From 0d1beaf0eca7f4f6dd90eebbd475a88d804bb54d Mon Sep 17 00:00:00 2001 From: Peter Tanner Date: Tue, 29 Oct 2024 17:07:20 +0800 Subject: [PATCH] Remove % comments in math to prevent `Missing \end{align*}` issue only on website. --- .markdownlint.json | 5 +++++ ...0-29-Idiots-guide-to-ELEC4402-Communications-Systems.md | 7 +------ 2 files changed, 6 insertions(+), 6 deletions(-) create mode 100644 .markdownlint.json diff --git a/.markdownlint.json b/.markdownlint.json new file mode 100644 index 0000000..6202e71 --- /dev/null +++ b/.markdownlint.json @@ -0,0 +1,5 @@ +{ + "MD013": false, + "no-duplicate-heading": false, + "no-inline-html": false +} \ No newline at end of file diff --git a/_posts/2024-10-29-Idiots-guide-to-ELEC4402-Communications-Systems.md b/_posts/2024-10-29-Idiots-guide-to-ELEC4402-Communications-Systems.md index 0c582e2..a013758 100644 --- a/_posts/2024-10-29-Idiots-guide-to-ELEC4402-Communications-Systems.md +++ b/_posts/2024-10-29-Idiots-guide-to-ELEC4402-Communications-Systems.md @@ -97,7 +97,6 @@ Calculate $C_n$ coefficient as follows from $x_p(t)$: $$ \begin{align*} - % C_n&=X_p(nf_s)\\ C_n&=\frac{1}{T_s} \int_{T_s} x_p(t)\exp(-j2\pi f_s t)dt\\ &=\frac{1}{T_s} X(nf_s)\quad\color{red}\text{(TODO: Check)}\quad\color{white}\text{$x(t-nT_s)$ is contained in the interval $T_s$} \end{align*} @@ -417,7 +416,6 @@ Calculate $C_n$ coefficient as follows from $x_p(t)$: $$ \begin{align*} - % C_n&=X_p(nf_s)\\ C_n&=\frac{1}{T_s} \int_{T_s} x_p(t)\exp(-j2\pi f_s t)dt\\ &=\frac{1}{T_s} X(nf_s)\quad\color{red}\text{(TODO: Check)}\quad\color{white}\text{$x(t-nT_s)$ is contained in the interval $T_s$} \end{align*} @@ -647,9 +645,6 @@ Bit error rate (BER) from matched filter outputs and filter output noise $$ \begin{align*} - % H_\text{opt}(f)&=\max_{H(f)}\left(\frac{s_{o1}-s_{o2}}{2\sigma_o}\right) - - % \text{BER}_\text{bin}&=p Q\left(\frac{s_{o1}-V_T}{\sigma_o}\right)+(1-p)Q\left(\frac{V_T-s_{o2}}{\sigma_o}\right)\text{, $p\rightarrow$Probability $s_1(t)$ sent, $V_T\rightarrow$Threshold voltage} Q(x)&=\frac{1}{2}-\frac{1}{2}\text{erf}\left(\frac{x}{\sqrt{2}}\right)\Leftrightarrow\text{erf}\left(\frac{x}{\sqrt{2}}\right)=1-2Q(x)\\ E_b&=d^2=\int_{-\infty}^\infty|s_1(t)-s_2(t)|^2dt\quad\text{Energy per bit/Distance}\\ T&=1/R_b\quad\text{$R_b$: Bitrate}\\ @@ -928,7 +923,7 @@ $$ Input has probability distribution $p_X(a_i)=P(X=a_i)$ -Channel maps alphabet $`\{a_1,\dots,a_M\} \to \{b_1,\dots,b_N\}`$ +Channel maps alphabet $\{a_1,\dots,a_M\} \to \{b_1,\dots,b_N\}$ Output has probabiltiy distribution $p_Y(b_j)=P(y=b_j)$