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2026-04-06T12:57:03Z
User contributions
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https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=3779
User:Caswto
2004-12-08T18:09:51Z
<p>Caswto: /* How a CD Player Works */</p>
<hr />
<div><center><br />
[[Image:P1010004.JPG|thumb|9-27-2004]] <br><br />
<br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center><br />
<br />
<br />
<br />
----<br />
=== How a CD Player Works ===<br />
<br />
<br />
[[Image:CDplayerdiagram.jpg|Description]]<br />
<br />
<br />
<br />
First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:<br />
<br />
<br />
<center><br />
[[Image:DAOutput.jpg|Description]]<br />
<br />
<math><br />
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT) <br />
</math><br />
</center><br />
<br />
<br />
Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.<br />
<br />
<br />
<center><br />
[[Image:DAfreqout.jpg|Description]] <br />
<br />
<br />
<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math><br />
</center><br />
where <br />
<center><br />
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)<br />
</math><br />
</center><br />
<br />
The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.<br />
<br />
Contributing Authors:<br />
<br />
[[User:caswto|Todd Caswell]]<br />
<br />
[[User:goeari|Aric Goe]]</div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=177
User:Caswto
2004-12-07T03:18:54Z
<p>Caswto: </p>
<hr />
<div><center><br />
[[Image:P1010004.JPG|thumb|9-27-2004]] <br><br />
<br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center><br />
<br />
<br />
<br />
=== How a CD Player Works ===<br />
<br />
<br />
[[Image:CDplayerdiagram.jpg|Description]]<br />
<br />
<br />
<br />
First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:<br />
<br />
<br />
<center><br />
[[Image:DAOutput.jpg|Description]]<br />
<br />
<math><br />
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT) <br />
</math><br />
</center><br />
<br />
<br />
Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.<br />
<br />
<br />
<center><br />
[[Image:DAfreqout.jpg|Description]] <br />
<br />
<br />
<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math><br />
</center><br />
where <br />
<center><br />
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)<br />
</math><br />
</center><br />
<br />
The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.<br />
<br />
Contributing Authors:<br />
<br />
[[User:caswto|Todd Caswell]]<br />
<br />
[[User:goeari|Aric Goe]]</div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=165
User:Caswto
2004-09-30T19:29:33Z
<p>Caswto: </p>
<hr />
<div><center><br />
[[Image:P1010004.JPG|thumb|9-27-2004]] <br><br />
<br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=119
User:Caswto
2004-09-30T19:29:06Z
<p>Caswto: </p>
<hr />
<div><center><br />
[[Image:K:\CLASS\Engr\455\2004\Photos\P1010004.JPG|thumb|9-27-2004]] <br><br />
<br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=118
User:Caswto
2004-09-30T19:27:40Z
<p>Caswto: </p>
<hr />
<div><center><br />
[[Image:P1010004.jpg|thumb|9-27-2004]] <br><br />
<br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=117
User:Caswto
2004-09-30T19:24:18Z
<p>Caswto: </p>
<hr />
<div><center><br />
[[Image:P1010004.jpg|thumb|9-27-2004]] <br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=116
User:Caswto
2004-09-30T19:11:23Z
<p>Caswto: </p>
<hr />
<div><center><br />
[[Image:P1010004.jpg|thumb|Description]] <br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=File:P1010004a.jpg&diff=3795
File:P1010004a.jpg
2004-09-30T19:10:14Z
<p>Caswto: </p>
<hr />
<div></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=115
User:Caswto
2004-09-30T19:02:56Z
<p>Caswto: </p>
<hr />
<div><center><br />
Image:P1010004.JPG <br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=114
User:Caswto
2004-09-30T19:00:19Z
<p>Caswto: </p>
<hr />
<div><center><br />
[[Image:file.jpg]]<br><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=File:P1010004.JPG&diff=3794
File:P1010004.JPG
2004-09-29T17:15:58Z
<p>Caswto: </p>
<hr />
<div></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=113
User:Caswto
2004-09-27T17:28:45Z
<p>Caswto: </p>
<hr />
<div><center><br />
Todd Caswell <br><br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=98
User:Caswto
2004-09-27T17:26:44Z
<p>Caswto: /* 509-374-2820 */</p>
<hr />
<div><center><br />
<center><br />
Todd Caswell<br />
509-374-2820<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=97
User:Caswto
2004-09-27T17:25:32Z
<p>Caswto: /* Todd Caswell */</p>
<hr />
<div><center><br />
<center><br />
Todd Caswell<br />
509-374-2820<br />
</center><br />
<br />
====509-374-2820====<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=96
User:Caswto
2004-09-27T17:20:08Z
<p>Caswto: /* 509-374-2820 */</p>
<hr />
<div><center><br />
====Todd Caswell====<br />
</center><br />
<br />
<center><br />
====509-374-2820====<br />
</center></div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=95
User:Caswto
2004-09-27T17:19:35Z
<p>Caswto: /* Todd Caswell */</p>
<hr />
<div><center><br />
====Todd Caswell====<br />
</center><br />
<br />
====509-374-2820====</div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=94
User:Caswto
2004-09-27T17:17:42Z
<p>Caswto: /* This is a test */</p>
<hr />
<div>====Todd Caswell====<br />
====509-374-2820====</div>
Caswto
https://fweb.wallawalla.edu/class-wiki/index.php?title=User:Caswto&diff=93
User:Caswto
2004-09-27T17:14:08Z
<p>Caswto: </p>
<hr />
<div>===This is a test===</div>
Caswto