\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}