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	<title>Comments on: Aliasing and the discrete-time Fourier transform</title>
	<atom:link href="http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/feed/" rel="self" type="application/rss+xml" />
	<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/</link>
	<description>Steve Eddins manages the Image &#38; Geospatial development team at The MathWorks and coauthored Digital Image Processing Using MATLAB. He writes here about image processing concepts, algorithm implementations, and MATLAB.</description>
	<lastBuildDate>Wed, 22 May 2013 10:54:29 +0000</lastBuildDate>
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	<item>
		<title>By: Steve</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-24387</link>
		<dc:creator>Steve</dc:creator>
		<pubDate>Mon, 08 Aug 2011 19:33:40 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-24387</guid>
		<description><![CDATA[Søren&#8212;Thanks, I fixed it.]]></description>
		<content:encoded><![CDATA[<p>Søren&mdash;Thanks, I fixed it.</p>
]]></content:encoded>
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	<item>
		<title>By: Mewada hiren</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-24385</link>
		<dc:creator>Mewada hiren</dc:creator>
		<pubDate>Mon, 08 Aug 2011 09:25:07 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-24385</guid>
		<description><![CDATA[Hello Sir,

How can i get the freq plot for 2-D signal i.e. image as we are not knowing that what is max freq component in image.]]></description>
		<content:encoded><![CDATA[<p>Hello Sir,</p>
<p>How can i get the freq plot for 2-D signal i.e. image as we are not knowing that what is max freq component in image.</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Søren</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-24377</link>
		<dc:creator>Søren</dc:creator>
		<pubDate>Mon, 01 Aug 2011 02:56:34 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-24377</guid>
		<description><![CDATA[It looks like this post was not tagged &quot;Fourier Transforms&quot;, so it doesn&#039;t show up on http://blogs.mathworks.com/steve/category/fourier-transforms/.]]></description>
		<content:encoded><![CDATA[<p>It looks like this post was not tagged &#8220;Fourier Transforms&#8221;, so it doesn&#8217;t show up on <a href="http://blogs.mathworks.com/steve/category/fourier-transforms/" rel="nofollow">http://blogs.mathworks.com/steve/category/fourier-transforms/</a>.</p>
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	</item>
	<item>
		<title>By: Steve</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23868</link>
		<dc:creator>Steve</dc:creator>
		<pubDate>Mon, 24 Jan 2011 15:26:19 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23868</guid>
		<description><![CDATA[Matteo&#8212;Thanks for the link.]]></description>
		<content:encoded><![CDATA[<p>Matteo&mdash;Thanks for the link.</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Matteo</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23867</link>
		<dc:creator>Matteo</dc:creator>
		<pubDate>Mon, 24 Jan 2011 15:12:28 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23867</guid>
		<description><![CDATA[Steve, an excellent, enjoyable, easy to read paper from the seismic folks:
Aliasing for the layperson
http://www.cseg.ca/publications/recorder/2001/04apr/apr01-aliasing.pdf

Cheers
Matteo]]></description>
		<content:encoded><![CDATA[<p>Steve, an excellent, enjoyable, easy to read paper from the seismic folks:<br />
Aliasing for the layperson<br />
<a href="http://www.cseg.ca/publications/recorder/2001/04apr/apr01-aliasing.pdf" rel="nofollow">http://www.cseg.ca/publications/recorder/2001/04apr/apr01-aliasing.pdf</a></p>
<p>Cheers<br />
Matteo</p>
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		<title>By: Steve</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23700</link>
		<dc:creator>Steve</dc:creator>
		<pubDate>Thu, 11 Nov 2010 13:55:40 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23700</guid>
		<description><![CDATA[Anand&#8212;You should only plot to 50 Hz (half the sampling frequency). In your second plot, the 90 Hz signal has been aliased to 10 Hz.

I&#039;d also like to suggest some simplifications to your code. You don&#039;t need those loops to create your signals x1 and x2.

&lt;pre class=&quot;code&quot;&gt;
n = 0:49;
x1 = 10*sin(2*pi*n*f1/F1);
x2 = 10*sin(2*pi*n*f2/F1);
&lt;/pre&gt;

Also, I suggest that you not use &quot;clear all&quot;. If you want to clear your base workspace variables, just use &quot;clear&quot;.
]]></description>
		<content:encoded><![CDATA[<p>Anand&mdash;You should only plot to 50 Hz (half the sampling frequency). In your second plot, the 90 Hz signal has been aliased to 10 Hz.</p>
<p>I&#8217;d also like to suggest some simplifications to your code. You don&#8217;t need those loops to create your signals x1 and x2.</p>
<pre class="code">
n = 0:49;
x1 = 10*sin(2*pi*n*f1/F1);
x2 = 10*sin(2*pi*n*f2/F1);
</pre>
<p>Also, I suggest that you not use &#8220;clear all&#8221;. If you want to clear your base workspace variables, just use &#8220;clear&#8221;.</p>
]]></content:encoded>
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	<item>
		<title>By: Anand</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23699</link>
		<dc:creator>Anand</dc:creator>
		<pubDate>Thu, 11 Nov 2010 05:53:58 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-23699</guid>
		<description><![CDATA[how should i see the aliasing effect??
with my code i cant see overlapping of spectrums??
code:
&lt;pre class=&quot;code&quot;&gt;
clear all;
f1=10;F1=100;f2=90;F2=100;
for n=1:50,
    x1(n)=10*sin(2*pi*n*f1/F1);
    fr1(n)=n/25*F1/2;
end
y1=fft(x1,50);
plot(fr1,abs(y1));
xlabel(&#039;frequency in Hz&#039;);
ylabel(&#039;Amplitude&#039;);
figure;
for n=1:50,
    x2(n)=10*sin(2*pi*n*f2/F1);
    fr2(n)=n/25*F1/2;
end
y2=fft(x2,50);
plot(fr2,abs(y2));
xlabel(&#039;frequency in Hz&#039;);
&lt;/pre&gt;]]></description>
		<content:encoded><![CDATA[<p>how should i see the aliasing effect??<br />
with my code i cant see overlapping of spectrums??<br />
code:</p>
<pre class="code">
clear all;
f1=10;F1=100;f2=90;F2=100;
for n=1:50,
    x1(n)=10*sin(2*pi*n*f1/F1);
    fr1(n)=n/25*F1/2;
end
y1=fft(x1,50);
plot(fr1,abs(y1));
xlabel('frequency in Hz');
ylabel('Amplitude');
figure;
for n=1:50,
    x2(n)=10*sin(2*pi*n*f2/F1);
    fr2(n)=n/25*F1/2;
end
y2=fft(x2,50);
plot(fr2,abs(y2));
xlabel('frequency in Hz');
</pre>
]]></content:encoded>
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	<item>
		<title>By: Chandrakanth R. Terupally</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-22793</link>
		<dc:creator>Chandrakanth R. Terupally</dc:creator>
		<pubDate>Wed, 03 Mar 2010 18:13:17 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-22793</guid>
		<description><![CDATA[Dave,

Its actually simple to relate what you have learnt with that Steve blogged. Here it is how: the two frequencies were 1 and 2pi-1 which is 1 &amp; 5.28 rad/s. Now remember what sampling theorem says  - that freq of sampling Fs must be at least twice that of the highest frequency in the signal, right? Steve&#039;s example didn&#039;t honour sampling theorem as Fs was only 1 rad/s (T=1) and hence ended up with aliasing effect.]]></description>
		<content:encoded><![CDATA[<p>Dave,</p>
<p>Its actually simple to relate what you have learnt with that Steve blogged. Here it is how: the two frequencies were 1 and 2pi-1 which is 1 &amp; 5.28 rad/s. Now remember what sampling theorem says  &#8211; that freq of sampling Fs must be at least twice that of the highest frequency in the signal, right? Steve&#8217;s example didn&#8217;t honour sampling theorem as Fs was only 1 rad/s (T=1) and hence ended up with aliasing effect.</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Steve</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-22766</link>
		<dc:creator>Steve</dc:creator>
		<pubDate>Thu, 25 Feb 2010 12:20:07 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-22766</guid>
		<description><![CDATA[Dave&#8212;Very good question.  Yes, I will explain that in another blog post.]]></description>
		<content:encoded><![CDATA[<p>Dave&mdash;Very good question.  Yes, I will explain that in another blog post.</p>
]]></content:encoded>
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	<item>
		<title>By: Dave S.</title>
		<link>http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-22765</link>
		<dc:creator>Dave S.</dc:creator>
		<pubDate>Thu, 25 Feb 2010 09:15:12 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.mathworks.com/steve/2010/02/22/aliasing-and-the-discrete-time-fourier-transform/#comment-22765</guid>
		<description><![CDATA[Hi Steve,

First let me say I really appreciate and enjoy you explaining the Fourier transforms, wish they would have taught us this in Math in such a detail.

I&#039;m at a loss with the way you described the alaising problem. I have come to know it as a problem, which occurs when the sampling rate of your discreet signal is not at least twice the amount of the highest exisiting frequency. But I can&#039;t see how this fits in with the alaising you discribed above. Would you be so kind and explain that alaising thing next time you got time?

Greetings from Germany]]></description>
		<content:encoded><![CDATA[<p>Hi Steve,</p>
<p>First let me say I really appreciate and enjoy you explaining the Fourier transforms, wish they would have taught us this in Math in such a detail.</p>
<p>I&#8217;m at a loss with the way you described the alaising problem. I have come to know it as a problem, which occurs when the sampling rate of your discreet signal is not at least twice the amount of the highest exisiting frequency. But I can&#8217;t see how this fits in with the alaising you discribed above. Would you be so kind and explain that alaising thing next time you got time?</p>
<p>Greetings from Germany</p>
]]></content:encoded>
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