☰

方波脉冲函数背后的网格及其频域

tag-icon • tag-icon tikz-pgf
方波脉冲函数背后的网格及其频域

关于如何优雅地在绘制的两个函数后面放置一个网格，您有什么想法吗？：

% Author: Izaak Neutelings (January 2021)
% http://pgfplots.net/tikz/examples/fourier-transform/
% https://tex.stackexchange.com/questions/127375/replicate-the-fourier-transform-time-frequency-domains-correspondence-illustrati
% https://www.dspguide.com/ch13/4.htm
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage{pgfplots}



\begin{document}


% RECTANGULAR FUNCTION

\begin{tikzpicture}
  \def\xmin{-0.7*\T} % min x axis
  \def\xmax{3.0}     % max x axis
  \def\ymin{-0.4}    % min y axis
  \def\ymax{1.7}     % max y axis
  \def\A{0.67*\ymax} % amplitude
  \def\T{0.31*\xmax} % period
  \colorlet{myblue}{blue!80!black}
  \colorlet{mydarkblue}{myblue!80!black}
  \tikzstyle{xline}=[myblue,thick]
  \def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}
  \tikzstyle{myarr}=[myblue!50,-{Latex[length=3,width=2]}]
  \def\N{80}

  \message{^^JRectangular function}
  \draw[->,thick] (0,\ymin) -- (0,\ymax) node[left] {$y$};
  \draw[->,thick] (-\xmax,0) -- (\xmax+0.1,0) node[below=1,right=1] {$t$ [s]};
  \draw[xline,very thick,line cap=round]
    ({-\T},{\A}) -- ({\T},{\A}) node[black,right=0,scale=0.9] {$A$}
    ({-\T},0) -- ({-0.9*\xmax},0)
    ({ \T},0) -- ({0.9*\xmax},0);
  \draw[xline,dashed,thin,line cap=round]
    ({-\T},0) --++ (0,{\A})
    ({ \T},0) --++ (0,{\A});
  \tick{{ -\T},0}{90} node[right=1,below=-1,scale=1] {$-T$};
  \tick{{  \T},0}{90} node[right=1,below=-1,scale=1] {$T$};
  %\tick{0,{ \A}}{  0} node[left=-1,scale=0.9] {$A$};
\end{tikzpicture}


% RECTANGULAR FUNCTION - frequency domain
\begin{tikzpicture}
  \def\xmin{-0.7*\T} % min x axis
  \def\xmax{3.0}     % max x axis
  \def\ymin{-0.4}    % min y axis
  \def\ymax{1.7}     % max y axis
  \def\A{0.67*\ymax} % amplitude
  \def\T{0.31*\xmax} % period
  \colorlet{myblue}{blue!80!black}
  \colorlet{mydarkblue}{myblue!80!black}
  \tikzstyle{xline}=[myblue,thick]
  \def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}
  \tikzstyle{myarr}=[myblue!50,-{Latex[length=3,width=2]}]
  \def\N{80}
  \message{^^JRectangular function - frequency domain}
  \def\T{0.30*\xmax} % period
  \def\A{0.70*\ymax} % amplitude
  \draw[->,thick] (0,\ymin) -- (0,\ymax) node[left] {$g$};
  \draw[->,thick] (-\xmax,0) -- (\xmax+0.1,0) node[below=1,right=1] {$\omega$ [rad/s]};
  \draw[xline,samples=\N,smooth,variable=\t,domain=-0.94*\xmax:0.94*\xmax]
    plot(\t,{\A*sin(360/(\T)*\t)/(2*pi)*(\T)/\t});
  \tick{{-3*\T},0}{90} node[left=  5,below=-2,scale=0.85] {\strut$-\dfrac{3\pi}{T}$};
  \tick{{-2*\T},0}{90} node[left=  5,below=-2,scale=0.85] {\strut$-\dfrac{2\pi}{T}$};
  \tick{{  -\T},0}{90} node[left=  4,below= 0,scale=0.85] {\strut$-\dfrac{\pi}{T}$};
  \tick{{   \T},0}{90} node[right= 0,below= 0,scale=0.85] {\strut$ \dfrac{\pi}{T}$};
  \tick{{ 2*\T},0}{90} node[right=-1,below=-2,scale=0.85] {\strut$ \dfrac{2\pi}{T}$};
  \tick{{ 3*\T},0}{90} node[right=-1,below=-2,scale=0.85] {\strut$ \dfrac{3\pi}{T}$};
  \tick{0,{\A}}{0} node[left=-1,scale=0.8] {$2TA$};
  \node[mydarkblue,right,scale=0.9] at (0.2*\xmax,\A)
    {$2A\dfrac{\sin(T\omega)}{\omega}$}; %g(\omega) = 
\end{tikzpicture}

\end{document}

感谢您的帮助

在此处输入图片描述

答案1

您可以使用gridTikZ 提供的路径：

% Author: Izaak Neutelings (January 2021)
% http://pgfplots.net/tikz/examples/fourier-transform/
% https://tex.stackexchange.com/questions/127375/replicate-the-fourier-transform-time-frequency-domains-correspondence-illustrati
% https://www.dspguide.com/ch13/4.htm
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage{pgfplots}



\begin{document}


% RECTANGULAR FUNCTION

\begin{tikzpicture}
  \def\xmin{-0.7*\T} % min x axis
  \def\xmax{3.0}     % max x axis
  \def\ymin{-0.4}    % min y axis
  \def\ymax{1.7}     % max y axis
  \def\A{0.67*\ymax} % amplitude
  \def\T{0.31*\xmax} % period
  \colorlet{myblue}{blue!80!black}
  \colorlet{mydarkblue}{myblue!80!black}
  \tikzstyle{xline}=[myblue,thick]
  \def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}
  \tikzstyle{myarr}=[myblue!50,-{Latex[length=3,width=2]}]
  \def\N{80}

  \message{^^JRectangular function}
  \draw[step=0.5*\T,lightgray] (-\xmax,\ymin) grid (\xmax,\ymax);

  \draw[->,thick] (0,\ymin) -- (0,\ymax) node[left] {$y$};
  \draw[->,thick] (-\xmax,0) -- (\xmax+0.1,0) node[below=1,right=1] {$t$ [s]};
  \draw[xline,very thick,line cap=round]
    ({-\T},{\A}) -- ({\T},{\A}) node[black,right=0,scale=0.9] {$A$}
    ({-\T},0) -- ({-0.9*\xmax},0)
    ({ \T},0) -- ({0.9*\xmax},0);
  \draw[xline,dashed,thin,line cap=round]
    ({-\T},0) --++ (0,{\A})
    ({ \T},0) --++ (0,{\A});
  \tick{{ -\T},0}{90} node[right=1,below=-1,scale=1] {$-T$};
  \tick{{  \T},0}{90} node[right=1,below=-1,scale=1] {$T$};
  %\tick{0,{ \A}}{  0} node[left=-1,scale=0.9] {$A$};
\end{tikzpicture}


% RECTANGULAR FUNCTION - frequency domain
\begin{tikzpicture}
  \def\xmin{-0.7*\T} % min x axis
  \def\xmax{3.0}     % max x axis
  \def\ymin{-0.4}    % min y axis
  \def\ymax{1.7}     % max y axis
  \def\A{0.67*\ymax} % amplitude
  \def\T{0.31*\xmax} % period
  \colorlet{myblue}{blue!80!black}
  \colorlet{mydarkblue}{myblue!80!black}
  \tikzstyle{xline}=[myblue,thick]
  \def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}
  \tikzstyle{myarr}=[myblue!50,-{Latex[length=3,width=2]}]
  \def\N{80}
  \message{^^JRectangular function - frequency domain}
  \def\T{0.30*\xmax} % period
  \def\A{0.70*\ymax} % amplitude
    \draw[step=0.5*\T,lightgray] (-\xmax,\ymin) grid (\xmax,\ymax);
  
  
  \draw[->,thick] (0,\ymin) -- (0,\ymax) node[left] {$g$};
  \draw[->,thick] (-\xmax,0) -- (\xmax+0.1,0) node[below=1,right=1] {$\omega$ [rad/s]};
  \draw[xline,samples=\N,smooth,variable=\t,domain=-0.94*\xmax:0.94*\xmax]
    plot(\t,{\A*sin(360/(\T)*\t)/(2*pi)*(\T)/\t});
  \tick{{-3*\T},0}{90} node[left=  5,below=-2,scale=0.85] {\strut$-\dfrac{3\pi}{T}$};
  \tick{{-2*\T},0}{90} node[left=  5,below=-2,scale=0.85] {\strut$-\dfrac{2\pi}{T}$};
  \tick{{  -\T},0}{90} node[left=  4,below= 0,scale=0.85] {\strut$-\dfrac{\pi}{T}$};
  \tick{{   \T},0}{90} node[right= 0,below= 0,scale=0.85] {\strut$ \dfrac{\pi}{T}$};
  \tick{{ 2*\T},0}{90} node[right=-1,below=-2,scale=0.85] {\strut$ \dfrac{2\pi}{T}$};
  \tick{{ 3*\T},0}{90} node[right=-1,below=-2,scale=0.85] {\strut$ \dfrac{3\pi}{T}$};
  \tick{0,{\A}}{0} node[left=-1,scale=0.8] {$2TA$};
  \node[mydarkblue,right,scale=0.9] at (0.2*\xmax,\A)
    {$2A\dfrac{\sin(T\omega)}{\omega}$}; %g(\omega) = 
\end{tikzpicture}

\end{document}

在此处输入图片描述

相关内容