<div dir="ltr"><p style="margin:0px 0px 1em;padding:0px;border:0px;font-variant-numeric:inherit;font-variant-east-asian:inherit;font-stretch:inherit;line-height:inherit;font-family:Arial,"Helvetica Neue",Helvetica,sans-serif;font-size:15px;vertical-align:baseline;box-sizing:inherit;clear:both;color:rgb(36,39,41)">This example is taken from a <a href="https://dspillustrations.com/pages/posts/misc/convolution-examples-and-the-convolution-integral.html" rel="nofollow noreferrer" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(0,89,153)">tutorial</a> related to convolution integral.</p><p style="margin:0px 0px 1em;padding:0px;border:0px;font-variant-numeric:inherit;font-variant-east-asian:inherit;font-stretch:inherit;line-height:inherit;font-family:Arial,"Helvetica Neue",Helvetica,sans-serif;font-size:15px;vertical-align:baseline;box-sizing:inherit;clear:both;color:rgb(36,39,41)">I would like to export this example as animation in mp4 format. So far, the code looks like this :</p><pre class="gmail-lang-py gmail-prettyprint gmail-prettyprinted" style="margin-top:0px;margin-bottom:1em;padding:12px 8px;border:0px;font-variant-numeric:inherit;font-variant-east-asian:inherit;font-stretch:inherit;line-height:inherit;font-family:Consolas,Menlo,Monaco,"Lucida Console","Liberation Mono","DejaVu Sans Mono","Bitstream Vera Sans Mono","Courier New",monospace,sans-serif;font-size:13px;vertical-align:baseline;box-sizing:inherit;width:auto;max-height:600px;overflow:auto;background-color:rgb(239,240,241);border-radius:3px;color:rgb(57,51,24)"><code style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:Consolas,Menlo,Monaco,"Lucida Console","Liberation Mono","DejaVu Sans Mono","Bitstream Vera Sans Mono","Courier New",monospace,sans-serif;vertical-align:baseline;box-sizing:inherit;white-space:inherit"><span class="gmail-kwd" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(16,16,148)">import</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> scipy</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">integrate

</span><span class="gmail-com" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(133,140,147)"># Calculate the overall convolution result using Simpson integration</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">

plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">plot</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">t</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> f1</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">t</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">),</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> label</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">=</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">r</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$f_1(\tau)$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">)</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">
plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">plot</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">t</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> f_shift</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">t</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">),</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> label</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">=</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">r</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$f_2(t_0-\tau)$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">)</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">
plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">plot</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">t</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> prod</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">t</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">),</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> </span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'r-'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> label</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">=</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">r</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$f_1(\tau)f_2(t_0-\tau)$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">)</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">
plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">grid</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-kwd" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(16,16,148)">True</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">);</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">xlabel</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">r</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$\tau$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">);</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">ylabel</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">r</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$x(\tau)$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">)</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> </span><span class="gmail-com" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(133,140,147)"># il</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">
plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">text</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(-</span><span class="gmail-lit" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">4</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> </span><span class="gmail-lit" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">0.6</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> </span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$t_0=%.2f$'</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> </span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">%</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> t0</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> bbox</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">=</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">dict</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">fc</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">=</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'white'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">))</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> </span><span class="gmail-com" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(133,140,147)"># il</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">

plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">plot</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">t</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> convolution</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">,</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> label</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">=</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$(f_1*f_2)(t)$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">)</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">

</span><span class="gmail-com" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(133,140,147)"># recalculate the value of the convolution integral at the current time-shift t0</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">
plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">grid</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-kwd" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(16,16,148)">True</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">);</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">xlabel</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$t$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">);</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> plt</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">.</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">ylabel</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">(</span><span class="gmail-str" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(125,39,39)">'$(f_1*f_2)(t)$'</span><span class="gmail-pun" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">)</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)"> </span><span class="gmail-com" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(133,140,147)"># il</span><span class="gmail-pln" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;box-sizing:inherit;color:rgb(48,51,54)">