peter/peter-tanner.github.io
1
0
Fork 0
mirror of https://github.com/peter-tanner/peter-tanner.github.io.git synced 2024-11-30 12:00:18 +08:00
Code Issues Packages Projects Releases Wiki Activity

Remove % comments in math to prevent Missing \end{align*} issue only

Browse Source 
on website.
This commit is contained in:
Peter 2024-10-29 17:07:20 +08:00
parent dde25e8714
commit 0d1beaf0ec
2 changed files with 6 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

5
.markdownlint.json Normal file
View File

@ -0,0 +1,5 @@
{
"MD013": false,
"no-duplicate-heading": false,
"no-inline-html": false
}

7
_posts/2024-10-29-Idiots-guide-to-ELEC4402-Communications-Systems.md
View File

@ -97,7 +97,6 @@ Calculate $C_n$ coefficient as follows from $x_p(t)$:
$$ $$
\begin{align*} \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\\ 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 $T_s$} &=\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*} \end{align*}
@ -417,7 +416,6 @@ Calculate $C_n$ coefficient as follows from $x_p(t)$:
$$ $$
\begin{align*} \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\\ 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 $T_s$} &=\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*} \end{align*}
@ -647,9 +645,6 @@ Bit error rate (BER) from matched filter outputs and filter output noise
$$ $$
\begin{align*} \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)\\ 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}\\ 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}\\ T&=1/R_b\quad\text{$R_b$: Bitrate}\\
@ -928,7 +923,7 @@ $$
Input has probability distribution $p_X(a_i)=P(X=a_i)$ 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 $p_Y(b_j)=P(y=b_j)$ Output has probabiltiy distribution $p_Y(b_j)=P(y=b_j)$