\begin{tikzpicture}
\begin{axis}[
axis on top=true,
axis equal,
axis lines*=middle,
enlargelimits = false, clip=false,
xmin=-1.5,
xmax=2.5,
ymin=-1,
ymax=1,
axis line style={->,>=stealth},
xlabel={$\mathrm{Re}\{z\}$},
ylabel={$\mathrm{Im}\{z\}$},
every axis x label/.style={
at={(ticklabel* cs:1)},
anchor=north,
},
every axis y label/.style={
at={(ticklabel* cs:1)},
anchor=south,
},
%xmajorgrids,
%ymajorgrids,
xtick={-1.33, -0.75, 0.5, 2},
xticklabels={$-\frac{1}{0.75}$, $-0.75$, $0.5$, $2$},
xticklabel style={yshift=-0.2cm},
ytick=\empty,
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}]
\draw (axis cs:0,0) circle [black!50, dashed, line width=2pt, radius=1];
\addplot [line width=1pt,mark=x, only marks, mark size = 3pt]
table[row sep=crcr]{
	0.5 0 \\
	-0.75 0 \\
	0.565685 0.565685 \\
	0.565685 -0.565685 \\
};

\addplot [line width=1pt,mark=*, only marks, mark size = 3pt, mark options={fill=white}]
table[row sep=crcr]{
	2 0 \\
	-1.33333 0 \\
	0.883884 -0.883884 \\
	0.883884 0.883884 \\
};

% Annotations
\draw[red!40, thick, fill=red!20] (axis cs: 1.25, 0) ellipse (1.75cm and 0.25cm);
\draw[blue!40, thick, fill=blue!20] (axis cs: -1, 0) ellipse (1cm and 0.25cm);
\draw[green!40, thick, fill=green!20, rotate around={45:(0.707,0.707)}] (axis cs: 0.707, 0.707) ellipse (0.75cm and 0.25cm);
\draw[green!40, thick, fill=green!20, rotate around={-45:(0.707,-0.707)}] (axis cs: 0.707, -0.707) ellipse (0.75cm and 0.25cm);
\end{axis}

\begin{axis}[
name=plot2,
at= (plot1.east), anchor=west, xshift=2cm,
width=0.6\textwidth,
height=0.5\textwidth,
%at=(plot1.below south east), anchor=above north east,
axis lines*=middle,
enlargelimits = upper, clip=true,
scale only axis,
axis line style={->,>=stealth},
xlabel={$\omega$},
ylabel={$\angle H(e^{j\omega})$ (deg)},
every axis x label/.style={
	at={(ticklabel* cs:1)},
	anchor=north,
},
every axis y label/.style={
	at={(ticklabel* cs:1)},
	anchor=south,
},
xmin=0, xmax=1,
xtick={0, 0.25, 0.5, 0.75, 1},
xticklabels ={$0$, $\pi/4$, $\pi/2$, $3\pi/4$, $\pi$},
xticklabel style={xshift=0.1cm},
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 [smooth, black, line width=1pt]
table[row sep=crcr]{
	0 7.9342e-31 \\
	0.02 -16.4081 \\
	0.04 -32.8087 \\
	0.06 -49.2255 \\
	0.08 -65.7433 \\
	0.1 -82.5385 \\
	0.12 -99.9141 \\
	0.14 -118.345 \\
	0.16 -138.5362 \\
	0.18 -161.4783 \\
	0.2 -188.4051 \\
	0.22 -220.3778 \\
	0.24 -257.1099 \\
	0.26 -295.6652 \\
	0.28 -331.5157 \\
	0.3 -361.7197 \\
	0.32 -385.9806 \\
	0.34 -405.3475 \\
	0.36 -421.0441 \\
	0.38 -434.0568 \\
	0.4 -445.0996 \\
	0.42 -454.6749 \\
	0.44 -463.1377 \\
	0.46 -470.7434 \\
	0.48 -477.6797 \\
	0.5 -484.0884 \\
	0.52 -490.0794 \\
	0.54 -495.7403 \\
	0.56 -501.143 \\
	0.58 -506.3484 \\
	0.6 -511.4101 \\
	0.62 -516.3767 \\
	0.64 -521.2944 \\
	0.66 -526.2088 \\
	0.68 -531.1669 \\
	0.7 -536.2191 \\
	0.72 -541.422 \\
	0.74 -546.8407 \\
	0.76 -552.5529 \\
	0.78 -558.6542 \\
	0.8 -565.2644 \\
	0.82 -572.5373 \\
	0.84 -580.6732 \\
	0.86 -589.935 \\
	0.88 -600.6686 \\
	0.9 -613.3201 \\
	0.92 -628.4338 \\
	0.94 -646.5875 \\
	0.96 -668.1853 \\
	0.98 -693.0508 \\
};
\end{axis}
\end{tikzpicture}