<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" 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="new1">
  <name>Application of Interpolation - Oversampling in CD Players</name>
  <metadata>
  <md:version>2.3</md:version>
  <md:created>2003/01/15</md:created>
  <md:revised>2005/09/16 15:09:10.770 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="schniter">
      <md:firstname>Phil</md:firstname>
      
      <md:surname>Schniter</md:surname>
      <md:email>schniter@ee.eng.ohio-state.edu</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="jago">
      <md:firstname>Adan</md:firstname>
      
      <md:surname>Galvan</md:surname>
      <md:email>jago@rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>cd players</md:keyword>
    <md:keyword>interpolation</md:keyword>
    <md:keyword>oversampling</md:keyword>
  </md:keywordlist>

  <md:abstract/>
</metadata>


  <content>
    
    <section id="sec2">
      <name>Application of Interpolation- Oversampling in CD Players</name>

      <para 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 target="fig3" strength="9"/>)  With
	such a narrow transition band, this would be a difficult (and
	expensive) filter to build.
      </para>

      <figure id="fig3">
	<media type="image/png" src="m10444fig3.png"/>
      </figure>

      <para 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 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 id="fig4">
	<media type="image/png" src="m10444fig4.png"/>
      </figure>


    </section>
  </content>
  
</document>
