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	<id>https://fweb.wallawalla.edu/class-wiki/index.php?action=history&amp;feed=atom&amp;title=Hw13</id>
	<title>Hw13 - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://fweb.wallawalla.edu/class-wiki/index.php?action=history&amp;feed=atom&amp;title=Hw13"/>
	<link rel="alternate" type="text/html" href="https://fweb.wallawalla.edu/class-wiki/index.php?title=Hw13&amp;action=history"/>
	<updated>2026-05-18T11:12:52Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.43.0</generator>
	<entry>
		<id>https://fweb.wallawalla.edu/class-wiki/index.php?title=Hw13&amp;diff=10174&amp;oldid=prev</id>
		<title>Victor.shepherd at 20:53, 16 December 2010</title>
		<link rel="alternate" type="text/html" href="https://fweb.wallawalla.edu/class-wiki/index.php?title=Hw13&amp;diff=10174&amp;oldid=prev"/>
		<updated>2010-12-16T20:53:39Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&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 13:53, 16 December 2010&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-l3&quot;&gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&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;div&gt;**b)      &amp;lt;math&amp;gt; DFT(e^{j2 \pi lk/N}x(k)\!&amp;lt;/math&amp;gt;&lt;/div&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;div&gt;**b)      &amp;lt;math&amp;gt; DFT(e^{j2 \pi lk/N}x(k)\!&amp;lt;/math&amp;gt;&lt;/div&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;div&gt;**c)      &amp;lt;math&amp;gt;\sum\limits_{k=0}^{N-1} x(k)y(k)^{*}=c\sum\limits_{k=0}^{N-1} X(n)Y(n)^{*}&amp;lt;/math&amp;gt;&lt;/div&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;div&gt;**c)      &amp;lt;math&amp;gt;\sum\limits_{k=0}^{N-1} x(k)y(k)^{*}=c\sum\limits_{k=0}^{N-1} X(n)Y(n)^{*}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&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;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&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;[[image:P1010216.JPG ]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Victor.shepherd</name></author>
	</entry>
	<entry>
		<id>https://fweb.wallawalla.edu/class-wiki/index.php?title=Hw13&amp;diff=10165&amp;oldid=prev</id>
		<title>Victor.shepherd at 01:56, 16 December 2010</title>
		<link rel="alternate" type="text/html" href="https://fweb.wallawalla.edu/class-wiki/index.php?title=Hw13&amp;diff=10165&amp;oldid=prev"/>
		<updated>2010-12-16T01:56:58Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&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 18:56, 15 December 2010&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;===* &lt;/del&gt;HW #13 - Derive the following realtions:&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;HW #13 - Derive the following realtions:&lt;/div&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;div&gt;**a)      &amp;lt;math&amp;gt;DFT(x(k-l))\!&amp;lt;/math&amp;gt;&lt;/div&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;div&gt;**a)      &amp;lt;math&amp;gt;DFT(x(k-l))\!&amp;lt;/math&amp;gt;&lt;/div&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;div&gt;**b)      &amp;lt;math&amp;gt; DFT(e^{j2 \pi lk/N}x(k)\!&amp;lt;/math&amp;gt;&lt;/div&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;div&gt;**b)      &amp;lt;math&amp;gt; DFT(e^{j2 \pi lk/N}x(k)\!&amp;lt;/math&amp;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;**c)      &amp;lt;math&amp;gt;\sum\limits_{k=0}^{N-1} x(k)y(k)^{*}=c\sum\limits_{k=0}^{N-1} X(n)Y(n)^{*}&amp;lt;/math&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;===&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;**c)      &amp;lt;math&amp;gt;\sum\limits_{k=0}^{N-1} x(k)y(k)^{*}=c\sum\limits_{k=0}^{N-1} X(n)Y(n)^{*}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Victor.shepherd</name></author>
	</entry>
	<entry>
		<id>https://fweb.wallawalla.edu/class-wiki/index.php?title=Hw13&amp;diff=10164&amp;oldid=prev</id>
		<title>Victor.shepherd: Created page with &#039;===* HW #13 - Derive the following realtions: **a)      &lt;math&gt;DFT(x(k-l))\!&lt;/math&gt; **b)      &lt;math&gt; DFT(e^{j2 \pi lk/N}x(k)\!&lt;/math&gt; **c)      &lt;math&gt;\sum\limits_{k=0}^{N-1} x(k)y…&#039;</title>
		<link rel="alternate" type="text/html" href="https://fweb.wallawalla.edu/class-wiki/index.php?title=Hw13&amp;diff=10164&amp;oldid=prev"/>
		<updated>2010-12-16T01:56:23Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;#039;===* HW #13 - Derive the following realtions: **a)      &amp;lt;math&amp;gt;DFT(x(k-l))\!&amp;lt;/math&amp;gt; **b)      &amp;lt;math&amp;gt; DFT(e^{j2 \pi lk/N}x(k)\!&amp;lt;/math&amp;gt; **c)      &amp;lt;math&amp;gt;\sum\limits_{k=0}^{N-1} x(k)y…&amp;#039;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;===* HW #13 - Derive the following realtions:&lt;br /&gt;
**a)      &amp;lt;math&amp;gt;DFT(x(k-l))\!&amp;lt;/math&amp;gt;&lt;br /&gt;
**b)      &amp;lt;math&amp;gt; DFT(e^{j2 \pi lk/N}x(k)\!&amp;lt;/math&amp;gt;&lt;br /&gt;
**c)      &amp;lt;math&amp;gt;\sum\limits_{k=0}^{N-1} x(k)y(k)^{*}=c\sum\limits_{k=0}^{N-1} X(n)Y(n)^{*}&amp;lt;/math&amp;gt;===&lt;/div&gt;</summary>
		<author><name>Victor.shepherd</name></author>
	</entry>
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