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  <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Application of Interpolation - Oversampling in CD Players</name>
  <metadata xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
  <md:version xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2.3</md:version>
  <md:created xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2003/01/15</md:created>
  <md:revised xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2005/09/16 15:09:10.770 GMT-5</md:revised>
  <md:authorlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
      <md:author xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="schniter">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Phil</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Schniter</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">schniter@ee.eng.ohio-state.edu</md:email>
    </md:author>
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    <md:maintainer xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="jago">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Adan</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Galvan</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">jago@rice.edu</md:email>
    </md:maintainer>
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  <md:keywordlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">cd players</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">interpolation</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">oversampling</md:keyword>
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  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/"/>
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  <content xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    
    <section xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="sec2">
      <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Application of Interpolation- Oversampling in CD Players</name>

      <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para3">
	The digital audio signal on a CD is a
	<m:math>
	  <m:apply>
	    <m:times/>
	    <m:cn>44.1</m:cn>
	    <m:ci>kHz</m:ci>
	  </m:apply>
	</m:math> sampled representation of a continuous signal
	with bandwidth
	<m:math>
	  <m:apply>
	    <m:times/>
	    <m:cn>20</m:cn>
	    <m:ci>kHz</m:ci>
	  </m:apply>
	</m:math>. With a standard ZOH-DAC, the analog reconstruction
	filter would have passband edge at
	<m:math>
	  <m:apply>
	    <m:times/>
	    <m:cn>20</m:cn>
	    <m:ci>kHz</m:ci>
	  </m:apply>
	</m:math> and stopband edge at
	<m:math>
	  <m:apply>
	    <m:times/>
	    <m:cn>24.1</m:cn>
	    <m:ci>kHz</m:ci>
	  </m:apply>
	</m:math>.  (See <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig3" strength="9"/>)  With
	such a narrow transition band, this would be a difficult (and
	expensive) filter to build.
      </para>

      <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="fig3">
	<media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="m10444fig3.png"/>
      </figure>

      <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para4">
	If digital interpolation is used prior to reconstruction, the
	effective sampling rate can be increased and the
	reconstruction filter's transition band can be made much
	wider, resulting in a much simpler (and cheaper) analog
	filter. <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig4" strength="9"/> illustrates the
	case of interpolation by <m:math><m:cn>4</m:cn></m:math>.  The
	reconstruction filter has passband edge at
	<m:math>
	  <m:apply>
	    <m:times/>
	    <m:cn>20</m:cn>
	    <m:ci>kHz</m:ci>
	  </m:apply>
	</m:math> and stopband edge at
	<m:math>
	  <m:apply>
	    <m:times/>
	    <m:cn>156.4</m:cn>
	    <m:ci>kHz</m:ci>
	  </m:apply>
	</m:math>, resulting in a much
	wider transition band and therefore an easier filter design.
      </para>

      <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="fig4">
	<media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="m10444fig4.png"/>
      </figure>


    </section>
  </content>
  
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