Reproduction of a showcase of TeX

fourier.tex

\documentclass{ltjarticle}

% Reproduction of 
% http://blog.revolutionanalytics.com/2014/01/the-fourier-transform-explained-in-one-sentence.html
%

\usepackage[paperwidth=10cm, paperheight=5cm]{geometry}

\usepackage[svgnames]{xcolor}

\usepackage{fontspec}
\usepackage{tikz}

\setmainfont{Helvetica Neue Light Italic}

\begin{document}
\begin{tikzpicture}[remember picture,overlay]
  \shade[outer color=gray!5,inner color=white] (current page.south west) rectangle (current page.north east);
\end{tikzpicture}
    \[
        \textcolor{DarkOrchid}{X_{\textcolor{LimeGreen}{k}}} = 
        \textcolor{Fuchsia}{\frac{1}{N} \sum_{n=0}^{N-1}} 
        \textcolor{RoyalBlue}{x_n} \textcolor{Red}{e^{i
        \textcolor{Orange}{2\pi} \textcolor{LimeGreen}{k} \textcolor{Fuchsia}{\frac{n}{N}}}}
    \]

    \small
    To find \textcolor{DarkOrchid}{the energy at}
    \textcolor{LimeGreen}{a particular frequency},
    \textcolor{Red}{spin} \textcolor{RoyalBlue}{your signal}
    \textcolor{Orange}{around a circle} \textcolor{LimeGreen}{at that frequency},
    and \textcolor{Fuchsia}{average a bunch of points along that path}.

    \thispagestyle{empty}
\end{document}