【Markdown】

底标和顶标

形如 $\underset{1<x<100}{\max }f(x)$ 中的 1<x<100 ，或者$\sum _{n=0}^{N-1}$中的$n=0$和$N-1$这种，总之是位于正上或者正下方的标记，语法格式是

\limts_{底标}^{顶标}
例：
\max\limits_{1<x<100}f(x) $\Rightarrow \underset{1<x<100}{\max }f(x)$
\sum\limits_{n=0}^{N-1} $\Rightarrow \sum _{n=0}^{N-1}$

规律：“_”后接下标，“^”后接上标，这个和角标的规律一样，且不分先后顺序。

分数

语法格式：

\frac{分子}{分母}
例：
\frac{z}{z-a} $\Rightarrow \frac{z}{z-a}$
\frac{1}{12} $\Rightarrow \frac{1}{12}$

空格

nbsp&nbsp;nbsp&nbsp;nbsp \\&nbsp;
emsp&emsp;emsp&emsp;emsp \\&emsp;

nbsp nbsp nbsp
emsp emsp emsp

矩阵

\begin{matrix}
abcdefg & hyjklmn& opq \
rst & uvw& xyz \
\end{matrix} \tag{1}

$$\begin{array}{ccc}abcdefg& hyjklmn& opq\\ rst& uvw& xyz\end{array}$$

\begin{aligned}
f(x)&=\tfrac{1}{12} \cdot r, & g(x) &= \tfrac{1}{24} \cdot x, & x&<12 \
f(x)&=1, &g(x) &= \tfrac{1}{8} \cdot x - 1, & 12 &\le x < 16 \
f(x)&=1, &g(x) &= 1, & x &\ge 16
\end{aligned}

$$\begin{array}{rlrlrl}f(x)& =\frac{1}{12}\cdot r,& g(x)& =\frac{1}{24}\cdot x,& x& <12\\ f(x)& =1,& g(x)& =\frac{1}{8}\cdot x-1,& 12& \le x<16\\ f(x)& =1,& g(x)& =1,& x& \ge 16\end{array}$$

\begin{aligned}
x(n) &= x_{ep}(n) + x_{op}(n) = x_r(n) + jx_i(n)\
X(k)& = Re[X(k)]+jIm[X(k)] =X_{ep}[X(k)] + X_{op}[X(k)]\
\end{aligned}\
\left{\begin{aligned}
Re[X(k)] &= DFT[x_{ep}(n)] &X_{ep}(k) &= DFT[x_r(n)] \
jIm[X(k)] &= DFT[x_{op}(n)]&X_{op}(k) &= DFT[jx_i(n)]\
\end{aligned}\right.

$$\begin{gathered} \begin{array}{rl}x(n)& =x_{ep}(n)+x_{op}(n)=x_r(n)+j{x}_i(n)\\ X(k)& =Re[X(k)]+jIm[X(k)]=X_{ep}[X(k)]+X_{op}[X(k)]\end{array} \\ \{\begin{array}{rlrl}Re[X(k)]& =DFT[x_{ep}(n)]& X_{ep}(k)& =DFT[x_r(n)]\\ jIm[X(k)]& =DFT[x_{op}(n)]& X_{op}(k)& =DFT[j{x}_i(n)]\end{array} \end{gathered}$$