\def\fs{16}
\begin{tikzpicture} 
\begin{axis}[
axis lines*=middle,
enlargelimits = upper, clip=false,
width=\textwidth,
height=0.5\textwidth,
ymin=0,
ymax=2.2,
xmin=-30,
xmax=30,
axis line style={->,>=stealth},
xlabel={$\omega$},
ylabel={$X(e^{j\omega})$ = $X(e^{j\Omega T})$},
yticklabel style = {yshift=-0.3cm},
xticklabel style = {yshift=-0.1cm},
every axis x label/.style={
	at={(ticklabel* cs:1)},
	anchor=north,
},
every axis y label/.style={
	at={(ticklabel* cs:1)},
	anchor=south,
},
ytick={1, 2},
yticklabels={$40$, $80$},
xtick={-24, -16, -8,  8, 16, 24},
xticklabels={$-3\pi$, $-2\pi$, $-\pi$, $\pi$, $2\pi$, $3\pi$},
every outer y axis line/.append style={white!15!black},
every y tick label/.append style={font=\color{white!15!black}},
legend style={draw=white!15!black,fill=white,legend cell align=left}]

\addplot[black, line width=1pt, domain=-30:30, samples=201] {rect(x, 0*\fs - 10, 0*\fs + 10) + rect(x, \fs - 10, \fs + 10) + rect(x, -\fs - 10, -\fs + 10) + rect(x, 2*\fs - 10, 2*\fs + 10) + rect(x, -2*\fs - 10, -2*\fs + 10)};
\end{axis}

% extra x axis
\begin{axis}[yshift=-1cm,
axis lines*=middle,
enlargelimits = upper, clip=false,
xmin=-30,
xmax=30,
width=\textwidth,
height=0.5\textwidth,
hide y axis,
axis line style={->,>=stealth},
xlabel={$\Omega$},
xticklabel style = {yshift=-0.1cm},
every axis x label/.style={
	at={(ticklabel* cs:1)},
	anchor=north,
},
xtick={-24, -16, -8,  8, 16, 24},
xticklabels={\scriptsize $-240\pi$, \scriptsize $-160\pi$, \scriptsize $-80\pi$, \scriptsize $80\pi$, \scriptsize $160\pi$, \scriptsize $240\pi$},
every outer y axis line/.append style={white!15!black},
every y tick label/.append style={font=\color{white!15!black}},
legend style={draw=white!15!black,fill=white,legend cell align=left}]
\addplot[draw=none] {1};
\end{axis}

\end{tikzpicture}