From fd55ab5fb49e7f88cffeeec24a70539a23df6ad8 Mon Sep 17 00:00:00 2001 From: TheM14 Date: Mon, 7 Sep 2026 11:20:54 +0800 Subject: [PATCH] Fix the syntax in docs --- THIRD_PARTY_NOTICES.md | 2 +- docs/binaural.en.md | 2 +- docs/binaural.md | 2 +- docs/math.en.md | 18 +++++++++--------- docs/math.md | 18 +++++++++--------- 5 files changed, 21 insertions(+), 21 deletions(-) diff --git a/THIRD_PARTY_NOTICES.md b/THIRD_PARTY_NOTICES.md index 622a656..99ede7b 100644 --- a/THIRD_PARTY_NOTICES.md +++ b/THIRD_PARTY_NOTICES.md @@ -10,7 +10,7 @@ 第 5.2.2 节（Table 1 的 $Q=8$/ $Q=4$ 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 AAC/SBR 64 complex QMF bank；打包的 $64\times10$ 表是公开 640-tap prototype 的 diff --git a/docs/binaural.en.md b/docs/binaural.en.md index 77063b8..5a4d77d 100644 --- a/docs/binaural.en.md +++ b/docs/binaural.en.md @@ -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 $Q=8$/ $Q=4$ 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 ISO/IEC 14496-3/AMD1:2003, subclause 4.B.18.2, stored as the polyphase diff --git a/docs/binaural.md b/docs/binaural.md index ad0d924..43bbdff 100644 --- a/docs/binaural.md +++ b/docs/binaural.md @@ -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 $Q=8$/ $Q=4$ 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） 的 64 complex QMF bank；打包的 $64\times10$ 表是公开 640-tap prototype diff --git a/docs/math.en.md b/docs/math.en.md index 4c3e0a4..f3a1d59 100644 --- a/docs/math.en.md +++ b/docs/math.en.md @@ -177,7 +177,7 @@ Let $\mathcal A_b$ denote the 64-band analysis-QMF operator with polyphase histo $$ X_{c,b,t}= -\mathcal A_b\!\left( +\mathcal A_b\left( \widetilde x_c[64t],\ldots,\widetilde x_c[64t+63]; \mathbf s^{\mathrm A}_{c,t} \right). @@ -243,7 +243,7 @@ $$ F_k= \sum_{n=0}^{63} \mathrm{zone}_n -\exp\!\left(-j\frac{2\pi kn}{64}\right). +\exp\left(-j\frac{2\pi kn}{64}\right). $$ ### 7.2 Modulation and synthesis @@ -268,7 +268,7 @@ Let $\mathcal S$ denote polyphase synthesis with a 640-value synthesis window an $$ \mathbf y_{o,t}= -\mathcal S\!\left( +\mathcal S\left( \mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t} \right). $$ @@ -277,7 +277,7 @@ Object output is $$ y_o[64t+r]= -\mathrm{clip}\!\left( +\mathrm{clip}\left( 16\,\mathbf y_{o,t}[r],-1,1 \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]= -\mathrm{clip}\!\left( +\mathrm{clip}\left( x_{\mathrm{LFE,core}}[n-1217],-1,1 \right). $$ @@ -301,7 +301,7 @@ The lateral and longitudinal grids use $N=62$; the height grid uses $N=15$. The $$ q_N(k)= -\min\!\left( +\min\left( 32767, \left\lfloor\frac{32768k}{N}+\frac12\right\rfloor \right). @@ -322,11 +322,11 @@ Their maximum runtime value is $32767/32768$, not exactly 1. For conversion to the ADM grid: $$ -k_1=\mathrm{round}\!\left(\frac{62q_1}{32767}\right), +k_1=\mathrm{round}\left(\frac{62q_1}{32767}\right), \quad -k_2=\mathrm{round}\!\left(\frac{62q_2}{32767}\right), +k_2=\mathrm{round}\left(\frac{62q_2}{32767}\right), \quad -k_3=\mathrm{round}\!\left(\frac{15q_3}{32767}\right), +k_3=\mathrm{round}\left(\frac{15q_3}{32767}\right), $$ $$ diff --git a/docs/math.md b/docs/math.md index 59c314c..d4bd414 100644 --- a/docs/math.md +++ b/docs/math.md @@ -177,7 +177,7 @@ $$ $$ X_{c,b,t}= -\mathcal A_b\!\left( +\mathcal A_b\left( \widetilde x_c[64t],\ldots,\widetilde x_c[64t+63]; \mathbf s^{\mathrm A}_{c,t} \right). @@ -243,7 +243,7 @@ $$ F_k= \sum_{n=0}^{63} \mathrm{zone}_n -\exp\!\left(-j\frac{2\pi kn}{64}\right). +\exp\left(-j\frac{2\pi kn}{64}\right). $$ ### 7.2 调制与合成 @@ -268,7 +268,7 @@ $$ $$ \mathbf y_{o,t}= -\mathcal S\!\left( +\mathcal S\left( \mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t} \right). $$ @@ -277,7 +277,7 @@ $$ $$ y_o[64t+r]= -\mathrm{clip}\!\left( +\mathrm{clip}\left( 16\,\mathbf y_{o,t}[r],-1,1 \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]= -\mathrm{clip}\!\left( +\mathrm{clip}\left( x_{\mathrm{LFE,core}}[n-1217],-1,1 \right). $$ @@ -301,7 +301,7 @@ $$ $$ q_N(k)= -\min\!\left( +\min\left( 32767, \left\lfloor\frac{32768k}{N}+\frac12\right\rfloor \right). @@ -322,11 +322,11 @@ $$ 转换为 ADM 网格时： $$ -k_1=\mathrm{round}\!\left(\frac{62q_1}{32767}\right), +k_1=\mathrm{round}\left(\frac{62q_1}{32767}\right), \quad -k_2=\mathrm{round}\!\left(\frac{62q_2}{32767}\right), +k_2=\mathrm{round}\left(\frac{62q_2}{32767}\right), \quad -k_3=\mathrm{round}\!\left(\frac{15q_3}{32767}\right), +k_3=\mathrm{round}\left(\frac{15q_3}{32767}\right), $$ $$