File:Lissajous phase.svg

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Original file (SVG file, nominally 785 × 745 pixels, file size: 130 KB)

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Description
English: Figure showing several Lissajous figures for different phase delays. [1] was used for reference.
Date
Source Own work
Author Krishnavedala
SVG development
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This diagram was created with LaTeX and converted to SVG using dvisvgm.
LaTeX source code
\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}

Licensing

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I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
You may select the license of your choice.

File history

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Date/TimeThumbnailDimensionsUserComment
current23:15, 23 April 2015Thumbnail for version as of 23:15, 23 April 2015785 × 745 (130 KB)Krishnavedala (talk | contribs)fixed issues
23:14, 23 April 2015Thumbnail for version as of 23:14, 23 April 2015785 × 745 (112 KB)Krishnavedala (talk | contribs)converted using {{w|dvisvgm}}
22:34, 20 August 2014Thumbnail for version as of 22:34, 20 August 2014797 × 750 (292 KB)Krishnavedala (talk | contribs){{Information |Description ={{en|1=Figure showing several Lissajous figures for different phase delays. [http://hg.tedpavlic.com/courses/osu/ece209/file/7b7c6399beca/lab1_intro/lab1_intro_lissajous/lab1_intro_lissajous.tex] was used for reference.}...

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