Fix the syntax in docs
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@@ -10,7 +10,7 @@
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第 5.2.2 节(Table 1 的 $Q=8$/
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第 5.2.2 节(Table 1 的 $Q=8$/
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$Q=4$ 系数,delay 6):
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$Q=4$ 系数,delay 6):
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$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr)$$
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$$G_q^p[n] = g^p[n]\cdot\exp\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr)$$
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64-band QMF analysis 即 ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节的 MPEG-4
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64-band QMF analysis 即 ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节的 MPEG-4
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AAC/SBR 64 complex QMF bank;打包的 $64\times10$ 表是公开 640-tap prototype 的
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AAC/SBR 64 complex QMF bank;打包的 $64\times10$ 表是公开 640-tap prototype 的
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+1
-1
@@ -166,7 +166,7 @@ The hybrid analysis kernels are defined in [3GPP TS 26.405 / ETSI TS 126 405](ht
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Section 5.2.2 (Table 1 $Q=8$/
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Section 5.2.2 (Table 1 $Q=8$/
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$Q=4$ coefficients, delay 6):
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$Q=4$ coefficients, delay 6):
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$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
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$$G_q^p[n] = g^p[n]\cdot\exp\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
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The QMF analysis table is the MPEG-4 AAC/SBR 64 complex QMF bank of
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The QMF analysis table is the MPEG-4 AAC/SBR 64 complex QMF bank of
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ISO/IEC 14496-3/AMD1:2003, subclause 4.B.18.2, stored as the polyphase
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ISO/IEC 14496-3/AMD1:2003, subclause 4.B.18.2, stored as the polyphase
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+1
-1
@@ -151,7 +151,7 @@ hybrid 分析核定义于 [3GPP TS 26.405 / ETSI TS 126 405](https://www.etsi.or
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第 5.2.2 节(Table 1 的 $Q=8$/
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第 5.2.2 节(Table 1 的 $Q=8$/
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$Q=4$ 系数,delay 6):
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$Q=4$ 系数,delay 6):
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$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
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$$G_q^p[n] = g^p[n]\cdot\exp\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
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QMF analysis 表即 MPEG-4 AAC/SBR(ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节)
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QMF analysis 表即 MPEG-4 AAC/SBR(ISO/IEC 14496-3/AMD1:2003 第 4.B.18.2 节)
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的 64 complex QMF bank;打包的 $64\times10$ 表是公开 640-tap prototype
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的 64 complex QMF bank;打包的 $64\times10$ 表是公开 640-tap prototype
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+9
-9
@@ -177,7 +177,7 @@ Let $\mathcal A_b$ denote the 64-band analysis-QMF operator with polyphase histo
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$$
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$$
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X_{c,b,t}=
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X_{c,b,t}=
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\mathcal A_b\!\left(
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\mathcal A_b\left(
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\widetilde x_c[64t],\ldots,\widetilde x_c[64t+63];
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\widetilde x_c[64t],\ldots,\widetilde x_c[64t+63];
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\mathbf s^{\mathrm A}_{c,t}
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\mathbf s^{\mathrm A}_{c,t}
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\right).
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\right).
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@@ -243,7 +243,7 @@ $$
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F_k=
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F_k=
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\sum_{n=0}^{63}
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\sum_{n=0}^{63}
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\mathrm{zone}_n
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\mathrm{zone}_n
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\exp\!\left(-j\frac{2\pi kn}{64}\right).
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\exp\left(-j\frac{2\pi kn}{64}\right).
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$$
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$$
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### 7.2 Modulation and synthesis
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### 7.2 Modulation and synthesis
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@@ -268,7 +268,7 @@ Let $\mathcal S$ denote polyphase synthesis with a 640-value synthesis window an
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$$
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$$
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\mathbf y_{o,t}=
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\mathbf y_{o,t}=
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\mathcal S\!\left(
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\mathcal S\left(
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\mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t}
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\mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t}
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\right).
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\right).
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$$
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$$
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@@ -277,7 +277,7 @@ Object output is
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$$
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$$
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y_o[64t+r]=
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y_o[64t+r]=
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\mathrm{clip}\!\left(
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\mathrm{clip}\left(
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16\,\mathbf y_{o,t}[r],-1,1
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16\,\mathbf y_{o,t}[r],-1,1
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\right)G_{\mathrm{clip}},
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\right)G_{\mathrm{clip}},
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$$
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$$
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@@ -290,7 +290,7 @@ LFE bypasses the object matrix and inverse QMF and uses a 1217-sample delay. Aft
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$$
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$$
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y_{\mathrm{LFE}}[n]=
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y_{\mathrm{LFE}}[n]=
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\mathrm{clip}\!\left(
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\mathrm{clip}\left(
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x_{\mathrm{LFE,core}}[n-1217],-1,1
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x_{\mathrm{LFE,core}}[n-1217],-1,1
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\right).
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\right).
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$$
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$$
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@@ -301,7 +301,7 @@ The lateral and longitudinal grids use $N=62$; the height grid uses $N=15$. The
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$$
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$$
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q_N(k)=
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q_N(k)=
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\min\!\left(
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\min\left(
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32767,
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32767,
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\left\lfloor\frac{32768k}{N}+\frac12\right\rfloor
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\left\lfloor\frac{32768k}{N}+\frac12\right\rfloor
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\right).
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\right).
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@@ -322,11 +322,11 @@ Their maximum runtime value is $32767/32768$, not exactly 1.
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For conversion to the ADM grid:
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For conversion to the ADM grid:
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$$
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$$
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k_1=\mathrm{round}\!\left(\frac{62q_1}{32767}\right),
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k_1=\mathrm{round}\left(\frac{62q_1}{32767}\right),
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\quad
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\quad
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k_2=\mathrm{round}\!\left(\frac{62q_2}{32767}\right),
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k_2=\mathrm{round}\left(\frac{62q_2}{32767}\right),
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\quad
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\quad
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k_3=\mathrm{round}\!\left(\frac{15q_3}{32767}\right),
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k_3=\mathrm{round}\left(\frac{15q_3}{32767}\right),
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$$
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$$
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$$
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$$
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+9
-9
@@ -177,7 +177,7 @@ $$
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$$
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$$
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X_{c,b,t}=
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X_{c,b,t}=
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\mathcal A_b\!\left(
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\mathcal A_b\left(
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\widetilde x_c[64t],\ldots,\widetilde x_c[64t+63];
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\widetilde x_c[64t],\ldots,\widetilde x_c[64t+63];
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\mathbf s^{\mathrm A}_{c,t}
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\mathbf s^{\mathrm A}_{c,t}
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\right).
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\right).
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@@ -243,7 +243,7 @@ $$
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F_k=
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F_k=
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\sum_{n=0}^{63}
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\sum_{n=0}^{63}
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\mathrm{zone}_n
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\mathrm{zone}_n
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\exp\!\left(-j\frac{2\pi kn}{64}\right).
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\exp\left(-j\frac{2\pi kn}{64}\right).
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$$
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$$
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### 7.2 调制与合成
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### 7.2 调制与合成
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@@ -268,7 +268,7 @@ $$
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$$
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$$
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\mathbf y_{o,t}=
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\mathbf y_{o,t}=
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\mathcal S\!\left(
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\mathcal S\left(
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\mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t}
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\mathbf R_{o,t},W,\mathbf s^{\mathrm S}_{o,t}
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\right).
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\right).
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$$
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$$
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@@ -277,7 +277,7 @@ $$
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$$
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$$
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y_o[64t+r]=
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y_o[64t+r]=
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\mathrm{clip}\!\left(
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\mathrm{clip}\left(
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16\,\mathbf y_{o,t}[r],-1,1
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16\,\mathbf y_{o,t}[r],-1,1
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\right)G_{\mathrm{clip}},
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\right)G_{\mathrm{clip}},
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$$
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$$
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@@ -290,7 +290,7 @@ LFE 不经过对象矩阵或 inverse QMF,而是使用 1217-sample 延迟。输
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$$
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$$
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y_{\mathrm{LFE}}[n]=
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y_{\mathrm{LFE}}[n]=
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\mathrm{clip}\!\left(
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\mathrm{clip}\left(
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x_{\mathrm{LFE,core}}[n-1217],-1,1
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x_{\mathrm{LFE,core}}[n-1217],-1,1
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\right).
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\right).
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$$
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$$
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@@ -301,7 +301,7 @@ $$
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$$
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$$
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q_N(k)=
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q_N(k)=
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\min\!\left(
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\min\left(
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32767,
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32767,
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\left\lfloor\frac{32768k}{N}+\frac12\right\rfloor
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\left\lfloor\frac{32768k}{N}+\frac12\right\rfloor
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\right).
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\right).
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@@ -322,11 +322,11 @@ $$
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转换为 ADM 网格时:
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转换为 ADM 网格时:
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$$
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$$
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k_1=\mathrm{round}\!\left(\frac{62q_1}{32767}\right),
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k_1=\mathrm{round}\left(\frac{62q_1}{32767}\right),
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\quad
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\quad
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k_2=\mathrm{round}\!\left(\frac{62q_2}{32767}\right),
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k_2=\mathrm{round}\left(\frac{62q_2}{32767}\right),
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\quad
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\quad
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k_3=\mathrm{round}\!\left(\frac{15q_3}{32767}\right),
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k_3=\mathrm{round}\left(\frac{15q_3}{32767}\right),
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$$
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$$
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$$
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$$
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