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<!DOCTYPE html>
<html><!-- InstanceBegin template="/Templates/LPSA.dwt" codeOutsideHTMLIsLocked="false" -->
<head>
<link href="./css/LinePhysSystAnal.css" rel="stylesheet" type="text/css">
<link href="mailto:echeeve1@swarthmore.edu" rev="made">
<meta content="en-us" http-equiv="Content-Language">
<meta content="text/html; charset=windows-1252" http-equiv="Content-Type">
<meta content="Erik Cheever, Swarthmore College" name="author">
<meta content="ALL" name="ROBOTS">
<script src="./js/Overlib/overlib.js"><!-- overLIB (c) Erik Bosrup --></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
</script>
<!-- "{% static './js/MathJax-2.7.1/MathJax.js?config=TeX-MML-AM_CHTML'%}"> -->
<script type="text/javascript" async
src="./js/MathJax-2.7.1/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<script
src="./js/jquery/jquery-3.3.1.min.js"
integrity=""
crossorigin="anonymous"></script>
<script src="./js/jquery/jquery-toc.js"></script>
<!-- InstanceBeginEditable name="doctitle" -->
<meta content="csv" name="keywords">
<meta content="csv" name="description">
<title>Convolution Interactive Visualization</title>
<script src="./js/highcharts/highcharts.js"></script>
<script src="./js/highcharts/modules/exporting.js"></script>
<script src="./js/CI.js"></script>
<!-- InstanceEndEditable -->
<script src="./js/LPSA.js" type="text/javascript"></script>
</head>
<body>
<ul id="NavHeader">
<li id="current"><a href="https://lpsa.swarthmore.edu/Convolution/CI.html">Convolution Interactive Visualization</a></li>
<li id="current"><a href="help.html">Interactive Help and Guide</a></li>
</ul>
<table align="center">
<tbody>
<tr>
<td align="right"><div id="timePlot" style="width:500px; height:300px;float:right; "></div> </td>
<td><div id="lambdaPlot" style="width:500px; height:300px;float:right;clear:right; "></div></td>
</tr>
<tr>
<td align="right">
<form id="funcsDropDown">
<table border="0" align="center">
<tbody>
<tr>
<td align="right">Select <font color="#FF0000""> h(t)</font>: </td>
<td><select id="h_of_t_dd" onchange="staticCalcs();"></select></td>
</tr>
<tr>
<td align="right">Select <font color="#72B2F2">f(t)</font>: </td>
<td><select id="f_of_t_dd" onchange="staticCalcs();"></select></td>
</tr>
<tr>
<td align="right">Show complete solution? </td>
<td><input type="checkbox" id="showSoln" checked onchange="dynamicCalcs();"></td>
</tbody>
</table>
</form>
<div id="timeCtrl" style="text-align:center;"></div>
<p class="noindent"> The value of the convolution at this time is <font color="#008000"> y(<span id="y_t0Text" )></span>) = <span id="dispConvValue"> </font></span>.
<br />
<div style="color:red; font-weight:200; font-size:larger; display:none;" id="bothImpulseFuncs"></div>
<p class="noindent">The functions used for the current example are <sup><a href="#mynote">[*]</a></sup>: </p>
<p class="equation"><font color="#FF0000"> h(t)</font>=<span id="h_of_t_text" class="greek"></span> <font color="#72B2F2">f(t)</font>=
<span id="f_of_t_text" class="greek"></span>.
</p>
<p class="equation">
\[y(t)=\int_{-\infty}^{+\infty}{h(t-\lambda)\cdot f(\lambda)\cdot d\lambda}=\int_{0^-}^t{h(t-\lambda)\cdot f(\lambda)\cdot d\lambda}\]
<br></p>
</td>
<td><div id="convPlot" style="width:500px; height:300px;float:right;clear:right; "></div></td>
</tr>
</tbody>
</table>
<!-- InstanceBeginEditable name="MainText" -->
<!-- InstanceEndEditable -->
<hr class="fullWidth">
<p id="mynote" class="noindent">[*] <span class="note">Note: All functions are implicitly multiplied by the unit step function, <span class="greek">γ</span>(t), so they are equal to 0 for t<0</span>.
<br>© Copyright 2005 to 2022 <a href="http://www.swarthmore.edu/NatSci/echeeve1">Erik Cheever</a>. This is a recap (w/permission) by <a href="https://www.linkedin.com/in/ghaznavi-ghoushchi">M. B. Ghaznavi-Ghoushchi</a> 2024. This page may be freely used for educational purposes.
Ref: <a href="https://lpsa.swarthmore.edu/Convolution/CI.html">Convolution Visualization</a>
</body>
<!-- InstanceEnd -->
</html>