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	<id>https://en.formulasearchengine.com/index.php?action=history&amp;feed=atom&amp;title=Window_function</id>
	<title>Window function - Revision history</title>
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	<updated>2026-04-06T02:12:01Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.43.0-wmf.28</generator>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=226907&amp;oldid=prev</id>
		<title>en&gt;Bgwhite: WP:CHECKWIKI error fix #26. Convert HTML to wikicode. Do general fixes and cleanup if needed. - using AWB (10514)</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=226907&amp;oldid=prev"/>
		<updated>2014-12-15T08:09:20Z</updated>

		<summary type="html">&lt;p&gt;&lt;a href=&quot;/index.php?title=WP:CHECKWIKI&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:CHECKWIKI (page does not exist)&quot;&gt;WP:CHECKWIKI&lt;/a&gt; error fix #26. Convert HTML to wikicode. Do &lt;a href=&quot;https://en.wikipedia.org/wiki/GENFIXES&quot; class=&quot;extiw&quot; title=&quot;wikipedia:GENFIXES&quot;&gt;general fixes&lt;/a&gt; and cleanup if needed. - using &lt;a href=&quot;/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt; (10514)&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 10:09, 15 December 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Nice to satisfy you, my title &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Jerald Stella and I &lt;/del&gt;really &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;feel comfortable when people use the full name&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;My   [http://warrenmooretgqn.newsvine.com/_news/2014/08/06/25191930-up-in-arms-about-online-spilleautomater-for-mac-maskiner spille automater]   [http://victoacevedo.buzznet.com/user/journal/18527200/warning-signs-de-beste-norske/ de beste norske spilleautomater] husband   [https://www.rebelmouse.com/chrismahmood/fall-in-love-with-spilleautoma-669535048.html spilleautomater norske] &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I chose to reside in District of Columbia. What   [http://journals&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fotki.com/dieterswanson/dieterswanson/entry/stksqwtrddwqs/ Vi tilbyr de beste spilleautomater du kan spilleet] I adore   [http://www.kiwibox.com/majorcollazo/blog/entry/117084429/norske-automater-may-not-exist/?pPage=0 spilleautomater] performing &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;driving &lt;/del&gt;but &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I can&lt;/del&gt;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;t make it my [http://www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;alexa.com/search?q=profession&amp;amp;r=topsites_index&amp;amp;p=bigtop profession] truly.   [http&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//journals.fotki.com/dieterswanson/dieterswanson/entry/stfqtgksfsfrg/ automater på nett] The job   [&lt;/del&gt;http://&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;www.purevolume&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/shennaharley/posts/6907353/Finding+The+Best+Vi+Tilbyr+De+Beste+Spilleautomater+Du+Kan+Spilleet Vi tilbyr de beste norske spilleautomater du kan spille på nettet] I&#039;ve been occupying for many years is a database administrator. I&#039;m not great at webdesign but you may want to check my website: http://warrenmooretgqn.newsvine.com/_news/2014/08/01/25113558-what-the-pentagon-can-teach-you-about-spill-sikkert-hos-spilleautomaterpnettco&lt;/del&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Selected of the author is Gabrielle Lattimer. Fish keeping &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;something her brother doesn&#039;t &lt;/ins&gt;really &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;like but she does&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Idaho is where her home is going to be &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;she will usually never move&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Software developing &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;what she totally does &lt;/ins&gt;but &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;she&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s always longed her own business&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;She has become running and maintaining the best blog here&lt;/ins&gt;: http://&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;prometeu&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;net&lt;/ins&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Take a look at &lt;/ins&gt;my &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;blog&lt;/ins&gt;: [http://&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;prometeu&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;net clash of clans hack no survey&lt;/ins&gt;]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Feel free to   [https://www.rebelmouse.com/shermanwalls/best-nine-tips-for-orgesspill-648799609.html on the internet spilleautomater] visit &lt;/del&gt;my &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;web page :&lt;/del&gt;: [http://&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;warrenmooretgqn&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;newsvine.com/_news/2014/08/01/25113558-what-the-pentagon-can-teach-you-about-spill-sikkert-hos-spilleautomaterpnettco Her kan du prøve deg på spilleautomater på nettet&lt;/del&gt;]&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Bgwhite</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=226906&amp;oldid=prev</id>
		<title>en&gt;Glrx: rvt C++ code; out of place here; this article is not a how-to and is not a discussion about algorithms that compute filter coeffs</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=226906&amp;oldid=prev"/>
		<updated>2014-03-02T22:27:26Z</updated>

		<summary type="html">&lt;p&gt;rvt C++ code; out of place here; this article is not a how-to and is not a discussion about algorithms that compute filter coeffs&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 00:27, 3 March 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Unreferenced|date=January 2008}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Nice to satisfy you&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;my title &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Jerald Stella and I really feel comfortable when people use the full name. My   &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://warrenmooretgqn.newsvine.com/_news/2014/08/06/25191930-up-in-arms-about-online-spilleautomater-for-mac-maskiner spille automater]   &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://victoacevedo.buzznet.com/user/journal/18527200/warning-signs-de-beste-norske/ de beste norske spilleautomater&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;husband   [https://www.rebelmouse.com/chrismahmood/fall-in-love-with-spilleautoma-669535048.html spilleautomater norske&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and I chose to reside in District of Columbia. What   &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://journals.fotki.com/dieterswanson/dieterswanson/entry/stksqwtrddwqs/ Vi tilbyr de beste spilleautomater du kan spilleet] I adore   &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www.kiwibox.com/majorcollazo/blog/entry/117084429/norske-automater-may-not-exist/?pPage=0 spilleautomater&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;performing &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;driving but I can&#039;t make it my &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www.alexa.com/search?q=profession&amp;amp;r=topsites_index&amp;amp;p=bigtop profession] truly.   &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://journals.fotki.com/dieterswanson/dieterswanson/entry/stfqtgksfsfrg/ automater på nett&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The job   [http://www.purevolume.com/shennaharley/posts/6907353/Finding+The+Best+Vi+Tilbyr+De+Beste+Spilleautomater+Du+Kan+Spilleet Vi tilbyr de beste norske spilleautomater du kan spille på nettet&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I&#039;ve been occupying for many years is &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;database administrator. I&#039;m not great at webdesign but you may want to check my website: http://warrenmooretgqn.newsvine&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/_news/2014/08/01/25113558-what-the-pentagon-can-teach-you-about-spill-sikkert-hos-spilleautomaterpnettco&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In [[geometry]], an &#039;&#039;&#039;improper rotation&#039;&#039;&#039;&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;also called &#039;&#039;&#039;rotoreflection&#039;&#039;&#039; or &#039;&#039;&#039;rotary reflection&#039;&#039;&#039; &lt;/del&gt;is&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, depending on context, a &lt;/del&gt;[[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;linear transformation&lt;/del&gt;]] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;or &lt;/del&gt;[[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;affine transformation&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;] which &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the combination of a &lt;/del&gt;[[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Rotation (geometry)|rotation&lt;/del&gt;]] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;about an axis and &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reflection in a plane&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In 3D, equivalently it is the combination of a rotation and an &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[inversion in a point]] on the axis&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Therefore it is also called a &#039;&#039;&#039;rotoinversion&#039;&#039;&#039; or &#039;&#039;&#039;rotary inversion&#039;&#039;&#039;&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Feel free to   &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;https://www&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;rebelmouse&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/shermanwalls/best-nine-tips-for-orgesspill-648799609&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;html on &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;internet spilleautomater&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;visit my web page :: &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://warrenmooretgqn&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;newsvine&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;_news&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2014&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;08&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;01&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;25113558-what-&lt;/ins&gt;the&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-pentagon-&lt;/ins&gt;can&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-teach-you-about-spill-sikkert-hos-spilleautomaterpnettco Her kan du prøve deg på spilleautomater på nettet&lt;/ins&gt;]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In both cases the operations commute&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Rotoreflection and rotoinversion  are &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;same if they differ in [[angle of rotation&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;] by 180°, and the point of inversion is in the plane of reflection.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;An improper rotation of an object thus produces a rotation of its &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[mirror image]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The axis is called the &#039;&#039;&#039;rotation-reflection axis&#039;&#039;&#039;&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This is called an &#039;&#039;&#039;&#039;&#039;n&#039;&#039;-fold improper rotation&#039;&#039;&#039; if the angle of rotation is 360°&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;n&#039;&#039;. The notation &#039;&#039;&#039;&#039;&#039;S&amp;lt;sub&amp;gt;n&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sub&amp;gt;&#039;&#039;&#039;&#039;&#039; (&#039;&#039;S&#039;&#039; for &#039;&#039;Spiegel&#039;&#039;, German for [[mirror]]) denotes the symmetry group generated by an &#039;&#039;n&#039;&#039;-fold improper rotation (not to be confused with the same notation for [[symmetric group]]s). The notation &amp;lt;math&amp;gt;\bar{n}&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; is used for &#039;&#039;&#039;&#039;&#039;n&#039;&#039;-fold rotoinversion&#039;&#039;&#039;, i.e. rotation by an angle of rotation of 360°&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;n&#039;&#039; with inversion. &lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In a wider sense, an &quot;improper rotation&quot; may be defined as any &#039;&#039;&#039;[[Euclidean group#Direct and indirect isometries|indirect isometry]]&#039;&#039;&#039;, i.e., an element of &#039;&#039;E&#039;&#039;(3)\&#039;&#039;E&#039;&#039;&amp;lt;sup&amp;gt;+&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sup&amp;gt;(3) (see [[Euclidean group]]): thus it can also be a pure reflection in a plane, or have a [[glide reflection|glide plane]]. An indirect isometry is an [[affine transformation]] with an [[orthogonal matrix]] that has a determinant of −1.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A &#039;&#039;&#039;proper rotation&#039;&#039;&#039; is an ordinary rotation. In &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;wider sense, a &quot;proper rotation&quot; is defined as a &#039;&#039;&#039;direct isometry&#039;&#039;&#039;, i.e., an element of &#039;&#039;E&#039;&#039;&amp;lt;sup&amp;gt;+&amp;lt;/sup&amp;gt;(3): it &lt;/del&gt;can &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;also be the identity, a rotation with a translation along the axis, or a pure translation. A direct isometry is an affine transformation with an orthogonal matrix that has a determinant of 1.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In either the narrower or the wider senses, the composition of two improper rotations is a proper rotation, and the composition of an improper and a proper rotation is an improper rotation.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;When studying the symmetry of a physical system under an improper rotation (e.g., if a system has a mirror symmetry plane), it is important to distinguish between [[vector (geometry)|vector]]s and [[pseudovector]]s (as well as [[scalar (mathematics)|scalars]] and [[pseudoscalar (mathematics)|pseudoscalar]]s, and in general; between [[tensor]]s and [[pseudotensor]]s), since the latter transform differently under proper and improper rotations (in 3 dimensions, pseudovectors are invariant under inversion).&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==See also==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;*[[Isometry]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;*[[Orthogonal group]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Euclidean symmetries]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Lie groups]&lt;/del&gt;]&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Glrx</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=3327&amp;oldid=prev</id>
		<title>en&gt;Aquegg: /* Ultraspherical window */ avoid potential confusion with imaginary i</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=3327&amp;oldid=prev"/>
		<updated>2014-02-03T08:30:12Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Ultraspherical window: &lt;/span&gt; avoid potential confusion with imaginary i&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Window_function&amp;amp;diff=3327&amp;amp;oldid=226905&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>en&gt;Aquegg</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=226905&amp;oldid=prev</id>
		<title>en&gt;Bob K: Undid revision 508438088 by 14.139.241.194 (talk)</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Window_function&amp;diff=226905&amp;oldid=prev"/>
		<updated>2012-08-21T12:28:54Z</updated>

		<summary type="html">&lt;p&gt;Undid revision 508438088 by &lt;a href=&quot;/wiki/Special:Contributions/14.139.241.194&quot; title=&quot;Special:Contributions/14.139.241.194&quot;&gt;14.139.241.194&lt;/a&gt; (&lt;a href=&quot;/index.php?title=User_talk:14.139.241.194&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;User talk:14.139.241.194 (page does not exist)&quot;&gt;talk&lt;/a&gt;)&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Window_function&amp;amp;diff=226905&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>en&gt;Bob K</name></author>
	</entry>
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