
64-band QMF analysis 即 ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节的 MPEG-4 64-band QMF analysis 即 ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节的 MPEG-4
AAC/SBR 64 complex QMF bank；打包的 $64\times10$ 表是公开 640-tap prototype 的 AAC/SBR 64 complex QMF bank；打包的 $64\times10$ 表是公开 640-tap prototype 的
docs/binaural.en.md
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@@ -166,7 +166,7 @@ The hybrid analysis kernels are defined in [3GPP TS 26.405 / ETSI TS 126 405](ht
Section 5.2.2 (Table 1 $Q=8$/ Section 5.2.2 (Table 1 $Q=8$/
$Q=4$ coefficients, delay 6): $Q=4$ coefficients, delay 6):
$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$ $$G_q^p[n] = g^p[n]\cdot\exp\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
The QMF analysis table is the MPEG-4 AAC/SBR 64 complex QMF bank of The QMF analysis table is the MPEG-4 AAC/SBR 64 complex QMF bank of
ISO/IEC 14496-3/AMD1:2003, subclause 4.B.18.2, stored as the polyphase ISO/IEC 14496-3/AMD1:2003, subclause 4.B.18.2, stored as the polyphase
docs/binaural.md
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@@ -151,7 +151,7 @@ hybrid 分析核定义于 [3GPP TS 26.405 / ETSI TS 126 405](https://www.etsi.or
第 5.2.2 节（Table 1 的 $Q=8$/ 第 5.2.2 节（Table 1 的 $Q=8$/
$Q=4$ 系数，delay 6）： $Q=4$ 系数，delay 6）：
$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$ $$G_q^p[n] = g^p[n]\cdot\exp\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
QMF analysis 表即 MPEG-4 AAC/SBR（ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节） QMF analysis 表即 MPEG-4 AAC/SBR（ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节）
的 64 complex QMF bank；打包的 $64\times10$ 表是公开 640-tap prototype 的 64 complex QMF bank；打包的 $64\times10$ 表是公开 640-tap prototype
docs/math.en.md
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@@ -177,7 +177,7 @@ Let $\mathcal A_b$ denote the 64-band analysis-QMF operator with polyphase histo
$$ $$
X_{c,b,t}= X_{c,b,t}=
\mathcal A_b\!\left( \mathcal A_b\left(
\widetilde x_c[64t],\ldots,\widetilde x_c[64t+63]; \widetilde x_c[64t],\ldots,\widetilde x_c[64t+63];
\mathbf s^{\mathrm A}_{c,t} \mathbf s^{\mathrm A}_{c,t}
\right). \right).
@@ -243,7 +243,7 @@ $$
F_k= F_k=
\sum_{n=0}^{63} \sum_{n=0}^{63}
\mathrm{zone}_n \mathrm{zone}_n
\exp\!\left(-j\frac{2\pi kn}{64}\right). \exp\left(-j\frac{2\pi kn}{64}\right).
$$ $$
### 7.2 Modulation and synthesis ### 7.2 Modulation and synthesis
@@ -268,7 +268,7 @@ Let $\mathcal S$ denote polyphase synthesis with a 640-value synthesis window an
$$ $$
\mathbf y_{o,t}= \mathbf y_{o,t}=
\mathcal S\!\left( \mathcal S\left(
\mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t} \mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t}
\right). \right).
$$ $$
@@ -277,7 +277,7 @@ Object output is
$$ $$
y_o[64t+r]= y_o[64t+r]=
\mathrm{clip}\!\left( \mathrm{clip}\left(
16\,\mathbf y_{o,t}[r],-1,1 16\,\mathbf y_{o,t}[r],-1,1
\right)G_{\mathrm{clip}}, \right)G_{\mathrm{clip}},
$$ $$
@@ -290,7 +290,7 @@ LFE bypasses the object matrix and inverse QMF and uses a 1217-sample delay. Aft
$$ $$
y_{\mathrm{LFE}}[n]= y_{\mathrm{LFE}}[n]=
\mathrm{clip}\!\left( \mathrm{clip}\left(
x_{\mathrm{LFE,core}}[n-1217],-1,1 x_{\mathrm{LFE,core}}[n-1217],-1,1
\right). \right).
$$ $$
@@ -301,7 +301,7 @@ The lateral and longitudinal grids use $N=62$; the height grid uses $N=15$. The
$$ $$
q_N(k)= q_N(k)=
\min\!\left( \min\left(
32767, 32767,
\left\lfloor\frac{32768k}{N}+\frac12\right\rfloor \left\lfloor\frac{32768k}{N}+\frac12\right\rfloor
\right). \right).
@@ -322,11 +322,11 @@ Their maximum runtime value is $32767/32768$, not exactly 1.
For conversion to the ADM grid: For conversion to the ADM grid:
$$ $$
k_1=\mathrm{round}\!\left(\frac{62q_1}{32767}\right), k_1=\mathrm{round}\left(\frac{62q_1}{32767}\right),
\quad \quad
k_2=\mathrm{round}\!\left(\frac{62q_2}{32767}\right), k_2=\mathrm{round}\left(\frac{62q_2}{32767}\right),
\quad \quad
k_3=\mathrm{round}\!\left(\frac{15q_3}{32767}\right), k_3=\mathrm{round}\left(\frac{15q_3}{32767}\right),
$$ $$
$$ $$
docs/math.md
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@@ -177,7 +177,7 @@ $$
$$ $$
X_{c,b,t}= X_{c,b,t}=
\mathcal A_b\!\left( \mathcal A_b\left(
\widetilde x_c[64t],\ldots,\widetilde x_c[64t+63]; \widetilde x_c[64t],\ldots,\widetilde x_c[64t+63];
\mathbf s^{\mathrm A}_{c,t} \mathbf s^{\mathrm A}_{c,t}
\right). \right).
@@ -243,7 +243,7 @@ $$
F_k= F_k=
\sum_{n=0}^{63} \sum_{n=0}^{63}
\mathrm{zone}_n \mathrm{zone}_n
\exp\!\left(-j\frac{2\pi kn}{64}\right). \exp\left(-j\frac{2\pi kn}{64}\right).
$$ $$
### 7.2 调制与合成 ### 7.2 调制与合成
@@ -268,7 +268,7 @@ $$
$$ $$
\mathbf y_{o,t}= \mathbf y_{o,t}=
\mathcal S\!\left( \mathcal S\left(
\mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t} \mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t}
\right). \right).
$$ $$
@@ -277,7 +277,7 @@ $$
$$ $$
y_o[64t+r]= y_o[64t+r]=
\mathrm{clip}\!\left( \mathrm{clip}\left(
16\,\mathbf y_{o,t}[r],-1,1 16\,\mathbf y_{o,t}[r],-1,1
\right)G_{\mathrm{clip}}, \right)G_{\mathrm{clip}},
$$ $$
@@ -290,7 +290,7 @@ LFE 不经过对象矩阵或 inverse QMF，而是使用 1217-sample 延迟。输
$$ $$
y_{\mathrm{LFE}}[n]= y_{\mathrm{LFE}}[n]=
\mathrm{clip}\!\left( \mathrm{clip}\left(
x_{\mathrm{LFE,core}}[n-1217],-1,1 x_{\mathrm{LFE,core}}[n-1217],-1,1
\right). \right).
$$ $$
@@ -301,7 +301,7 @@ $$
$$ $$
q_N(k)= q_N(k)=
\min\!\left( \min\left(
32767, 32767,
\left\lfloor\frac{32768k}{N}+\frac12\right\rfloor \left\lfloor\frac{32768k}{N}+\frac12\right\rfloor
\right). \right).
@@ -322,11 +322,11 @@ $$
转换为 ADM 网格时： 转换为 ADM 网格时：
$$ $$
k_1=\mathrm{round}\!\left(\frac{62q_1}{32767}\right), k_1=\mathrm{round}\left(\frac{62q_1}{32767}\right),
\quad \quad
k_2=\mathrm{round}\!\left(\frac{62q_2}{32767}\right), k_2=\mathrm{round}\left(\frac{62q_2}{32767}\right),
\quad \quad
k_3=\mathrm{round}\!\left(\frac{15q_3}{32767}\right), k_3=\mathrm{round}\left(\frac{15q_3}{32767}\right),
$$ $$
$$ $$