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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/">Resampling with Rational Factor</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/">
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  <md:created xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2002/01/11</md:created>
  <md:revised xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2005/10/05 15:14:34.417 GMT-5</md:revised>
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      <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>
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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>
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    <md:maintainer xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="emaloney">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Erin</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Maloney</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">emaloney@rice.edu</md:email>
    </md:maintainer>
    <md:maintainer 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>
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    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">decimation</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/">resampling</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">sample-rate conversion</md:keyword>
  </md:keywordlist>

  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Describes the process of resampling, or sample-rate conversion.</md:abstract>
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    <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="para1">
      Interpolation by <m:math><m:ci>L</m:ci></m:math> and decimation
      by <m:math><m:ci>M</m:ci></m:math> can be combined to change the
      effective sampling rate of a signal by the rational factor
      <m:math><m:apply><m:divide/><m:ci>L</m:ci><m:ci>M</m:ci></m:apply></m:math>
      . This process is called <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">resampling</term> or
      <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">sample-rate conversion</term>. Rather than cascading an
      anti-imaging filter for interpolation with an anti-aliasing
      filter for decimation, we implement one filter with the minimum
      of the two cutoffs
      <m:math><m:interval><m:apply><m:divide/><m:pi/><m:ci>L</m:ci></m:apply>
      <m:apply><m:divide/><m:pi/><m:ci>M</m:ci></m:apply></m:interval></m:math>
      and the multiplication of the two DC gains
      (<m:math><m:ci>L</m:ci></m:math> and
      <m:math><m:cn>1</m:cn></m:math>), as illustrated in <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="fig1" strength="9"/>.
    </para>

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