\documentclass[10pt,border=0pt,tikz,class=scrartcl,multi=false]{standalone}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{lmodern}
\usepackage{mathtools,amssymb,gensymb}
\usepackage{pgfplots}
\usepackage{ifthen}
\pgfplotsset{compat=1.10}
\usetikzlibrary{positioning,calc,arrows,fit,backgrounds,decorations.text,shapes,matrix}

\title {Lissajous phase}
\author{Krishnatej Vedala}

\def\amplitude{1}
\newcommand{\LissajousCurve}[1]{
	\begin{tikzpicture}[anchor=center]\begin{axis}[draw, axis equal, clip=false,
	axis lines=center,
	xtick=\empty, ytick=\empty,
	xmin=-\amplitude-0.1, ymin=-\amplitude-0.1, xmax=\amplitude+0.1, ymax=\amplitude+0.4,
	xlabel={\Large$x(t)$}, ylabel={\Large$y(t)$}]
	\addplot[samples=100, domain=0:1, line width=2.5pt, variable=\t, >->] ({\amplitude*sin(deg(2*pi*t))},{\amplitude*sin(deg(2*pi*t)+#1)});
	\addplot[black,dotted] coordinates {
		(-\amplitude,\amplitude) (\amplitude,\amplitude) 
		(\amplitude,-\amplitude) (-\amplitude,-\amplitude) 
		(-\amplitude,\amplitude)};
	\end{axis}\end{tikzpicture}
}

\tikzset{
	plots/.style = {
		inner sep      = 0pt,
		align          = center,
		font           = \normalsize,
		transform shape,
		anchor = center,
		thick
	},
	graph/.style = {draw = none, scale = .75},
	info/.style = {font = \footnotesize, draw = none}
}

\tikzset{
	pics/graph_pic/.style n args = {3}{code={
		\node (-g) [scale=.65, plots, graph] {\LissajousCurve{#1}};
		\begin{scope}[x=(-g.south west), y=(-g.south), yshift=-6.6em]
		\node [plots, info] {
			$\underbrace{
				\left\{\begin{aligned}
				x(t)&=\sin(2\pi t)\\[-5pt]
				y(t)&=\sin\left(2\pi t-#2\right)
				\end{aligned}\right.}_{
				\begin{array}{@{}c@{}}
				\delta=#1^\circ\\
				\text{#3}
				\end{array}}$
		};
		\node (-c) [fit = (-g.north east), inner sep = 0pt] {};
		\end{scope}
	}}
}

\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[thick,auto,>=stealth']
\def\pp{10}

	\fill [fill=black!40] (0,0) rectangle (\pp,\pp);
	\fill [fill=black!40] (0,0) rectangle (-\pp,-\pp);
	\fill [fill=black!10] (0,0) rectangle (-\pp,\pp);
	\fill [fill=black!10] (0,0) rectangle (\pp,-\pp);

	\draw [decorate, decoration={brace,amplitude=17pt}] (0,\pp) -- node [pos=.5,anchor=south,yshift=15pt] { Positive slope (I \& IV)} (\pp,\pp);
	\draw [decorate, decoration={brace,amplitude=17pt}] (-\pp,\pp) -- node [pos=.5,anchor=south,yshift=15pt] { Negative slope (II \& III)} (0,\pp);
	\draw [decorate, decoration={brace,amplitude=17pt}] (\pp,\pp) -- node [pos=.5,anchor=south,xshift=15pt,rotate=-90] { Clockwise (I \& II)} (\pp,0);
	\draw [decorate, decoration={brace,amplitude=17pt}] (\pp,0) -- node [pos=.5,anchor=south,xshift=15pt,rotate=-90] { Counter clockwise (III \& IV)} (\pp,-\pp);

	\node [anchor=north east] at (\pp,\pp) {\Large\textrm I};
	\node [anchor=north west] at (-\pp,\pp) {\Large\textup{II}};
	\node [anchor=south west] at (-\pp,-\pp) {\Large\textup{III}};
	\node [anchor=south east] at (\pp,-\pp) {\Large\textup{IV}};

	\foreach[count=\i] \angle/\a/\b/\c in 
	{-315/7\pi/4/,
	-270/3\pi/2/(in ``quadrature''),
	-225/5\pi/4/,
	-180/\pi//(inverted),
	-135/3\pi/4/,
	-90/\pi/2/(in ``quadrature''),
	-45/\pi/4/,
	0/0//(in phase)}{
		\ifthenelse{\equal{\angle}{-270}}{\def\len{7.8}}{\def\len{6.8}}
		\ifthenelse{\equal{\b}{}}{
			\path pic (g-\i) at +(45*\i:\len) {graph_pic={\angle}{\a}{\c}};
		}{
			\path pic (g-\i) at +(45*\i:\len) {graph_pic={\angle}{\frac{\a}{\b}}{\c}};
		}
		\ifthenelse{\equal{\angle}{-270}}{
			\draw[dashed, semithick] (0,0) -- node [near end, sloped, above] 
			{\footnotesize$\delta=\angle^\circ$} ($(g-\i-g)-(0,8em)$);
		}{
			\draw[dashed, semithick] (0,0) -- node [near end, sloped, above] 
			{\footnotesize$\delta=\angle^\circ$} (g-\i-g);
		}
	}

	\draw [->, semithick, postaction={decorate, decoration={
		text along path, text={Increasing phase shift}, text align={center,left indent=3mm},raise=3pt}
	}] (1.5,0) arc (0:-315:1.5);

	\node [draw=black, thick, dashed, rectangle, rotate=90, align=center, anchor=south] at (-\pp-0.1,0) {\large
		LTI Lissajous figures are \textbf{ovals} with \emph{eccentricity} and\\
		\emph{direction of rotation} determined by phase shift $\delta$.
	};
\end{tikzpicture}
\end{document}