Sublime Text 支持 LaTeX

安装Latextools 通过安装工具,搜索安装LaTexTools Ctrl+shift+P, Install Package, LaTexTools 安装SmartPDF 为了支持反向搜索功能 设置SmartPDF,setting,options,在最下方的逆向搜索命令行,输入 "C:\Program Files\Sublime Text 3\sublime_text.exe" "%f:%l" 编译查看文档 Sublime里面 Ctrl+B,或F7即可编译查看文档了。 配置Latextools 默认情况下,LaTeXTools 使用 pdflatex编译,但是现在一般都是用 XeLaTeX,因此,这里还是需要一点改变的。 Preferences, Package Settings, Latex tools, Setting User 在 "builder_settings": { 增加如下内容: "program": "xelatex",

Matlab傅立叶变换

摘要 在本文中将以$x(t)=A\cos(2\pi ft+\phi)$的傅里叶变换为例介绍Matlab中如何进行傅里叶变换,主要介绍以下内容: 用数字方式(离散时间)描述信号$x(t)$ 利用傅里叶变换将离散信号$x[n]$变换到频域$X[k]$ 提取频域信号$X[k]$的幅值和相位谱,及功率谱 由频域信号恢复出时域信号 离散时间域表示 考虑一个正弦波$x(t)=A\cos(2\pi ft+\phi)$,其中$A=4$, $f=2\text{Hz}$,$\phi=\pi/4$(即$30^{\circ}$)。即: \begin{equation}\label{eq:xt} x(t)=4cos(2\pi 2t+\pi/4) \end{equation} 为将时域连续信号(模拟信号)$x(t)$存储到计算机中,我们需对其进行采样,根据Nyquist采样定律,采样频率一般需要大于信号频率的两倍。 下面看看这采样频率为8和32的情形 A=4; f=2; phi=pi/4; duration=2; fs=4*f; t=0:1/fs:duration-1/fs; x=A*cos(2*pi*f*t+phi); figure('Position',[500 300 400 300]) subplot(2,1,1) plot(t,x) hold on stem(t,x,':.','color',[0.5 0.5 0.5]) ylabel('fs=8') hold off fs=16*f; t=0:1/fs:duration-1/fs; x=A*cos(2*pi*f*t+phi); subplot(2,1,2) plot(t,x) hold on stem(t,x,':.','color',[0.5 0.5 0.5]) xlabel('time(s)') ylabel('fs=32')...

平行板间自然散热计算

图1. 散热片尺寸示意图 1. 平行板总的散热量求解 根据Bar-Cohen and Rohsenow (1984),平行板间的散热量可以通过如下公式求出: \begin{equation}\label{eq:ra} Ra_S=\dfrac{g\beta (T_S-T_{\infty})S^3}{\nu^2}Pr \end{equation} \begin{equation}\label{eq:nu} Nu=\left[ \dfrac{576}{(Ra_SS/L)^2}+\dfrac{2.873}{(Ra_SS/L)^{0.5}}\right] ^{-0.5} \end{equation} \begin{equation}\label{eq:h} h=Nuk/S \end{equation} \begin{equation}\label{eq:qconv} q_{conv} = hA(T_s-T_{\infty}) \end{equation} 如果绘出散热量与Fin数量间的关系,可以得到如图2。 图2. 散热量与Fin数量间的关系 2. 讨论 如果不考虑平行板间的相互影响,将所有翅片看做是单独的平板,那么$Nu$系数用如下方程计算 \begin{equation}\label{eq:nuB} Nu=\left[ 0.825+\dfrac{0.387Ra_L^{1/6}}{[1+(0.492/Pr)^{9/16}]^{8/27}}\right]^2 \end{equation} 两种方式的结果如下图。可以看到在翅片数量较少时,两种方式求解的结果相差不是很多;当翅片数量较多,翅片间距减小,两种方式的差异就明显了。 3. 最优翅片间距 对于散热片来说,减小翅片间距可以增加翅片数量,增加散热面积,提高散热能力。但是随着翅片间距的进一步减小,翅片间的空气阻力增加导致散...

BPSK

The equation representing a sine wave is as follows: $$A\cos(2\pi ft +\phi)$$ From above equation, it can be see that we can making changes to the amplitude, frequency, and phase of a sine wave to encode information. However, as frequency is the first derivative of phase, so frequency and phase of the sine wave equation can be collectively referred to as the phase angle. 请输入链接描述 Amplitude Modulation $$\sin(x)\sin(20x)$$ I/Q data RF communication systems use advanced forms of modulation to increase the amount of data that can be transmitted in a given amount of frequency spectrum. BPSK stands for Binary Phase Shift Keying. It is digital modulation technique. The code main from: Jaseem Vp Below is the Matlab code A=5; t=0:.001:1; f1=5; f2=3; N=length(t); ip = rand(1,N)>0.5; x=A.*sin(...

虚数漫谈

为什么需要虚数? 这部分内容来源于可汗学院的在线教程Introduction to complex numbers The answer is simple. The imaginary unit iii allows us to find solutions to many equations that do not have real number solutions. This may seem weird, but it is actually very common for equations to be unsolvable in one number system but solvable in another, more general number system. Here are some examples with which you might be more familiar. With only the counting numbers, we can't solve $x+8=1$; we need the integers for this! With only the integers, we can't solve $3x-1=0$; we need the rational numbers for this! With only the rational numbers, we can't solve $x^2=2$. Enter the irrational numbers and the real number system! And so, with only the real numbers, we can't solve $x^2=-1$. We need the imaginary numbers for this!...