User:Caswto - Revision history

Caswto: /* How a CD Player Works */

2004-12-08T18:09:51Z

How a CD Player Works

2004-12-07T03:18:54Z

← Older revision		Revision as of 20:18, 6 December 2004
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			=== How a CD Player Works ===


			[[Image:CDplayerdiagram.jpg\|Description]]



			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:


			<center>
			[[Image:DAOutput.jpg\|Description]]

			<math>
			\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
			</math>
			</center>


			Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.


			<center>
			[[Image:DAfreqout.jpg\|Description]]


			<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
			</center>
			where
			<center>
			<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
			</math>
			</center>

			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.

			Contributing Authors:

			[[User:caswto\|Todd Caswell]]

			[[User:goeari\|Aric Goe]]

2004-09-30T19:29:33Z

← Older revision		Revision as of 12:29, 30 September 2004
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	[[Image:~~K:\CLASS\Engr\455\2004\Photos\~~P1010004.JPG\|thumb\|9-27-2004]] <br>		[[Image:P1010004.JPG\|thumb\|9-27-2004]] <br>
	<br>		<br>
	Todd Caswell <br>		Todd Caswell <br>
	509-374-2820		509-374-2820
	</center>		</center>

2004-09-30T19:29:06Z

← Older revision		Revision as of 12:29, 30 September 2004
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	[[Image:P1010004.~~jpg~~\|thumb\|9-27-2004]] <br>		[[Image:K:\CLASS\Engr\455\2004\Photos\P1010004.JPG\|thumb\|9-27-2004]] <br>
	<br>		<br>
	Todd Caswell <br>		Todd Caswell <br>
	509-374-2820		509-374-2820
	</center>		</center>

2004-09-30T19:27:40Z

2004-09-30T19:24:18Z

← Older revision		Revision as of 12:24, 30 September 2004
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	<center>		<center>
	[[Image:P1010004.jpg\|thumb\|~~Description~~]] <br>		[[Image:P1010004.jpg\|thumb\|9-27-2004]] <br>
	Todd Caswell <br>		Todd Caswell <br>
	509-374-2820		509-374-2820
	</center>		</center>

2004-09-30T19:11:23Z

← Older revision		Revision as of 12:11, 30 September 2004
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	<center>		<center>
	Image:P1010004.~~JPG~~ <br>		[[Image:P1010004.jpg\|thumb\|Description]] <br>
	Todd Caswell <br>		Todd Caswell <br>
	509-374-2820		509-374-2820
	</center>		</center>

2004-09-30T19:02:56Z

2004-09-30T19:00:19Z

2004-09-27T17:28:45Z