From 32431bf045d994efaa493ad591424c0078c2be17 Mon Sep 17 00:00:00 2001 From: BlitherBoom812 Date: Fri, 10 May 2024 16:13:52 +0800 Subject: [PATCH] 20240510 --- source/_posts/Antenna.md | 31 +++++- source/_posts/Speech-SP.md | 112 ++++++++++++++++++++++ source/images/Antenna/1715324548326.png | Bin 0 -> 148839 bytes source/images/Antenna/1715324559069.png | Bin 0 -> 119171 bytes source/images/Antenna/1715324583382.png | Bin 0 -> 288582 bytes source/images/Antenna/1715324769403.png | Bin 0 -> 225992 bytes source/images/Antenna/1715325834911.png | Bin 0 -> 106063 bytes source/images/Antenna/1715328812089.png | Bin 0 -> 339291 bytes source/images/Speech-SP/1715172378465.png | Bin 0 -> 11414 bytes source/images/Speech-SP/1715172404966.png | Bin 0 -> 5768 bytes source/images/Speech-SP/1715172645812.png | Bin 0 -> 223196 bytes source/images/Speech-SP/1715172680511.png | Bin 0 -> 91043 bytes source/images/Speech-SP/1715173923794.png | Bin 0 -> 17629 bytes source/images/Speech-SP/1715174312556.png | Bin 0 -> 17345 bytes 14 files changed, 142 insertions(+), 1 deletion(-) create mode 100644 source/images/Antenna/1715324548326.png create mode 100644 source/images/Antenna/1715324559069.png create mode 100644 source/images/Antenna/1715324583382.png create mode 100644 source/images/Antenna/1715324769403.png create mode 100644 source/images/Antenna/1715325834911.png create mode 100644 source/images/Antenna/1715328812089.png create mode 100644 source/images/Speech-SP/1715172378465.png create mode 100644 source/images/Speech-SP/1715172404966.png create mode 100644 source/images/Speech-SP/1715172645812.png create mode 100644 source/images/Speech-SP/1715172680511.png create mode 100644 source/images/Speech-SP/1715173923794.png create mode 100644 source/images/Speech-SP/1715174312556.png diff --git a/source/_posts/Antenna.md b/source/_posts/Antenna.md index d85099ca..e4cf351f 100644 --- a/source/_posts/Antenna.md +++ b/source/_posts/Antenna.md @@ -582,4 +582,33 @@ Increase Input Impedance #### Monopole -![1713509771675](../images/Antenna/1713509771675.png) \ No newline at end of file +![1713509771675](../images/Antenna/1713509771675.png) + +## Loop Antennas + +### Small Loop + +![1715324583382](../images/Antenna/1715324583382.png) + +![1715324548326](../images/Antenna/1715324548326.png) + +![1715324559069](../images/Antenna/1715324559069.png) + +Infinite small loop radius; + +Infinite small wire radius; + +Uniform distribution. + +Resistance $R_r$ too small! + +### Finite-length loop antennas + +![1715325834911](../images/Antenna/1715325834911.png) + +![1715324769403](../images/Antenna/1715324769403.png) + + + +### Modes of Loop antennas + diff --git a/source/_posts/Speech-SP.md b/source/_posts/Speech-SP.md index 3b99636c..07c013cc 100644 --- a/source/_posts/Speech-SP.md +++ b/source/_posts/Speech-SP.md @@ -578,3 +578,115 @@ G_{TC} =\frac{min\{\sigma_{r,PCM}^{2}\}}{min\{\sigma_{r,TC}^{2}\}}=\frac{\vareps $$ #### 最佳正交变换 - KL 变换 + + +## 语音信号的参数编码 + +### 感觉加权滤波器 + +误差函数加权: + +$$ +J=\int_0^{f_s}\lvert s(f)-\hat{s}(f)\rvert^2\cdot\lvert w(f)\rvert^2df +$$ + +其中,加权滤波器满足 + +$$ +\int_0^{f_S}|w(f)|df= Const. +$$ + +当误差函数最小的时候,应当保证 + +$$ +|s(f)-\hat{s}(f)|^2\cdot|w(f)|=\frac{\gamma}{2}=\text{常数} +$$ + +可以选择如下的滤波器: + +$$ +w(z)=\frac{A(z)}{A\left(\frac{z}{\gamma}\right)}=\frac{1-\sum_{i=1}^P\alpha_iz^{-i}}{1-\sum_{i=1}^P\alpha_i\gamma^iz^{-i}},\quad0\leq\gamma\leq1 +$$ + +$\gamma$ 为加权因子,在 0-1 之间。 + +$\gamma=0$ 时变成逆滤波器,其频谱包络的峰值点就是语音谱的谷值点。 + +> 分析:语音信号是全极点模型产生的,即 $S(z) = GE(z)/A(z)$,与逆滤波器点频谱成反比。 + +![1715172645812](../images/Speech-SP/1715172645812.png) + +### 多脉冲激励线性预测声码器 + +![1715172680511](../images/Speech-SP/1715172680511.png) + +语音综合器的激励源有若干个不同位置和幅度的脉冲信号组成。 + +$$ +\hat{s}(n)=\hat{s}_0(n)+\sum_{k=1}^Mg_kh(n-n_k) +$$ + +其中 $\hat s_0(n)$ 是 LPC 综合器的零输入响应。 + +$$ +\begin{aligned}&e_{s}(n)=s(n)-\hat{s}(n)=s(n)-\hat{s}_{0}(n)-\sum_{k=1}^{M}g_{k}h(n-n_{k})\\&=\bar{e}(n)-\sum_{k=1}^Mg_kh(n-n_k)\end{aligned} +$$ + +用 $\bar{e}(n)=s(n)-\hat{s}_0(n)$ 表示输入语音减去零输入响应(受历史激励影响的部分)。 + +输入感觉加权滤波器,得到输出 + +$$ +\begin{aligned}e(n)&=e_{s}(n)*w(n)=\left[\bar{e}(n)-\sum_{k=1}^{M}g_{k}h(n-n_{k})\right]*w(n)\\&=\bar{e}_{w}(n)-\sum_{k=1}^{M}g_{k}h_{w}(n-n_{k})\end{aligned} +$$ + +从而,得到感觉加权滤波器的误差函数 + +$$ +E=\sum_{n=1}^Ne^2(n)=\sum_{n=1}^N\left[\bar{e}_w(n)-\sum_{k=1}^Mg_kh_w(n-n_k)\right]^2 +$$ + +选择合适的 $n_k$, $g_k$ 使得上面的误差函数最小 + +$$ +\frac{\partial E}{\partial n_j}=0,\quad j=1,\cdots M\\\frac{\partial E}{\partial g_j}=0,\quad j=1,\cdots M +$$ + +上面那个方程很复杂,会导出非线性的方程; + +从下面的那个方程可以推出 + +$$ +\sum_{k=1}^Mg_kR_{hh}(n_k,n_j)=R_{eh}(n_j),\quad j=1,\cdots M +$$ + +其中 + +$$ +R_{eh}(n_j)=\sum_{n=1}^N\bar{e}_w(n)\cdot h_w(n-n_j)\\R_{hh}(n_k,n_j)=\sum_{n=1}^Nh_w(n-n_k)h_w(n-n_j) +$$ + +此时可改写最小均方误差 + +$$ +E_{min}=\sum_{n=1}^N[\bar{e}_w(n)]^2-\sum_{k=1}^Mg_kR_{eh}(n_k) +$$ + +最优解的计算涉及到非线性方程的求解,不太现实。考虑采用次优搜索,一个一个求解。 + +当只有一个脉冲时 + +$$ +g_1R_{hh}(n_1,n_1)=R_{eh}(n_1)\\ +E_{min}=\sum_{n=1}^N[\bar{e}_w(n)]^2-g_1R_{eh}(n_1) +$$ + +消元得到 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