Grid behind a square pulse function and it's frequency domain

Question

Any idea on how to elegantly put a grid behind the two functions plotted here?:

% 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,{\Asin(360/(\T)\t)/(2pi)(\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}

Thanks for your help

Please make your question self-sustained so that it is understandable without following external links. This will ensure that your posts stays helpful for future users even if the links stops working. — samcarter_is_at_topanswers.xyz, Dec 17 '22 at 15:48
You can not ask about external code on this site. You need to create you own MWE. - see https://tex.meta.stackexchange.com/questions/228/ive-just-been-asked-to-write-a-minimal-working-example-mwe-what-is-that — hpekristiansen, Dec 17 '22 at 15:50

score 7 · Accepted Answer · answered Dec 17 '22 at 17:42

You can use the grid path provided by TikZ:

% 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,{\Asin(360/(\T)\t)/(2pi)(\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}

+1 expanding from beamer to tikz, great! – Dr. Manuel Kuehner Dec 17 '22 at 18:03 — Dr. Manuel Kuehner, Dec 17 '22 at 18:03
@Dr.ManuelKuehner :P beamer and tikz are siblings – samcarter_is_at_topanswers.xyz Dec 17 '22 at 18:06 — samcarter_is_at_topanswers.xyz, Dec 17 '22 at 18:06

Grid behind a square pulse function and it's frequency domain

1 Answers1